Program
3 Nov, Mon  
09:30  Welcome and Opening address 
10:00 
Adán Cabello, University of Seville Quantum contextuality and the E principle Abstract We consider general probabilistic theories admitting sharp measurements (i.e., nondemolition, repeatable and causing minimal disturbance). We define "event" as the postmeasurement state of a sharp measurement. An event is characterized by the outcomes of a set of comeasurable sharp measurements. Two characterizations are equivalent when both produce indistinguishable postmeasurement states. Two events are said to be exclusive when there is a sharp measurement that perfectly distinguishes between them. The exclusivity (E) principle states that any set of n pairwise exclusive events is nwise exclusive. We show that the E principle, together with the assumptions that two experiments can be independent and that any exclusivity graph is physically feasible: (1) single out the quantum limit of the simplest qutrit noncontextuality inequality (KCBS), (2) single out the Tsirelson bound of the simplest Bell inequality (CHSH), (3) for any m>2, single out the maximum quantum violation of the Belltype inequalities that detect true mbody quantum nonlocality, (4) explain why all extremal nonlocal boxes in the 3party, 2setting, 2outcome scenario are not quantum, and (5) single out the entire set of correlations achievable with quantum systems for selfcomplementary exclusivity graphs. No other proposed principle is so successful in explaining quantum correlations. We compare the sharp measurements approach to quantum correlations (sometimes called the "graph" or "contextuality approach") discussed here and the demolition measurementsmulti party approach (sometimes called "box" or "deviceindependent approach"). We argue that there are quantum limits of Bell inequalities that cannot be explained within the deviceindependent approach, but which might be understood with the contextuality approach. Finally, we note that the E principle is implied by many postulates proposed to reconstruct quantum theory from physical principles. 
10:45  Coffee/Tea Break 
11:15 
Marcin Wieśniak , University of Gdańsk Some subtle issues of KochenSpecker experiment Abstract Experiments supporting the KochenSpecker theorem are probably the most challenging ones in Quantum Information Processing. Not only is their success dependent on traditional loopholes, such as the effciency or the source fidelity loophole, but also those unique for these for the theorem, for example the measurement compatibility loophole. Still, it is commonly believed that these experiments conform the correctness of quantum mechanics and the failure of noncontextual hidden variable theories. I point out some more subtle issues that need to be taken into account in realizing a contextuality experiment, and how we dealt with them (or not) realizing the pentagram inequality experiment in Vienna. I will particularly focus on attempts to close the compatibility loophole. I will also remind the argument due to Mermin, why even imperfectly conducted experiments falsify NCHV models. 
12:00 
Tobias Fritz, Perimeter Institute for Theoretical Physics Quantum contextuality cannot be characterized in terms of a graph invariant Abstract Recently, connections between quantum contextuality and graph theory have become popular. In this talk, I will sketch the more general approach to quantum contextuality and nonlocality developed in arXiv:1212.4084, and explain our proof that quantum contextuality cannot be fully characterized by a graph invariant of an orthogonality graph. 
12:45 
A little bit of this and that 
13:00  Lunchbreak 
14:30 
Harald Weinfurter, Ludwig Maximilian University of Munich Bell tests with more and fewer loopholes Abstract We presents experiments on Bell tests with one and two photons, in two and more dimensions and with atoms separated by 20 m. Though no KochenSpeckerlike contradiction, finite statistics is less a problem. Which other loopholes are then still open in such experiments? 
15:15 
Panel discussions 
19:00  Evening activities 
4 Nov, Tues  
10:00 
Renato Renner, ETH, Zurich Noncontextuality and free choice Abstract That certain settings of an experiment can be chosen “freely”, i.e., independently of other parameters, is a basic assumption that underlies almost any analysis in physics. The goal of this talk is to explain how this assumption connects to the notion of (non)contextuality. 
10:45  Coffee/Tea Break 
11:15 
Shane Mansfield, University of Oxford, Department of Computer Science Contextual Semantics Abstract The contextual semantics approach uses the language of sheaf theory to provide a powerful, theoryindependent, unified formalism for treating nonlocality and contextuality. We will provide a short overview, introducing the basic framework before proceeding to briefly mention a number of applications and structural insights on the nature of contextuality. These include a hierarchy of contextuality, developments on the characterisation of contextuality by means of topological invariants, the canonical transformation of contextual correlations into nonlocal ones, and the structural reasons for macroscopic realism and monogamy of contextual inequalities. 
12:00 
Wiesław Laskowski, University of Gdańsk Incompatibility of local hiddenvariable models  a surprising feature of quantum correlations Abstract We show a quantum state with explicit local hiddenvariable models for correlations between any fixed number of subsystems which cannot be extended to a model simultaneously describing correlations between different numbers of subsystems. The explicit models we discuss may involve several settings per observer and the way to disqualify them involves only two settings per party. We also show a stronger result by exhibiting separable twoparty reduced states such that any threeparty(global)state compatible with these marginals violates local realism. Hence, we obtain that violation of local realism of multipartite states can be certified from information only about separable marginals. 
12:45 
A little bit of this and that 
13:00  Lunchbreak 
14:30 
Gustavo Lima, University of Concepción Experimental implementation of an eightdimensional KochenSpecker set and observation of its connection with the GreenbergerHorneZeilinger theorem Abstract For eightdimensional quantum systems there is a KochenSpecker (KS) set of 40 quantum yesno tests that is related to the GreenbergerHorneZeilinger (GHZ) proof of Bell’s theorem. We will present our experimental implementation of this KS set using an eightdimensional Hilbert space spanned by the linear transverse momentum of single photons. In addition, we show that, if the system is prepared in initial states that are formally equivalent to a threequbit GHZ and W states, then the results of a subset of 16 yesno tests violate a noncontextuality inequality that is formally equivalent to the threeparty Mermin’s Bell inequality. These experimental results highlight the connection between quantum contextuality and nonlocality for eightdimensional quantum systems. 
15:15 
Panel discussions 
19:00  Evening activities 
5 Nov, Wed  
10:00 
Paweł Horodecki, Gdańsk University of Technology Title and abstract to be advised

10:45  Coffee/Tea Break 
11:15 
JanÅke Larsson, Linköping University Memory cost of quantum contextuality Abstract Quantum systems show contextuality. More precisely, it is impossible to reproduce the quantummechanical predictions using a noncontextual realist model, i.e., a model where the outcome of one measurement is independent of the choice of compatible measurements performed in the measurement context. There has been several attempts to quantify the amount of contextuality for specific quantum systems, for example, in the number of rays needed in a KS proof, or the number of terms in certain inequalities, or in the violation, noise sensitivity, and other measures. This talk is about another approach: to use a simple contextual model that reproduces the quantummechanical contextual behaviour, but not necessarily all quantum predictions. The amount of contextuality can then be quantified in terms of additional resources needed as compared with a similar model without contextuality. In this case the contextual model needs to keep track of the context used, so the appropriate measure would be memory. Another way to view this is as a memory requirement to be able to reproduce quantum contextuality in a realist model. The model we will use can be viewed as an extension of Spekkens’ toy model [Phys. Rev. A 75, 032110 (2007)], and the relation is studied in some detail. To reproduce the quantum predictions for the PeresMermin square, the memory requirement is more than one bit in addition to the memory used for the individual outcomes in the corresponding noncontextual model. 
12:00 
Matthias Kleinmann, University of the Basque Country, Bilbao, Spain Loopholes in contextuality experiments Abstract The classification and treatment of loopholes in Belltype experiments is much better developed than for noncontextuality experiments. In fact, for the latter mostly adhoc methods are known. For example when sequential measurements are used, one has to make a convincing argument why measurements that have been performed earlier in a sequence should not influence those that come later. But even if no influence is assumed, noncontextual models can explain the findings of overly naive contextuality experiments. I discuss such models and how they can be refuted by additional measurements and compensating terms in the corresponding noncontextuality inequality. 
12:45 
A little bit of this and that 
13:00  Lunchbreak 
14:30 
Guilherme Xavier, Centre for Optics and Photonics Advances in quantum contextuality and nonlocality experiments fueled by optical and electronical instrumentation Abstract Recent improvements in general instrumentation are allowing improved experiments in quantum information and foundations of quantum mechanics, which would be unthinkable a few years ago. Today we can manipulate quantum systems with many dimensions, and soon will be able to reliably transmit them over long distances. Devices and techniques originally developed for other purposes in engineering and applied physics are successfully making their way to aid contextuality and nonlocality experiments. For example, field programmable gate arrays (FPGAs) are becoming ubiquitous in such experimental demonstrations. We will also discuss the impact of other devices and techniques such as spatial light modulators, active phase and polarizationstabilization in optical fibers, and new specialty optical fibers. 
15:15 
Panel discussions 
19:00  BBQ evening at East Coast Park 
6 Nov, Thurs  
10:00 
Otfried Guehne, University of Siegen Various Dimensions of Contextuality Abstract In this talk I will discuss the relation between contextuality and the dimension of quantum systems. First, I will present methods how one can bound the possible sequential quantum correlations and how this can be used to characterize the dimension of the quantum system. Second, I will present an approach to generalize the PeresMermin square to (nearly) arbitrary finitedimensional and infinitedimensional systems. 
10:45  Coffee/Tea Break 
11:15 
Antoni Wojcik, Adam Mickiewicz University How to quantify contextuality Abstract We will present three, recently proposed (A. Grudka et al. Phys. Rev. Lett. 112 (2014) 120401), measures of contextuality, namely mutual information of contextuality, relative entropy of contextuality and contextuality cost. We will also show some analytical results for these measures applied to some known contextual systems. Joint work with A. Grudka, K. Horodecki, M. horodecki, P.horodecki, P. Joshi and W. Kłobus. 
12:00 
Rafael Rabelo, Universidade Federal de Minas Gerais Multigraph approach to quantum nonlocality and contextuality Abstract Noncontextuality and Bell inequalities can be expressed as bounds for positive linear combinations of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph called the exclusivity graph of the inequality. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grötschel–Lovász–Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimising the inequality over the theta body and calculating the Lovász number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bellinequality (and similar) scenarios. An interesting question is whether there is a graphtheoretical concept which accounts for this problem. We show that, for any given Npartite Bell inequality, an edgecoloured multigraph composed of N singlecolour graphs can be used to encode the relationships of exclusivity between each partyʼs parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lovász number that applies to these edgecoloured multigraphs. We calculate upper bounds for this number using a hierarchy of semidefinite programs, considering I3, I3322 and the three bipartite Bell inequalities whose exclusivity graph is a pentagon. An interesting feature of the multigraphtheoretical approach introduced is that it can be applied not only to Bell scenarios but also to more general ones, where, in each party, contextualitylike restrictions may exist. 
12:45 
A little bit of this and that 
13:00  Lunchbreak 
14:30 
Fabio Sciarrino, Sapienza University of Rome Higher quantum dimensionality by exploiting the photonic orbital angular momentum Abstract In quantum information processing based on optical techniques, single photons oﬀers a variety of degrees of freedom in which information can be encoded. By exploiting these resources, it is possible to implement highdimensional quantum states, or qudits, which enable higher security in quantum cryptographic protocols, as well as implications in fundamental quantum mechanics theory. In the last few years, many improvements have been achieved for qudit states with d = 3, d = 4 and even larger value. In this framework, the orbital angular momentum of photons, being deﬁned in an inﬁnitely dimensional Hilbert space, oﬀers a promising resource for highdimensional optical quantum information protocols. We introduced and tested experimentally a series of optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum (OAM) of single photons and vice versa [1,2,3]. Our schemes exploit an optical device, the socalled “qplate”, a suitably patterned nonuniform birefringent plate, which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. Our experiments prove that these schemes are reliable, eﬃcient and have a high ﬁdelity. We will present the experimental generation and manipulation of a hybrid ququart encoded in the polarization and orbital angular momentum of a single photon with fundamentel test of quantum mechanics [4,5,6,7,8]. Finally we will discuss how purely OAM encoded qudit states can be adopted to perform experiments on the exclusivity principle [9,10].

15:15 
Panel discussions 
19:00  Evening activities 
7 Nov, Fri  
10:00 
Marcelo Terra Cunha, Universidade Federal de Minas Gerais Coloured Graphs for Nonlocal Contextuality Abstract In a recent paper a refinement of the graphapproach for contextuality was introduced (J. Phys. A 47, 424021). This refinement uses edgecoloured graphs and a new graphtheoretical invariant: the coloured Lovász number. In this talk I want to address some properties and examples of this new number, after addressing some details of how to obtain upper and lower bounds to it. From these examples, some conjectures can be stated as well as the properties of some coloured graphs made from some “basic pieces” can be explained. Finally, some interesting examples of “contextulocality” can be shown: i.e. a Bell scenario where the same set of data allows for Bell violation and for each participant to locally violate noncontextuality inequalities. This is a collective work in progress at Belo Horizonte. 
10:45  Coffee/Tea Break 
11:15 
Marcin Pawłowski , University of Gdańsk RACboxes Abstract We study a problem of interconvertibility of two supraquantum resources: one is so called PRbox, which violates CHSH inequality up to maximal algebraic bound, and second is so called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It has been known, that PRbox supplemented with one bit of communication can be used to simulate RAC. We ask the converse question: to what extent RAC can simulate PRbox? To this end we introduce RACbox: a box such that supplemented with one bit of communication offers RAC. As said, PRbox can simulate RACbox. The question we raise, is whether any racbox can simulate PRbox. We show that a nonsignaling racbox indeed can simulate PRbox, hence those two resources are equivalent. We also provide an example of signalling EACbox which cannot simulate PRbox. We give a resource inequality between RACboxes and PRboxes, and show that it is saturated. 
12:00 
Marcin Markiewicz , University of Gdańsk Contextuality in time. A new insight into multipartite temporal quantum correlations Abstract Temporal quantum correlations are correlations between outcomes of measurements performed on a single quantum system in different instances of time. Nonclassical behaviour of such correlations can be treated as a manifestation of quantum contextuality in time.

12:45 
A little bit of this and that 
13:00  Lunchbreak 
15:15  End of event 