The summer school Solstice of Foundations 2019 took place on June 17-21, 2019, in Zürich, Switzerland, and was followed by a workshop on the interface between mathematical physics and quantum information theory, hosted by SwissMap.

**Organizers**

**Foundations summer school**

Lídia del Rio, ETH Zurich

Nuriya Nurgalieva, ETH Zurich

**SwissMap workshop**

Anton Alexeev, U. Geneva

Renato Renner, ETH Zurich

Lídia del Rio, ETH Zurich

### Lectures and programme

#### Thomas Galley, Perimeter Institute, Canada: **Deriving quantum postulates from principles [slides]**

There are many ways of understanding quantum theory: as a non-classical logic, a non-classical probability theory and more generally as some form of operational theory. In this lecture I will show that different ways of viewing quantum theory allow us to have more efficient axiomatisations than in the standard approach. I will cover operational quantum logic and use Gleason’s theorem to show how we can recover quantum theory from a minimal number of postulates about the structure of measurements. I will then proceed to describe quantum theory as a generalised probabilistic theory (GPT) and show that many quantum properties are in fact generically non-classical. Following this I will show how to make modifications to the measurements postulates of quantum theory, and how to derive state spaces for systems in theories with the same pure states and dynamics as quantum theory, but different measurement postulates. In a final part I will show how composition of systems imposes strict constraints on how we can modify the measurement postulates of quantum theory, and specifically how the property of associativity of systems rules out all modifications. This allows us to derive the measurement postulates of quantum theory from basic features of the operational framework. References:

- A. Wilce, “Quantum logic and probability theory,” in The Stanford Encyclopedia of Philosophy (E. N. Zalta, ed.), Metaphysics Research Lab, Stanford University, spring 2017 ed., 2017.
- P. Janotta and H. Hinrichsen, “Generalized probability theories: what determines the structure of quantum theory?,” Journal of Physics A Mathematical General, vol. 47, p. 323001, Aug 2014.
- L. Masanes, T. D. Galley, and M. P. Müller, “The measurement postulates of quantum mechanics are operationally redundant,” arXiv:1811.11060, Nov 2018

#### Valerio Scarani, National University of Singapore:** Bell non-locality and applications [book chapter]**

- * Definition, loopholes, interpretations
- * Formalisation: Fine theorem, local polytope
- * Application: device-independent certification.
- * Example: Self-testing.

Main reference: my lecture notes on Bell’s theorem.

#### Tony Short, University of Bristol, UK: **Time in quantum mechanics**

These lectures will explore our understanding of time in quantum theory. We will begin with a general overview, considering in particular the differences between space and time in quantum theory. Next we will consider quantum clocks, beginning with a model of an `ideal’ clock (with *H=vp*) and then considering finite dimensional and thermodynamic clocks. Key questions are how clocks should be defined, how to assess their accuracy, and the ultimate limitations on them. Finally, we will consider a possible way to understand the flow of time in terms of correlations between a system and a clock within a single static entangled state.

Interesting general perspectives on time:

- “Time in quantum mechanics – vol 1”, editors J. Gonzalo Muga, Rafael Sala Mayato, Iñigo L. Egusquiza, Lecture Notes in Physics 734, Springer (2008)
- “Time in Physics”, editors Renato Renner and Sandra Stupar, Tutorials, Schools, and Workshops in the Mathematical Sciences, Springer (2017)

Quantum clocks:

- “Autonomous Quantum Machines and Finite-Sized Clocks”, Mischa P. Woods, Ralph Silva, and Jonathan Oppenheim. Annales Henri Poincaré, 20, 125-218 (2019)
- “Autonomous Quantum Clocks: Does Thermodynamics Limit Our Ability to Measure Time?”, Paul Erker, Mark T. Mitchison, Ralph Silva, Mischa P. Woods, Nicolas Brunner, and Marcus Huber. Phys. Rev. X 7, 031022 (2017)
- “Quantum clocks are more accurate than classical ones, Mischa P. Woods, Ralph Silva, Gilles Pütz, Sandra Stupar, and Renato Renner. quant-ph arXiv:1806.00491 (2018)
- “Clock-driven quantum thermal engines”, Artur S.L. Malabarba, Anthony J. Short, and Philipp Kammerlander. New J. Phys. 17, 045027 (2015)

Time as correlations in a static entangled state:

- “Evolution without evolution: Dynamics described by stationary observables”, Don N. Page and William K. Wootters. Phys. Rev. D 27, 2885 (1983)
- “Quantum time”, Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Phys. Rev. D 92, 045033 (2015)

#### Sandu Popescu, University of Bristol, UK: **Dynamic **non-locality

#### Ralph Silva, ETH Zurich, Switzerland: **Pre- and post-selection**

#### Lev Vaidman, Tel Aviv University, Israel: **Past of a quantum particle [slides]**

Bohr preached not to talk about it, Wheeler said we can, but only when we have a definite retrodiction. According to Bohm the past might be surrealistic and according to Aharonov not only the past, but even the present and future are fixed. I will argue that not only we can talk about the past in our world, but we can say much more than about the past of a classical system.

#### Mirjam Weilenmann, University of Vienna, Austria: **Causality I: classical, quantum and post-quantum causality**

Understanding cause-effect relationships is crucial for our scientific reasoning. In this lecture we will speak about causality and introduce mathematical tools for analysing cause-effect relationships. We will first introduce classical causality and the notion of interventions. We will further discuss the causal inference problem, including recent techniques involving entropy measures and graph inflation. In the second part, we will discuss the inadequacy of these classical tools in the quantum realm and introduce avenues to extend them. With this we set the scene for the lecture Causality II, where some tools for analysing quantum causality and its applications are discussed in-depth.

References and related literature:

- For an introduction to classical causality: Causality by Judea Pearl, https://dl.acm.org/citation.cfm?id=331969.
- For recent techniques for causal inference: graph inflation, https://arxiv.org/abs/1609.00672, and a review of entropic techniques, https://arxiv.org/abs/1709.08988.
- For the inadequacy of classical models for quantum causality: https://arxiv.org/abs/1208.4119.
- For quantum causal models: https://arxiv.org/abs/1609.09487.

#### V.Vilasini, University of York, UK: **Causality II: different methods and applications [**lecture notes part 1, part 2**]**

In these lectures, I will start by contrasting classical and quantum causality. To this effect, I will highlight some of the peculiar features of non-classical notions of causality and describe some theoretical possibilities beyond quantum theory that remain compatible with relativistic causality. While there are several theoretical frameworks for analysing these general notions of causality, I will focus on two of them, namely the Causal Box and the Process Matrix frameworks and describe how they handle superpositions of temporal/causal orders. The quantum switch is claimed to be an example of a physically implementable superposition of causal orders. By comparing the description of the quantum switch in these frameworks, I hope to fuel a discussion on whether it implements a superposition of causal orders or a superposition of temporal orders. Lastly, I will touch upon some of the applications that follow from asking these fundamental questions: such as that of superpositions of orders in communication/query complexity problems and the Causal Box framework in relativistic quantum cryptography.

References:

These lectures will be heavily based on my master thesis. Most of the relevant references for this talk can be found in the thesis. Following is a list of some of the main references:

- For classical causality: https://dl.acm.org/citation.cfm?id=331969.
- Why classical causal models cannot satisfactorily explain quantum causality: https://iopscience.iop.org/article/10.1088/1367-2630/17/3/033002.
- The quantum switch https://journals.aps.org/pra/abstract/10.1103/PhysRevA.88.022318, and a physical implementation of it https://advances.sciencemag.org/content/3/3/e1602589.
- Some frameworks for studying non-classical notions of causality (there are many others but we will focus on these): Causal Boxes https://ieeexplore.ieee.org/document/7867830, Process Matrices https://www.nature.com/articles/ncomms2076.
- Applications: computational advantage, complexity https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.250402,https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.100502, relativistic cryptography https://iopscience.iop.org/article/10.1088/1367-2630/ab0e3b.

#### Matthew Leifer, Chapman University, US – **Interpretations of quantum theory [lecture notes]**

Although quantum theory is about a century old, there is still little consensus about what it all means. In these lectures, I will start by explaining what I think should be the goals of an interpretation of quantum theory and why textbook accounts of quantum theory are inadequate. I will briefly review decoherence theory, which plays a role in accounting for the appearance of classical reality in most interpretations of quantum theory. Dozens of interpretations of quantum theory have been developed over the years, but four of them currently attract the most interest. These are modern variants of the Copenhagen interpretation (which I call Copenhagenish interpretations) as well as the “big three” realist interpretations: de Broglie-Bohm theory, Everett/many-worlds, and spontaneous collapse theories. I will give an overview of the modern perspective on de Broglie-Bohm theory, Everett/many-worlds, and Copenhagenish interpretations. Spontaneous collapse theories will not be covered in detail (mainly due to lack of time, but also because I view them as the least plausible of the “big three”).

References:

These are more relevant for supplementary reading after the summer school for those who want to know more details.

- Lectures 12-15 in my Perimeter Institute course on Quantum Foundations http://pirsa.org/C19002/2 cover similar material to my summer school lectures.* Maximilian Schlosshauer, Decoherence and the Quantum to Classical Transition (Springer, 2007). A detailed overview of the technical details of decoherence theory.
- Travis Norsen, Foundations of Quantum Mechanics (Springer, 2017). Chapters 7 and 9 are good on de Broglie Bohm and Spontaneous Collapse Theories.
- David Wallace, The Emergent Multiverse, (Oxford University Press, 2012) is a much more detailed account of modern Everett/Many-Worlds than I could ever hope to achieve.

#### Matthew Pusey, University of Oxford, UK – **Contextuality [lecture notes]**

I will present the Kochen-Specker theorem, which rules out pre-existing results for quantum measurements unless those results are ‘contextual’. I will then discuss the challenges of turning contextuality from a mathematical result about quantum theory into an experimental result about nature itself. I will focus on the approach to this due to Spekkens but will also attempt to summarise and compare other approaches.

I would encourage students to prepare by reading Spekkens’ original paper. It may also be of interest to examine a simple proof of the Kochen-Specker theorem presented by Mermin.

#### Gilles Brassard, Université de Montréal, Canada – **Could Einstein have been right? Quantum theory ***can* be local and realistic! [slides on pdf, keynote]

*can*be local and realistic!

One of the most surprising aspects of quantum theory is that it tells us that we live in a nonlocal universe. This idea was completely abhorrent to Einstein, who dismissed it as “spooky action at a distance”. Recent so-called loophole-free Bell experiments have confirmed nonlocality beyond any reasonable doubt. But have they really? I shall demonstrate that the mere experimental violation of a Bell inequality cannot be used as evidence for nonlocality since local-realistic universes that violate such inequalities are easy to imagine. Furthermore, no experiment whose purpose is to confirm the predictions of quantum theory can possibly be used as an argument in favour of nonlocality because any theory of physics that does not allow instantaneous signalling to occur and has reversible dynamics (such as unitary quantum theory) can be explained in a purely local and realistic universe. And if Einstein was right after all… once again?

Joint work with Paul Raymond-Robichaud (here and here).

#### Markus Müller, University of Vienna, Austria – **From observers to physics via information theory [notes on AIT and Solomonoff Induction]**

In these lectures, I will describe several puzzles and paradoxes from physics and philosophy, and show that they hint towards a view on the physical world that differs substantially from the usual intuition. These hints and ideas can be made rigorous with the tools of algorithmic information theory, which I will briefly introduce in the second part.

In the third part, I will discuss the metaphysically counterintuitive but consistent view that arises from such an approach. In particular, such views have the potential to resolve the paradoxes mentioned in the first part, they are consistent with everything that we observe, and they lead to surprising predictions like “probabilistic zombies”.

See also the abstract of my paper: https://arxiv.org/abs/1712.01826

More detailed list of topics and references:

- Algorithmic information theory / algorithmic probability

A good description can be found in the book “An Introduction to Kolmogorov Complexity and Its Applications” by Li and Vitanyi (Springer Verlag). - Solomonoff Induction

The following “Less Wrong” blog post gives a nice introduction:

https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuitive-explanation-of-solomonoff-induction - Paradoxes

To see that there is a lot that we do not yet understand, and to bring yourself into some serious (but necessary) metaphysical vertigo, read for example about Parfit’s “teletransportation paradox”, or have a look at the book “The Mind’s I” by Dennett and Hofstadter

#### Paolo Perinotti, University of Pavia, Italy –** From cellular automata to relativity**

In this lecture we will illustrate a recent approach to the foundations of relativistic quantum fields based on informational accounts of the theory of elementary systems. The framework of Operational Probabilistic Theories (OPTs) encompasses a wide variety of alternate theories abut elementary systems, tests and processes they can undergo, and it consists in universal rules about composition of systems and tests, and probabilities of events. Specific theories are then determined by the particular choice of mathematical objects representing tests and events. Relevant examples are quantum theory—which can be derived from informational axioms—, quantum theory on real Hilbert spaces, classical information theory, and Fermionic theory. The nature of elementary systems of an OPT is that of elementary information carriers, and there is no natural way of directly introducing mechanical concepts—such as space-time, mass, energy, and so on—in an OPT without referring to some additional structure outside the OPT itself.

In the first part, we will provide a fast review of the framework of OPTs we will then introduce the notion of a physical law in a purely informational scenario, and conclude that it is well described by a cellular automaton. We will show how a geometric picture of Space-time can be derived once a cellular automaton is provided. We will then restrict attention to Fermionic cellular automata, and furthermore we will take the simplest case of cellular automata on Cayley graphs of Abelian groups. There are surprisingly few of them: essentially two, which we call Weyl automata because once we embed them in their space-time, they are very well approximated by Weyl’s equations.

In the second part we will discuss the notion of change of inertial frame in a scenario where space-time is not fundamental, recurring to the original formulation of the principle of relativity. We then show how the changes of reference frame for the Weyl automaton correspond to a group isomorphic to the semi-direct product of the Poincaré group by a group of dilations, thus recovering the basic symmetry of Minkowski space-time.

## Posters

These were the posters presented by participants of the 2019 edition of Solstice of Foundations.

Akshata Shenoy | University of Geneva | Multiple Observer EPR-steering using sequential weak measurements |

Ali Asadian | Siegen university | Contextuality in phase spaceWe present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfil in order to construct Peres-Mermin square and similar scenarios. This approach offers a straightforward scheme for experimental implementations of the tests via modular variable measurements. In addition to the continuous variable case, our condition can also be applied to finite-dimensional systems in discrete phase space, using Heisenberg-Weyl operators. This approach, therefore, offers a unified picture of contextuality with a geometric flavour. |

Andreas Döring | Independent Researcher | Contextuality is Jordan structure is Quantum ProbabilityHow much can be learned about a quantum system by just considering the collection of all its contexts? It turns out that by keeping track of how contexts are contained within each other, i.e., by merely considering the partial order of contexts, one can extract a surprising amount of information uniquely (up to isomorphism), namely the projection lattice and hence the quantum logical structure, and the algebra of observables as a Jordan algebra, with anti-commutators as product, which gives quantum probability. This also provides a new perspective on Wigner’s theorem. Moreover, we can see precisely what is missing from a full description of the quantum system, namely time evolution, encoded by the Lie algebra structure on the algebra of observables. All results work in finite and infinite dimension, and also for von Neumann algebras, with the usual `2-dimensional’ exceptions.This is partly joint work with John Harding |

Andrew Simmons | Imperial College, London | |

Arian Jadbabaie | California Institute of Technology | Title: Mapping Quantum State Dynamics in Spontaneous EmissionAbstract: The evolution of a quantum state undergoing radiative decay depends on how its emission is detected. If the emission is detected in the form of energy quanta, the evolution is characterized by a quantum jump to a lower energy state. In contrast, detection of the wave nature of the emitted radiation leads to drastically different dynamics, driven by fluctuations of the emission field. Here, we investigate the diffusive dynamics of a superconducting artificial atom under continuous homodyne detection of its spontaneous emission. Detection is implemented by a phase-sensitive amplifier, allowing for a choice of measurement basis on the emission field. Using quantum state tomography, we characterize the correlation between the detected homodyne signal and the emitter’s state, and map out the conditional back-action of homodyne measurement. By tracking the diffusive quantum trajectories of the state as it decays, we characterize selective stochastic excitation induced by the choice of measurement basis. Our results demonstrate dramatic differences from the quantum jump evolution associated with photodetection and highlight how continuous field detection can be harnessed to control quantum evolution. |

Arijit Dutta | KIAS, Seoul | Title: Geometric extension of Clauser–Horne inequality to more qubits Abstract: We propose a geometric multiparty extension of Clauser–Horne (CH) inequality. The standard CH inequality can be shown to be an implication of the fact that statistical separation between two events, A and Bsatisfies the axioms of a distance. Our extension for tripartite case is based on triangle inequalities for the statistical separations of three probabilistic events. We show that Mermin inequality can be retrieved from our extended CH inequality for three subsystems in a particular scenario. With our tripartite CH inequality, we investigate quantum violations by GHZ-type and W-type states. Our inequalities are compared to another type, so-called N-site CH inequality. In addition we argue how to generalize our method for more subsystems and measurement settings. Our method can be used to write down several Bell-type inequalities in a systematic manner. |

Armin Tavakoli | University of Geneva | Title: Quantum communication games manifest preparation contextuality.Abstract: Communication games are scenarios in which distributed parties attempt to jointly complete a task with limited communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality whenever its predictions cannot be explained by a preparation noncontextual model. Here, we show that the ability of an operational theory to perform communication games is a measure of the degree of preparation contextuality in that theory. Subsequently, we show that all bipartite Bell inequalities are particular instances of preparation noncontextuality inequalities and thus that their violation implies preparation contextuality. We apply this to prove that all mixed quantum states of any finite dimension are preparation contextual. In addition, we present an experimental realization of a communication game involving three-level quantum systems from which we observe a strong violation of the constraints of preparation noncontextuality. |

Asaph Ho | Centre for Quantum Technologies, National University of Singapore | Title: Data-driven inference and observational completeness Abstract: We introduce data-driven inference as a protocol that, given a set of observed data, infers the mathematical description of the device that is both consistent with the observed data, in that it can reproduce the observed data, and is least committal, in that its range is of minimal volume in the space of output distributions. We introduce the notion of observational completeness, where an observationally complete set of states gives the same statistical information as the entire state space when data-driven inference is applied. Observational completeness thus plays in data-driven inference a role analogous to that of informational completeness in conventional quantum tomography. We characterize observational completeness and show that for qubit systems, a set of states are observationally complete for all informationally complete measurements if and only if the states are a 2-design. |

Aygül KOÇAK | Izmır Institute of Technology | ‘Kaleidoscope of Quantum Coherent States and Qudits” Aygül Koçak and Oktay K. Pashaev Department of Mathematics, Izmir Institute of Technology 35430 Urla, Izmir, Turkey aygulkocak@iyte.edu.tr, oktaypashaev@iyte.edu.trAbstract: The cat states as the superposition of Glauber coherent states generated by the Hadamard gate, represent qubit states and have been applied recently to description of a squeezed photon states. In our paper we derived the superposition of arbitrary number of coherent states generated by the Vandermonde unitary gate. It is associated with the n-th roots of unityand the regular n-polygon states. These states provide the set of arbitrary orthonormal quantum states, normalization of which is described by the set of generalized exponential functions with specific properties. This set of states represents kaleidoscope of Glauber coherent states, which is related with Kummer numbers. We show that these states can be used for description of qudit units of quantum information. The superposition of three coherent states with cubic roots of unity and its representation as qutrits is described in details. |

Baumann Veronika | USI Lugano | Agents in SuperpositionThe mathematical formalism of quantum theory has been celebrated for its success. Nevertheless, there are ongoing controversies: On the one hand, there is the conflict of the apparent collapse during a measurement with the unitarity evolution — the measurement problem. On the other hand, controversial discussions are led on how to understand and interpret the formalism. In Wigner’s friend experiments the subjective application of the measurement-update rule leads to contradicting statements of the agents involved. Since agents are unaware of their own superposition state their predictions will contradict those of agents to whom this superpositions accessible. These contradictions result from different formal descriptions of a measurement and can(not) be resolved differently for different interpretations. |

Charles Bédard | Université de Montréal | Kolmogorov Amplification from Bell Correlation [accepted to ISIT 2017]It was first observed by John Bell that quantum theory predicts correlations between measurement outcomes that lie beyond the explanatory power of local hidden variable theories. These correlations have traditionally been studied extensively in the probabilistic framework. A drawback of this perspective is that one is then forced to use in a single argument the outcomes of mutually-exclusive measurements. One of us has initiated an alternative approach, invoking only data at hand, in order to circumvent this issue. In this factual view, which is based on Kolmogorov complexity, we introduce mechanisms such as complexity amplification. We establish that this functionality is realizable, just as its probabilistic counterpart, hereby underlining that Bell correlations are a precious information-processing resource. |

David Schmid | Perimeter Institute | Contextual advantage for minimum error state discrimination Within the framework of generalized contextuality, we identify quantitative limits on the success probability for minimum error state discrimination in any experiment described by a noncontextual ontological model. These “noncontextuality inequalities” are violated by quantum theory, which implies a quantum advantage for state discrimination relative to noncontextual models. Furthermore, our noncontextuality inequalities are operationally formulated, so that any experimental violation of the inequalities is a witness of contextuality, independently of the validity of quantum theory. |

Dax Enshan Koh | Massachusetts Institute of Technology | Title: Further extensions of Clifford circuits and their classical simulation complexities.Abstract: Extended Clifford circuits straddle the boundary between classical and quantum computational power. Whether such circuits are efficiently classically simulable seems to depend delicately on the ingredients of the circuits. While some combinations of ingredients lead to efficiently classically simulable circuits, other combinations, which might just be slightly different, lead to circuits which are likely not. We extend the results of Jozsa and Van den Nest [Quant. Info. Comput. 14, 633 (2014)] by studying two further extensions of Clifford circuits. First, we consider how the classical simulation complexity changes when we allow for more general measurements. Second, we investigate different notions of what it means to “classically simulate” a quantum circuit. These further extensions give us 24 new combinations of ingredients compared to Jozsa and Van den Nest, and we give a complete classification of their classical simulation complexities. Our results provide more examples where seemingly modest changes to the ingredients of Clifford circuits lead to “large” changes in the classical simulation complexities of the circuits, and also include new examples of extended Clifford circuits that exhibit “quantum supremacy”, in the sense that it is not possible to efficiently classically sample from the output distributions of such circuits, unless the polynomial hierarchy collapses. |

Desmond Agbolade Ademola | Olabisi Onabanjo University | Guided Energy Theory of a Particle |

Do Thi Xuan Hung | ETH Zürich | Interplay between Decoherence and Doppler Cooling. (H. Do, C. Champenois, E. Hatifi, T. Durt) In elementary treatments of Doppler cooling, atoms are usually treated as a material point and quantum degrees of freedom are neglected. Cooling is seen as a mechanical process involving quantized exchanges of momentum between the atom and external photons. If we represent the atom by a spatial wave function or density matrix, then it is possible to understand the role played by quantum degrees of freedom and also to study quantitatively the decoherence undergone by the atom during the cooling process. In order to do so, we make use of the Ghirardi-Rimini-Weber process, which is an unraveling of the master equation associated to decoherence in position. We study in detail the interplay between quantum and classical degrees of freedom. |

Emanuele Polino | La Sapienza University of Rome | Title: Entanglement of photons in their dual wave-particle natureWave-particle duality is the most fundamental description of the nature of a quantum object which behaves like a classical particle or wave depending on the measurement apparatus. On the other hand, entanglement represents nonclassical correlations of composite quantum systems, being also a key resource in quantum information. Despite the recent observations of wave-particle superposition and entanglement, whether these two fundamental traits of quantum mechanics can emerge simultaneously remains an open issue. Here we introduce and experimentally realize a scheme that deterministically generates wave-particle entanglement of two photons. The elementary tool allowing this achievement is a scalable single-photon setup which can be extended to generate multiphoton wave-particle entanglement. |

Fatima-Zahra Siyouri | Mohammed V university | Title: The negativity ofWigner function as a measure of quantum correlations Abstract: In this work, we study comparatively the behaviors of Wigner function and quantum correlations for two quasi-Werner states formed with two general bipartite superposed coherent states. We show that the Wigner function can be used to detect and quantify the quantum correlations. However, we show that it is in fact not sensitive to all kinds of quantum correlations but only to entanglement. Then, we analyze the measure of non-classicality of quantum states based on the volume occupied by the negative part of the Wigner function. |

Gijs Leegwater | Erasmus University Rotterdam | When GHZ meet Wigner’s Friend – trouble for relativistic unitary, single-outcome quantum mechanicsA general argument is presented against relativistic, unitary, single-outcome quantum mechanics. This is done by combining the Wigner’s Friend thought experiment with measurements on a GHZ state, and describing the state of affairs in various reference frames. Assuming unitary quantum mechanics and single outcomes, the result is that the Born rule must be violated in some frame of reference: in that frame, outcomes obtain for which no corresponding term exists in the pre-measurement wavefunction. |

Giovanni Carù | University of Oxford | Strong non-locality in three-qubit states (Title TBC) |

Giulia Rubino | University of Vienna | Title: Experimental Verification of an Indefinite Causal OrderAbstract: Investigating the role of causal order in quantum mechanics has recently revealed that the causal distribution of events may not be a-priori well-defined in quantum theory. While this has triggered a growing interest on the theoretical side, creating processes without a causal order is an experimental task. In my poster I report the first decisive demonstration of a process with an indefinite causal order. To do this, my co-workers and I quantified how incompatible our set-up is with a definite causal order by measuring a ‘causal witness’. This mathematical object incorporates a series of measurements which are designed to yield a certain outcome only if the process under examination is not consistent with any well-defined causal order. In our experiment, we performed a measurement in a superposition of causal orders—without destroying the coherence—to acquire information both inside and outside of a ‘causally non-ordered process’. Using this information, we experimentally determined a causal witness, demonstrating by almost seven standard deviations that the experimentally implemented process does not have a definite causal order. |

Hakop Pashayan | University of Sydney | Title: From estimation of quantum probabilities to simulation of quantum circuits Abstract: We introduce a noise tolerant notion of simulation of quantum circuits, Efficient Polynomially Small In L 1 Norm (EPSILON) simulation, which is less stringent than exact sampling. We show that this notion is sufficient to ensure that an EPSILON simulator’s output is statistical indistinguishable from the genuine quantum system and preserves the useful computational power of the system. We present a method for enhancing additive polynomial precision quantum probability estimates to an EPSILON simulator for families of quantum circuits which satisfy a particular sparsity condition on the measurement outcomes. Finally we apply these result to the additive polynomial precision quantum probability estimates generated for quantum circuit families with polynomially bounded negativity in the quasi-probabilistic representation. |

Jeremy Steeger | University of Notre Dame | Title: Betting on quantum objectsAbstract: In quantum foundations, Dutch books arguments have been applied to beliefs about the outcomes of measurements, but not to beliefs about quantum objects prior to measurement. We rectify this situation by proving a quantum version of the probabilists’ Dutch book theorem that applies to both sorts of beliefs: treating the projection lattice of a finite-dimensional Hilbert space as a quantum logic, if the possible ideal beliefs an agent should have regarding propositions in the lattice are given by the restrictions of unit vector states to the lattice, then all and only the Born-rule probabilities avoid Dutch books. We then demonstrate the implications of this theorem for several operational and realist quantum logics. In the latter case, we show that the defenders of the eigenstate-value orthodoxy face a trilemma. Contrariwise, those who favor vague properties eschew the trilemma and admit all and only those beliefs about quantum objects that avoid Dutch books. |

Jessica Bavaresco | IQOQI Vienna | Optimal measurements for EPR steering in restrictive scenariosEPR steering is a form of quantum correlation intermediate between entanglement and Bell nonlocality that can be certified in a semi-device independent manner. In a bipartite scenario where Alice and Bob share a quantum state, we say their state is steerable when the resulting correlations between Alice’s measurements, outcomes, and Bob’s conditioned states exhibit nonlocal properties. From a fundamental and practical point of view, deciding weather a given entangled state is Einstein-Podolski-Rosen steerable or not (i.e. admits a local hidden state model) is a problem of crucial importance. Despite some particular results, no general method was known to decide if an arbitrary quantum state displays steerability in a particular scenario with N measurements of k outputs. In this work, we apply general methods to solve this problem by providing upper and lower bounds for the amount of white noise required to transform a steerable state into a unsteerable one. Our techniques are also applicable to the study the white noise robustness of the compatibility of N arbitrary unknown qudit measurements with k outputs. We prove that mutually-unbiased basis, SIC-POVMs, and other symmetric choices of measurements are not optimal for demonstrating steering of isotropic states. We also give numerical evidence that non-projective POVMs do not improve over projective ones for this task and present candidates for the optimal sets for measurements. |

Karthik H. S. | Raman Research Institute, Bangalore/GAP,University of Geneva | Joint Measurability, Uncertainty and Contextuality |

Manik Banik | Institute of Mathematical Sciences | Title: Bayesian Games, Social Welfare Solutions and Quantum Entanglement Abstract: Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in a numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes sum of all players’ payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is coined as quantum social welfare advice (SWA). Interestingly, we show that any two-qubit pure entangled states, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task. |

Maria Quadeer | Institute of Mathematical Sciences, Chennai | Title: Random Access Codes: The Quantum AdvantageAbstract: We investigate the task of d-level random access codes (d-RACs) and consider the possibility of encoding classical strings of d-level symbols (dits) into a quantum system of dimension d’ strictly less than d. We show that the average success probability of recovering one (randomly chosen) dit from the encoded string can be larger than that obtained in the best classical protocol for the task. Our result is intriguing as we know from Holevo’s theorem (and more recently from Frenkel-Weiner’s result [Commun. Math. Phys. 340, 563 (2015)]) that there exist communication scenarios wherein quantum resources prove to be of no advantage over classical resources. A distinguishing feature of our protocol is that it establishes a stronger quantum advantage in contrast to the existing quantum d-RACs where d-level quantum systems are shown to be advantageous over their classical d-level counterparts.Reference: arxiv: 1703.01996 |

Mariami Gachechiladze | University of Siegen | Hypergraph states, their entanglement properties, local and nonlocal graphical transformations |

Markus Frembs | Imperial College London | No-signalling and contextuality [We study contextuality in the no-signalling condition and show how the structure of presheaves provides a natural setup for this research. In particular, we construct the probabilistic presheaf in resemblance to the spectral presheaf (as defined in the topos approach to quantum theory) by attaching probability distributions to contexts. Invoking Gleason’s theorem shows that quantum states are in one-to-one correspondence with global sections of the probabilistic presheaf in dimension at least three under the locality constraint imposed by no-signalling. We thus achieve a reduction of general no-signalling theories to quantum correlations by means of a global rather than a local perspective – in contrast to information theoretic principles such as information causality.] |

Matteo Rosati | Scuola Normale Superiore, Pisa | Adaptive interferometry and single-mode measurements do not increase the capacity of coherent-state decoders.A class of Adaptive Decoders (AD’s) for coherent-state sequences is studied, including in particular the most common technology for optical-signal processing, e.g., interferometers, coherent displacements and photon-counting detectors. More generally we consider AD’s comprising adaptive procedures based on passive multi-mode Gaussian unitaries and arbitrary single-mode destructive measurements. For classical communication on quantum phase-insensitive Gaussian channels with a coherent-state encoding, we show that the AD’s optimal information transmission rate is not greater than that of a single-mode decoder. The proof relies on showing that the AD can be interpreted as an entirely classical programmable channel with feedback. Our result implies that the ultimate classical capacity of quantum phase-insensitive Gaussian channels is unlikely to be achieved with an AD. |

Maxime Jacquet | University of St Andrews | Title: Positive-negative frequency conversion at a refractive index front Abstract: We analytically calculate the laboratory-frame spectrum of light spontaneously emitted from the vacuum as a result of the mixing of waves with positive and negative frequency at an optical horizon in a dispersive medium. We perform a stimulated experiment in which energy is converted from positive to negative frequency waves. |

Mirjam Weilenmann | University of York | The entropy vector method is unable to certify non-classicality in linelike causal structuresCausal structures are important for the foundations of quantum mechanics because of Bell’s theorem. In addition, understanding cause in a quantum mechanical sense is essential for device independent cryptography. While in the simplest causal structures, the problem of certifying non-classicality is well-understood, in more complicated cases it is not. We consider the question of whether the joint entropies of a set of observed random variables can lead to useful certificates of non-classicality. We find that for a family of causal structures that include the usual bipartite Bell structure they do not, in spite of the existence of non-classical correlations. We furthermore find that for many causal structures non-Shannon entropic inequalities give additional constraints on the sets of possible entropy vectors in the classical case. They hence lead to tighter approximations to the set of realisable entropy vectors. |

Mithuna | Cambridge university | Title: Which Conjectures Will Prove That Quantum Computing Is More Powerful Than Classical? Abstract: Current attempts to show that quantum computers are more powerful than classical ones have tried to prove that if this is not true, the Polynomial Hierachy will collapse. However, they fall just short of this because each attempt has required certain conjectures to be proved first. These conjectures relate to a handful of #P-hard problems. We attempt to show that if the analogous conjectures for any #P-complete problem is proved, it will imply the same result: classical computers cannot simulate quantum ones unless the polynomial hierarchy collapses. We hope this will make it easier to prove this key belief. |

Mojtaba Aliakbarzadeh | Queensland university of technology | Title: Sheaf-theoretical and Operational approach of contextualityRecent works in the area of contextuality have unied the congurations of Bell inequality and Kochen-Specker theorem, and also have generalized the standard notation of contextuality to areas beyond quantum theory. Two formalisms which have been used for these aims are the Sheaf theory approach due to Abramsky and Brandenburger [1] and the Operational theory defined by Spekkens [3]. In this research, we will show a formally robust connection between these two approaches. We especially focus on the concept of non-signaling in our comparison between these two approaches, and also the case of outcome determinism in KS theory [2].References [1] Abramsky, S. and Brandenburger, A. (2011). The sheaf-theoretic structure of non-locality and contextuality. New Journal of Physics, 13(11):113036. [2] Kunjwal, R. and Spekkens, R. W. (2015). From the Kochen-Specker Theorem to Noncontextuality Inequalities without Assuming Determinism. Physical Review Letters. [3] Spekkens, R. W. (2005). Contextuality for preparations, transformations, and unsharp measurements. Physical Review A, 71(5):52108. |

Mordecai Waegell | Institute for Quantum Studies, Chapman University | The Minimum Complexity of Kochen-Specker Sets Does Not Scale With Dimension |

Nitica Sakharwade | Perimeter Institute of Theoretical Physics | Bi-directional Teleportation and Dense coding in the butterfly networkWe consider a channel-capacity constrained two-way signalling scenario between Alice and Bob mediated by the middle-men Mukul and Megha in the butterfly network, to show and prove optimal protocols for bi-directional teleportation and bi-directional super-dense coding. |

Núria Muñoz Garganté | University of the Basque Country UPV/EHU | Are there operational differences between real and complex quantum theory?A straightforward question about the mathematical structure of quantum theory is, why quantum theory is formulated over complex rather than real Hilbert spaces. Surprisingly, the answer to this question is not simple and both formulations turned out to be vastly equivalent, cf. [Stueckelberg, Helv. Phys. Acta 33, 727 (1960); M. McKague et al., Phys. Rev. Lett. 102, 020505 (2009)]. However there is a difference when it comes to certain aspects of the time evolution [Barnum et al., New J. Phys. 16, 123029 (2014)]. Here we investigate whether such differences can be lifted to an operational difference between real and complex quantum theory. |

Omid Charrakh | Munich Center for Mathematical Philosophy (LMU Munich) | On the Reality of the Wavefunction |

Paul Boes | Freie Universität Berlin | Justification of statistical ensembles from thermodynamic transitions |

Paul Knott | University of Nottingham | Quantum Darwinism and the Emergence of Objectivity |

Paul Raymond-Robichaud | Université de Montréal | Title: The structure and equivalence of no-signalling and local-realistic theories.Abstract: We provide a framework to describe mathematically all local-realistic structures as well as no-signalling theories. We show that in the case of reversible dynamics, these two concepts are equivalent. This implies as a corollary that quantum theory has a local-realistic interpretation.Joint work with Gilles Brassard. |

Pawel Blasiak | Polish Academy of Sciences, Kraków | Title: Is single-particle interference spooky? Abstract: It is said about quantum interference that “In reality, it contains the only mystery”. Indeed, together with non-locality it is often considered as the characteristic feature of quantum theory which can not be explained in any classical way. In this work we are concerned with a restricted setting of a single particle propagating in multi-path interferometric circuits, that is physical realisation of a qudit. It is shown that this framework, including collapse of the wave function, can be simulated with classical resources without violating the locality principle. We present a local ontological model whose predictions are indistinguishable from the quantum case. ’Non-locality’ in the model appears merely as an epistemic effect arising on the level of description by agents whose knowledge is incomplete. This result suggests that the real quantum mystery should be sought in the multi-particle behaviour, since single-particle interference is explicable within local hidden variable framework.Reference: P. Blasiak “Is single-particle interference spooky?” arXiv: 1701.02552 [quant-ph] |

Philippe Allard Guérin | University of Vienna | Exponential communication complexity advantage from quantum superposition of the direction of communication |

Ralph Silva | University of Geneva | TITLE: Autonomous quantum clocks: does thermodynamics limit our ability to measure time?ABSTRACT: Time remains one of the least well understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium — a prerequisite for any system to function as a clock — powered by minimal resources, namely two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond. |

Raouf Dridi | 1Qbit technologies | Two Topos Interpretations for Measurement Based Quantum Computation |

Raul Corrêa | Universidade Federal de Minas Gerais | Title: ‘Quantum Cheshire Cat’ as simple quantum interference. Reference: R. Corrêa, M. F. Santos, C. H. Monken and P. L. Saldanha. New J. Phys. 17, 053042 (2015). Abstract: In 2013, Aharonov et al. suggested that a photon could be separated from its polarization in an experiment involving pre- and post-selection [New J. Phys. 15, 113015, (2013)]. They named the effect ‘quantum Cheshire Cat’, in a reference to the cat that is separated from its grin in the novel Alice’s Adventures in Wonderland. Following these ideas, Denkmayr et al. performed a neutron interferometric experiment and interpreted the results suggesting that neutrons were separated from their spin [Nat. Commun. 5, 4492, (2014)]. In both papers, the authors use the concept of weak value to draw their conclusions, in which a pointer interacts weakly with the system that is to be measured, while pre- and post-selection in the system of interest leave the pointer in a state to be read, which informs the weak value [Phys. Rev. Lett. 60, 1351 (1988)]. Nonetheless, with this formalism, the authors can choose to keep the degrees of freedom associated to the pointers out of the physical analysis while looking exclusively at the weak values, and the attempt to attribute a physical reality to them leads to most of the controversy. In our work [New J. Phys. 17, 053042 (2015)] we show that by taking the pointers degrees of freedom into account, both the theoretical predictions and experimental results that motivated the somewhat unusual ‘Cheshire Cat’ interpretation can be explained as simple quantum interference. Therefore, no detachment between the photon and its polarization or between the neutron and its magnetic moment is actually required. In our opinion, the aforementioned paradoxical conclusions, presented as the ‘quantum Cheshire Cat’ effect, are one more apparent paradox that arises whenever we attribute physical reality to quantum superposition states, for instance when describing a quantum particle inside an interferometer prior to its detection. Our results provide a better understanding of the phenomenon reinforcing that no interpretation stranger than standard quantum mechanics is required. |

Roberto Salazar | National Gdansk University of Technology, National Quantum Information Center | Games and Monogamy in the Relativistic Causality Paradigm |

rukhsan ul haq | jncasr | Iterants,Idempotents and Clifford algebra in quantum foundations |

Sacha Schwarz | Institute of Applied Physics, University of Bern | Nonlocal Correlations of Entangled Two-Qudit States Using Energy-Time Entangled Photons |

Sally Shrapnel | University of Queensland | “Crazy causation can’t save quantum contextuality.” In this paper we look at quantum contextuality through the lens of causality. It is well-known that quantum mechanics does not admit of a non-contextual ontological model. Here we prove that this result still holds even when one allows for arbitrary causal structures. Our finding has negative implications for interpretations that posit unusual causal relations in the hope of saving “reality”. All such models, for example retro-causal models, will necessarily be contextual. |

Sebastián Murgueitio | University of Notre Dame | On the preparation independence assumption in the PBR theorem.In this poster I will explain that one of the main assumptions made by PBR, namely, the assumption that systems that are prepared independently have independent physical states (also known as the “preparation independence assumption”, or PIA), is problematic. I argue that the main motivations in favour of PIA are wanting, and I will also pose a dilemma: if we endorse a particular version of PIA (to be explained in detail in the poster) our ontological model no longer accounts for interactions, and if we do not endorse such particular version, then the proof of the PBR theorem is unsound. |

Shiva Barzili | Chapman university | |

Thomas Galley | University College London | Classification of all alternatives to the Born rule in terms of informational propertiesThe Born rule is one of the fundamental postulates of quantum theory which assigns probabilities to measurement outcomes. There have been many attempts to derive the Born rule, however these have often been deemed controversial. In this work we take a different approach and classify all possible alternatives to the Born rule. We divide the core postulates of quantum theory into two groups : the first characterises the structure and dynamics of pure states ; the second the structure of measurements and the corresponding outcome probabilities. We show that all possible alternatives to this second group of postulates are in correspondence with a class of representations of the unitary group. We then explore the properties of these alternative theories, such as the number of perfectly distinguishable states, to establish how they differ from quantum theory. We find that the property of bit symmetry (which states that all logical bits are equivalent) singles out the Born rule in all finite dimensions, assuming effects are not restricted. We also discuss composition of these systems with alternative Born rules. |

Tuğçe PARLAKGÖRÜR | Izmir Institute of Technology | APOLLONIUS REPRESENTATION OF QUBIT STATESTuğçe Parlakgörür and Oktay K. Pashaev Department of Mathematics, Izmir Institute of Technology 35430 Urla, Izmir, Turkey tugceparlakgorur@iyte.edu.tr, oktaypashaev@iyte.edu.trAbstractMotivatedby Möbius transformation, we introduce multiple qubit quantum states belonging to family of Apollonius circles in complex plane. For single qubit state, the ratio of probabilities becomes constant along Apollonius circles and has simple geometrical interpretation. For multiple qubit states, fidelity of transition between symmetric states (with respect to the unit circle) takes constant value along every Apollonius circle and its reflection. For two qubit states, this fidelity give us the concurrence of entanglement for pure quantum states with constant value along the Apollonius circle. In this representation of Apollonius quantum states with equi-concurrent state lines, we found simple geometrical interpretations of concurrence as a double area of rectangle inscribed to the circle and as a distance between intersection points of the circle with Apollonius circle. We show that our two qubit states are coming from the generic two qubit states by antipodal reduction of quantum state. Extensions of our results to multiple qubit states and arbitrary position of states in plane would be discussed. The work is supported by Tubitak grant 116F206. |

Vicky Wright | University of York | Qubits for Flatlanders – Complex numbers permeate quantum mechanics; from Schrodinger’s equation to commutation relations they ubiquitously emerge from the theory. How would real-vector-space quantum systems differ from their complex counterparts? We consider the simplest case of a two level system and find physical consequences of this abstract alteration. |