The first edition of Solstice of Foundations took place on June 18-23, 2017, in Zürich, Switzerland. It consisted of two events: the Quantum Foundations Summer School and a Contextuality workshop, dedicated to the 50th anniversary of the Kochen-Specker theorem.

### Organizers

**Summer school**

Lídia del Rio, ETH Zurich *(chair)*

Markus Müller, Western University

Raban Iten, ETH Zurich

**Workshop**

Adán Cabello, U. Sevilla

Stefan Wolf, U. Svizzera Italiana

## Quantum Foundations Summer School

### Lectures

**All lecture videos are available here.**

- Roger Colbeck, University of York, UK –
**Bell inequalities**[partial lecture notes] - Angela Karanjai, University of Sydney, Australia –
**Epistemic models**[lecture notes] - Matthew Leifer, Chapman University, US –
**No-go theorems**[slides: first lecture, second lecture] - Lluis Masanes, UCL, UK –
**Reconstructing quantum theory from operational principles**[lecture notes] - Renato Renner, ETH Zurich, Switzerland –
**Interpretations of quantum theory**[paper] - Katja Ried, U. Innsbruck, Austria –
**Causality**[slides] - Ana Belén Sainz, Perimeter Institute, Canada –
**Contextuality**[slides: first lecture, second lecture] - Robert W. Spekkens, Perimeter Institute, Canada –
**Experimental quantum foundations**[slides: first lecture, second lecture]

### Recommended reading

Our lecturers recommend the following additional resources.

Wherever possible we posted links to open access versions of the publications.

- Bell non-locality, a review by Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani and Stephanie Wehner.
- No return to classical reality, a review by David Jennings and Matthew Leifer. Extra: a review on psi-ontology theorems by Matthew Leifer, “for masochistic students.”
- Video recordings of the course on Foundations of Quantum Mechanics from Perimeter Institute. This lecture has been thought by different lecturers in different years; in reverse chronological order, you can watch the course as taught by Matthew Leifer, Lucien Hardyand Rob Spekkens. Each version covers different topics, with some core overlap.
- On the subject of generalized probabilistic theories and axiomatic derivations of quantum theory, see: Lucien Hardy, “Quantum theory from five reasonable axioms” , Jonathan Barrett, “Information processing in generalized probabilistic theories”, and Lluis Masanes and Markus P. Müller, “A derivation of quantum theory from physical requirements“. To see how to apply this formalism to the analysis of real experimental data, see: Michael D. Mazurek, Matthew F. Pusey, Ravi Kunjwal, Kevin J. Resch & Robert W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations”.
- On the subject of contextuality, see: N. David Mermin, “Hidden variables and the two theorems of John Bell”, and Robert W. Spekkens, “Contextuality for preparations, transformations, and unsharp measurements”.

**Contextuality workshop**

Fifty years ago, Simon Kochen and Ernst Specker proved that quantum theory cannot be explained with noncontextual models. Since then, the Kochen-Specker theorem has been seen as one of the basic results in foundations of quantum theory. At the same time, the questions the theorem raised and the methods the theorem used received little attention.

However, in the last decade, we have seen how the Kochen-Specker theorem has inspired some results which help us to understand quantum theory and which is the origin of the power of quantum systems for information processing and computation. There is increasing evidence that contextuality, that is, the impossibility of noncontextual models, is the notion that better captures the sense in which quantum theory is fundamentally different than classical physics. There is also increasing evidence that contextuality is the basic resource behind the quantum advantage for computation and information processing. Moreover, there is increasing evidence that the principle of exclusivity, considered by Specker the fundamental principle of quantum theory, is the fundamental principle that limits correlations in nature. More importantly, there is a growing community of young researchers worldwide actively engaged in advancing our knowledge on each of these fronts.

The aim of this workshop is bringing together to the ETH Zurich, the place where the Kochen-Specker theorem was conceived, leading researchers in all these fields in order to develop broader perspectives, draw connections between different approaches, stimulate collaborations, and envision objectives for future research.

### Speakers

- Simon Kochen, U. Princeton, USA
- Alastair Abbott, Institut Néel, France
- Joseba Alonso, ETH Zurich, Switzerland
- Chris Fuchs, University of Massachusetts Boston, USA
- Jürg Fröhlich, ETH Zurich, Switzerland
- Angela Karanjai, U. Sydney, Australia
- Marc-Olivier Renou, U. Geneva, Switzerland
- Otfried Gühne, U. Siegen, Germany
- Robert Raussendorf, U. British Columbia, Canada
- Ana Belén Sainz, Perimeter Institute, Canada
- Robert W. Spekkens, Perimeter Institute, Canada

### Abstracts

#### Simon Kochen – Quantum Mechanics in a New Key [slides] [video]

The talk will show how exactly the same intuitively plausible definitions of state, observable, symmetry, and dynamics of the Boolean structure of intrinsic properties of classical systems, when applied to the structure of extrinsic, relational quantum properties, lead to the standard quantum formalism, including the Schrödinger equation and the von Neumann–Lüders Projection Rule. This approach is then applied to resolving the paradoxes and difficulties of the orthodox interpretation.

#### Marc-Olivier Renou – Network-locality [slides]

In quantum nonlocality, distant observers performing local measurements on a shared entangled quantum state can observe strong correlations. It has no equivalent in classical physics. Indeed, the characterization of all possible classical probability distributions, achievable with a single local hidden variable model, is now a relatively well understood problem.

A direct generalization is to study several independent sources distributed in a network: we go from “Bell locality” to “Network-locality”. Here, a network features distant observers, as well as several independent sources distributing states to different subsets of observers. No practical method to characterize the set of classical probability distributions for networks is known.

In this talk, we focus on several network example, illustrating some characteristics of the problem which makes it hard: non-convexity, non-linearity. We introduce a geometrical approach to the triangle scenario, where three sources are distributed between three observers in a loop. With the approach, we find a new inequality and make a connection with computer science.

#### Angela Karanjai – Bounding complexity of stabilizer models

This talk will be about constraints on any model which reproduces the qubit stabilizer sub-theory. We show that the minimum number of classical bits required to specify the state of an n-qubit system must scale as ~ n(n-3)/2 in any model that does not contradict the predictions of the quantum stabilizer sub-theory. The Gottesman-Knill algorithm, which is a strong simulation algorithm is in fact, very close to this bound as it scales at ~n(2n+1). This is a result of state-independent contextuality which puts a lower bound on the minimum number of states a model requires in order to reproduce the statistics of the qubit stabilizer sub-theory.

#### Robert Raussendorf – Topological proofs of contextuality in quantum mechanics

We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by Mermin, as well as a different type of contextuality proofs based on symmetry transformations. The topological arguments presented can be used in the state-dependent and the state-independent case.

Joint work with Cihan Okay, Sam Roberts and Stephen D. Bartlett. See arXiv:1701.01888v1 (quant-ph)

#### Otfried Gühne – Contextuality and Temporal Correlations in Quantum Mechanics [slides]

Experimental tests of contextuality often make use of sequential measurements on single quantum systems. In this talk I will explore the temporal correlations that can arise, if a

sequence of measurements on a single quantum systems is made. First, I will discuss the complexity of such correlations and the difficulty to simulate them classically. Second, I will

present methods to characterize temporal correlations, allowing to compute the maximal violation of contextuality inequalities in quantum mechanics. Finally, I will show how the correlations can be used to estimate the dimension of the underlying quantum system.

#### Joseba Alonso – Quantum contextuality tests with a single trapped-ion qutrit [slides]

We report on the generation and observation of correlations in a local system beyond those allowed by purely classical models. These manifest in the violation of non-contextual inequalities. For this, we make use of a single qutrit encoded into electronic energy levels of a 40Ca+ ion in a cryogenic surface-electrode trap. In a first experiment we demonstrate sustained generation of stronger-than-classical correlations by performing over 50 million consecutive measurements on the same qutrit. We do this with a single, self-correcting sequence, randomizing the measurement settings on the go. Our results violate the relevant state-independent inequality [1] by 236 standard deviations. In a second experiment we explore the limits of quantum correlations using sequential measurements of five observables. Our measurements violate the most fundamental non-contextual inequality [2] by 18 standard deviations, while lying within one standard deviation of the quantum-mechanical prediction. Furthermore, we have gradually increased the complexity of our system to include up to 31 observables and found stronger-than-classical correlations in all prepared scenarios. Our findings indicate that the limits of correlations in our system are indeed consistent with QM, while clearly revealing contextuality even under the experimentally unavoidable lack of compatibility between sets of ideally compatible observables, thereby addressing the so-called compatibility loophole.

#### Robert W. Spekkens – Translating proofs of the Kochen-Specker theorem into noncontextuality inequalities that are robust to noise [slides]

The Kochen-Specker theorem rules out models of quantum theory that satisfy a particular assumption of context-independence: that sharp measurements are assigned outcomes both deterministically and independently of their context. This notion of noncontextuality is not suited to a direct experimental test because realistic measurements always have some degree of unsharpness due to noise. However, a generalized notion of noncontextuality has been proposed that is applicable to any experimental procedure, including unsharp measurements, but also preparations as well, and for which a quantum no-go result still holds. According to this notion, the model need only specify a probability distribution over the outcomes of a measurement in a context-independent way, rather than specifying a particular outcome. It also implies novel constraints of context-independence for the representation of preparations.

I will describe a general technique for deriving inequalities for generalized noncontextuality—i.e., inequalities that test whether a given set of experimental statistics is consistent with a generalized-noncontextual model. In particular, I consider how to translate proofs of the Kochen-Specker theorem into such inequalities. Both the case of state-independent and state-dependent proofs are considered. Unlike previous inequalities inspired by the Kochen-Specker theorem, this approach does not assume that the value-assignments are deterministic and therefore in the face of a violation of the inequality, the possibility of salvaging noncontextuality by abandoning determinism is no longer an option. The approach is operational in the sense that it does not presume quantum theory: a violation of these inequalities implies the impossibility of a noncontextual model for any operational theory that can account for the experimental observations, including any successor to quantum theory.

#### 12:00 Chris Fuchs – Is there a SIC in the sky when nobody looks?

#### Ana Belén Sainz – Kochen-Specker contextuality: a hypergraph approach with operational equivalences [slides]

Most work on contextuality so far has focused on specific examples and concrete proofs of the Kochen-Specker theorem, while general definitions and theorems about contextuality are sparse. For example, it is commonly believed that nonlocality is a special case of contextuality, but what exactly does this mean? In this work, that builds on the graph-theoretic approach of Cabello, Severini and Winter, we develop a hypergraph approach to study Kochen-Specker contextuality and Bell nonlocality in a unified manner. In this talk I will further focus on the relation between some sets of probabilistic models and graph invariants, and discuss principles to characterise quantum predictions.

#### Alastair Abbott – The (strong) Kochen-Specker theorem, the eigenstate-eigenvalue link, and quantum randomness [slides]

The Kochen-Specker theorem rules out the possibility of noncontextual hidden-variable formulations of quantum mechanics, and as a result (along with Bell’s Theorem) has played an grounding the belief that quantum mechanics is indeed intrinsically random. This common view is well summed up in the “Eigenstate-Eigenvalue link” which states that a system has a definite property with respect to an observable iff it is in an eigenstate of that observable.

Recent work has made strong progress in developing a device-independent understanding of contextuality and understanding contextuality without assuming outcome determinism. In this talk I will look in the other direction, and discuss what the Kochen-Specker Theorem and contextuality really tell us about quantum indeterminism and randomness. I will argue that there is a discrepancy between the conclusions of the principal no-go theorems (i.e., Bell, Kochen-Specker, etc.) and the E-E link, and prove a strengthened version of the Kochen-Specker Theorem which closes this gap and, given the relevant assumptions, proves the E-E link. In contrast to standard proofs of the Kochen-Specker theorem, this stronger result requires a novel constructive method of reduction between Kochen-Specker sets. I will finish by discussing briefly the connection between these results and quantum randomness, and in particular the relation between indeterminism, unpredictability and randomness.

#### Jürg Fröhlich – The ETH approach to quantum mechanics

A novel approach to Quantum Mechanics is outlined – called “ETH approach”, where “E” stands for “events”, “T” for “trees”, and “H” for “histories”.

The purpose of this approach is to add some precision to formulating Quantum Mechanics that helps to clarify what an “event” is in Quantum Mechanics and how to observe or record an event using “instruments”. The ultimate aim of this approach is to develop a “Quantum Theory without Observers”. The ETH approach is based on a precise definition of “open isolated systems” and on two basic principles: (i) the “principle of loss of direct access to information” in open isolated systems, and (ii) a principle that specifies the impact of an event happening at some time t onto the state of the system after time t. These principles imply that the dynamics of states of open isolated systems can be described in terms of a new kind of stochastic branching process with a “non-commutative state space”.

### Student posters

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

Ali Asadian | Siegen university | Germany | 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 | Germany | 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 | United Kingdom | |

Arian Jadbabaie | California Institute of Technology | USA | 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. |

Armin Tavakoli | University of Geneva | Switzerland | 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. |

Aygül KOÇAK | Izmır Institute of Technology | Turkey | ‘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 | Swizzerland | 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 | Canada | 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 | Canada | 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 | USA | 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 | Nigeria | Guided Energy Theory of a Particle |

Do Thi Xuan Hung | ETH Zürich | Switzerland | 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 | Italy | 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 | Morroco | 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 | The Netherlands | 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 | United Kingdom | Strong non-locality in three-qubit states (Title TBC) |

Giulia Rubino | University of Vienna | Austria | 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 | Australia | 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 | United States of America | 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 | Austria | 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 | India | Joint Measurability, Uncertainty and Contextuality |

Manik Banik | Institute of Mathematical Sciences | India | 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 | India | 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 | Germany | Hypergraph states, their entanglement properties, local and nonlocal graphical transformations |

Markus Frembs | Imperial College London | United Kingdom | 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 | Italy | 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 | United-Kingdom | 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 | UK | 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 | UK | 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 | Australia | 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 | United States | The Minimum Complexity of Kochen-Specker Sets Does Not Scale With Dimension |

Nitica Sakharwade | Perimeter Institute of Theoretical Physics | Canada | 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 | Spain | 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) | Germany | On the Reality of the Wavefunction |

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

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

Paul Raymond-Robichaud | Université de Montréal | Canada | 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 | Poland | 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 | Austria | Exponential communication complexity advantage from quantum superposition of the direction of communication |

Ralph Silva | University of Geneva | Switzerland | 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 | Canada | Two Topos Interpretations for Measurement Based Quantum Computation |

Raul Corrêa | Universidade Federal de Minas Gerais | Brazil | 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 | Poland | Games and Monogamy in the Relativistic Causality Paradigm |

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

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

Sally Shrapnel | University of Queensland | Australia | “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 | U.S.A | 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 | United State | |

Thomas Galley | University College London | United Kingdom | 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 | Turkey | 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.trAbstractMotivated by 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 | United Kingdom | 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. |

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