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Gonzalo de la Torre Carazo, ICFO - The Institute of Photonic Sciences
Locally quantum description and reversible dynamics single outnon-local quantum theory and correlations
Quantum theory allows for states with the surprising ability to exhibit nonlocal correlations(nonlocality). These correlations which have found many interesting applications recently are not as strong as allowed by our impossibility to signal arbitrarily fast [1]. In the questto understand what fundamental principles constrain nonlocality locally quantum theory has been proposed [2]. However there are infinite theories with a local description identical to quantum theory yet allowing stronger than quantum correlations [3]. We prove that it suffices to impose the reversibility of dynamics to single out the theory and correlations to be quantum for the case of two qubits. If a generalization of our result would hold for more than two qubits speed ups in reversible quantum computing would be completely determined by the local state space of quantum theory. Assuming the reversibility of dynamics as an axiom theories locally identical to quantum theory but differing in the achievable joint states would be ruled out. Conversely if an experiment would show stronger than quantum correlations either quantum theory would be invalidated already locally or imply the existence of fundamentally irreversible dynamics.

Akbar Fahmi Hashiyani, IPM and Sharif University of Technology
New Criteria for Testing Leggett’s Non-local Hidden Variable Models Versus Quantum Correlations
In 2003, Leggett proposed an alternative model for non-local correlations which is incompatible with quantum predictions [1]. It was shown that the Leggett model is incompatible with the experimentally observable quantum correlations [2]. Moreover, it was shown that quantum correlations are incompatible with any hidden variable model having a non trivial local part, such as Leggett’s model [3]. Conversely, others constructed a non-local hidden-variable model that reproduces the quantum correlation function for the singlet state [4].  In this Poster, without refer to any inequality, we show that the Leggett assumptions and its extension have internal inconsistency. Afterwards, we suggest a new inequality for testing quantum correlation verses any hidden variable model having a nontrivial local part and some type of non-local hidden-variable models which reproduce the quantum correlation function.
1-Found. Phys. 33. 1469 (2003)
2-Nature 446, 871, (2007); PRL 99, 210406 (2007); PRL99,210407 (2007)
3-Nature Phys., 4, 681-685, (2008); PRL 101, 050403 (2008)
4-arXiv:0907.2619 v3; JPA 41, 505301 (2008)

Chris Ferrie, IQC - University of Waterloo
Qubits as embarrassed colleagues: what do tax evasion and quantum state tomography have in common?
Quantum state estimation (a.k.a. "tomography'') plays a key role in designing quantum information processors.  As a problem it resembles probability estimation -- e.g. for classical coins or dice -- but with some subtle and important discrepancies.  We demonstrate an improved classical analogue that captures many of these differences:  the noisy coin.  Observations on noisy coins are unreliable -- an observer sees probably heads or probably tails.  So like a quantum system it cannot be sampled directly.  Unlike standard coins or dice whose worst-case estimation emphrisk scales as $1/N$ for all states noisy coins (and quantum states) have a worst-case risk that scales as $1/sqrtN$ and is overwhelmingly dominated by nearly-pure states.  The resulting optimal estimation strategies for noisy coins are surprising and counterintuitive.  We demonstrate some important consequences for quantum state estimation -- in particular that adaptive tomography can recover the $1/N$ risk scaling of classical probability estimation.

Rodrigo Gallego, ICFO - The Institute of Photonic Sciences
Fully non-local quantum correlations
Quantum Mechanics is a non-local theory but not asnon-local as the no-signalling principle allows. However there exist quantum correlations that exhibit maximalnon-locality: they are as non-local as any non-signalling correlations and thus have a local content quantified by the fraction $p_L$ of events admitting a local description equal to zero. Previous examples of maximal quantum non-locality between two parties require an infinite number of measurements and the corresponding Bell violation is not robust against noise. Here we show how every proof of the Kochen-Specker theorem gives rise to maximally non-local quantum correlations that involve a finite number of measurements and are robust against noise. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof providing an upper bound on the local content $p_Llesssim 0.22$. Our analysis certifies that these are the most non-local correlations ever reported.

Melvin Ho, National University of Singapore
Device-Independent Testing of Entangling Measurements
For a device-independent assessment of a measurement device we present bounds for the maximal CHSH violation if the measurement device is separable and also for projective measurements in the restricted case of qubits.

Peter Janotta, University of Wuerzburg
Limits on non-local correlations from the structure of the local state space
We show that bipartite correlations on the maximally entangled state in generalized probabilistic theories rely on the structure of the local state space. In particular they respect macroscopic locality if the local state space is strongly self-dual.

Pawel Kurzynski, Centre for Quantum Technologies, Singapore
Monogamy of multipartite Bell inequality violations
We show that the complementarity relation between dichotomic observables leads to the monogamy of Bell inequality violations. We introduce a simple condition for the squares of expectation values of complementary observables that is satisfied by all physical states. This condition is used to study multi-qubit correlation inequalities involving two settings per observer. In contrast with the two-qubit case a rich structure of possible violation patterns is shown to exist in the multipartite scenario.

Raymond Lal, University of Oxford
Causal structure in categorical quantum mechanics
Categorical quantum mechanics provides a new view on both quantum information and quantum foundations. This is achieved by using category theory to abstractly describe the information flow that occurs in scenarios such as quantum teleportation. This intuitive formalism has also led to insights into nonlocality and entanglement. However until now causal structure has only been implicit in the formalism. We introduce the notion of a 'causal category' to expose this implicit causal structure and we show how it formalises the interaction between quantum systems in a way that is compatible with relativistic constraints.

Matthew Pusey, Inperial College London
Stabilizer notation for Spekkens' toy theory
Spekkens has introduced a toy theory [Phys. Rev. A 75 032110 (2007)] in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. It also assists calculations within the theory for example of the number of possible states and transformations and enables superpositions to be defined for composite systems.

Sadegh Raeisi, Institute for Quantum Information Science
Micro-Macro Entanglement and Coarse-graining
We are studying the demonstration of entanglement in a micro-macro system. The entanglement is produced via parametric down conversion process between two photons and is being amplified through a phase-covariant cloner to entanglement between a photon and a beam of light. We introduce an analogous system which exploits an entanglement breaking amplifier and produces only classical correlation between the two parties. We show that it is hard to distinguish the outcomes of the two systems considering even a small inaccuracy in photon counting measurements. We model these inaccuracies as coarse-graining. The result is that for certain types of measurements small coarse-graining makes the classical and quantum mechanical correlation indistinguishable.

Benno Salwey, University of Montreal
Multipartite Entanglement - Classification by Symmetry Operations
Contrary to the bipartite case the intricite structure of multipartite is far from being resolved so far. We present a general criterion to distinguish inequivalent classes of states e.g. GHZ- and W-states for three qubit systems in systems of arbitrary size.

Yutaka Shikano, Tokyo Institute of Technology
Counterfactual Closed Timelike Curve
How should we deal with the closed timelike curves (CTCs) in quantum mechanics? The CTC has many paradoxical situations like the grandfather paradox. From the viewpoint of information processing, I will present the grandfather paradox. Furthermore, I will review the Deutsch and our answers. Our answer is called the post-selected CTC based on the idea of quantum teleportation. On considering the causality, I would like to discuss about the post-selected CTC.

Alessandro Tosini, Department of Physics Alessandro Volta
Testing axioms for quantum mechanics on probabilistic toy theories
In the wide range of fundamental physics the issue of Axiomatizing Quantum Mechanics is as relevant as ever. The idea of achieving the mathematical structure of the Quantum Theory as a representation of a fair operational framework (see ref. 1234) namely regarding the theory as a set of rules that allow the experimenter to predict future events on the basis of suitable tests has exhibited an unexpected theoretical power. In addition to causality the following postulates had recently been considered (see ref. 2): PFAITH (existence of a pure preparationally faithful state) and FAITHE (existence of a faithful effect). These postulates correspond to admit the possibility of preparing any state and calibrating any test by means of only local operations. The two postulates alone are not sufficient to isolate the Quantum Theory in the probabilistic scenario. An interesting postulate is PURIFY namely the purifiability of all states. More recently in ref. 3 a more extensive axiomatic approach has been considered adding to causality the postulates LDISCR (local discriminability principle namely the possibility of discriminating joint states by local measurements) and a stronger version of the PURIFY requiring the uniqueness of the purification up to reversible channels on the purifying system. In the present poster some concrete probabilistic models alternative to Quantum Mechanics are presented (see ref. 5).  The first model the two-box world is an extension of the Popescu-Rohrlich model (ref. 6) which achieves the greatest violation of the CHSH inequality compatible with the no-signaling principle. Through a preparationally faithful state chosen among the non local states of the original model it is possible to extend it to a probabilistic theory. The second model the two-clock world is actually a full class of models all having a disk as convex set of states for the local system. These models satisfy the PURIFY Postulate (allow purication of all the mixed states) but the purication is not unique up to reversible channels on the purifying system as required in refs. 3 and 4. The two-clock world naturally contains the the two-rebit world (qubits with real Hilbert space) as a particular realization. This model violates LDISCR and then the local observability principle.  The third model the spin-factor is an n-dimensional generalization of the clock. Here we see that the only dimension n = 3 allows teleportation according to the fact that the qubit is a realization of the 3-spin-factor. Finally the classical probabilistic theory is revisited in the probabilistic theories framework. In pointing out which postulates are violated by each model we also notice deep relations between the local and the non-local structures of the probabilistic theories. REFERENCES1. L. Hardy Quantum theory from five reasonable axioms quant-ph/0101012v4 (2001). 2. G. M. D'Ariano in Philosophy of quantum information and entanglement A. Bokulich and G. Jaeger eds. (Cambridge University Press Cambridge UK 2010). Also arXiv 0807.4383. 3. G. Chiribella G. M. D'Ariano P. Perinotti Probabilistic Theories with Purication Phys. Rev. A 81 062348 (2010). 4. G. Chiribella G. M. D'Ariano P. Perinotti Informational derivation of Quantum Theory arXiv 2011.6451 (2010). 5. G. M. D'Ariano and A. Tosini Testing axioms for Quantum Theory on Probabilistic toy-theories Quant. Inf. Proc. 9 95-141 (2010) (Special Issue on Foundations of Quantum Information) (also arXiv:0911.5409) .6. S. Popescu and D. Rohrlich Quantum non-locality as an axiom Found. Phys. 24 379 (1994). 7. L. Hardy Foliable Operational Structures for General Probabilistic Theories arXiv: 0912.4740 (2009) 8. L. Bombelli J. H. Lee D. Meyer and R. Sorkin Space-Time as a Causal Set Phys. Rev. Lett. 51 521 (1987) 9. L. Lamport Time clocks and the ordering of events in a distributed system Comm. ACM 21 558 (1978)10. G. M. D'Ariano and A. Tosini Space-time and special relativity from causal networks arXiv: 1008.4805 (2010) 11. G. M. D'Ariano The Quantum Field as a Quantum Computer arXiv (2010)

Eyuri Wakakuwa, University of Tokyo
Distillability and isotropy of nonlocal boxes
Bell correlation functions are often used as the figure of merit for analyzing the strength of correlations of a nonlocal box with binary inputs and outputs.  However stronger Bell correlations do not necessary imply distillability to stronger nonlocal correlations -- it is known that there is a nonlocal box exhibiting only a vanishing small inequality violation but can be converted to the maximally nonlocal box (the PR-box) by a distillation protocol consisting of local transformations of many copies of a given nonlocal box without using communication.  One could therefore consider the Bell correlation functions as insufficient for fully characterizing the properties of nonlocal boxes.  To address this we introduce a set of variables characterizing the anisotropy of nonlocal boxes namely the difference from the isotropic nonlocal box defined by adding uniformly random uncorrelated noise on outputs of a PR-box.  We explore the relationship between the distillability and isotropy and show that if a nonlocal box is more anisotropic it is more distillable by investigating protocol-independent properties of distillation.

Joel Wallman, University of Sydney
Preparation noncontextuality and universal quantum computation
Negativity in quasi-probability representations of quantum mechanics is often used as an indicator of nonclassical behaviour. We explore the relation between one definition of "nonclassical'' namely preparation noncontextuality and show that it limits the computational power of physical theories. In particular we show that no preparation noncontextual model can  be nonnegative for one class of gate sets that are universal for quantum computation. We also discuss the relation between the discrete Wigner function and an efficient simulation of a quantum computation.

Michael Westmoreland, Denison University
Locality Non-contextuality and Free Will in Modal Quantum Theory
Modal quantum theory (MQT) is a simplified cousin of ordinary Hilbert  space quantum theory.  Several important theorems of actual quantum theory have direct analogues in MQT including the Bell-Hardy theorem excluding local hidden variables the Kochen-Specker theorem excluding non-contextual hidden variables and the Conway-Kochen "free will theorem'' about entangled systems.  The proofs of these analogue theorems are similar to but much simpler than the originals.

Shane Mansfield, Oxford University
Hardy's Non-locality Paradox and Other Possibilistic Non-Locality Conditions
Hardy's non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is 'possibilistic' in the sense that one only distinguishes between possible outcomes (positive probability) and impossible outcomes (zero probability). Here we show that Hardy's paradox is quite universal: in any (2,2,l) or (2,k,2) Bell scenario, the occurence of Hardy's paradox is a necessary and sufficient condition for possibilistic non-locality. In particular, it subsumes all ladder paradoxes. This universality of Hardy's paradox is not true more generally: we find a new 'proof without inequalities' in the (2,3,3) scenario that can witness non-locality even for correlations that do not display the Hardy paradox. We discuss the ramifications of our results for the computational complexity of recognising possibilistic non-locality.

Karl Johan Paulsson, Oxford University
A diagrammatic approach to foundations of quantum mechanics
We look at two recent attempts by Coecke, Paquette and Pavlovic and Coecke and Perdrix to accommodate for classical structures in categorical quantum mechanics, through embedding and environmental coupling. We identify limitations of this approach, such as the inability to distinguish which 'wire' encodes which structure. We also look at further directions this line of research could take in the form of equivalences of the categorical notions of these structures. Finally we look at the grander picture to try and propose a way to achieve a diagrammatic notion to reason about foundations of physics. With this the hope is that we can extend the categorical approach beyond its current limitations in to a more physical approach.

Marco Piani, University of Waterloo
All non-classical correlations can be activated into distillable entanglement
We devise a protocol in which general non-classical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all non-classical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing non-classicality: Mixed entangled states can be arbitrarily more non-classical than separable and pure entangled states.

Aleks Kissinger, University of Oxford
Synthesising Physical Theories
Automated theorem provers are a software tool that takes a set of mathematical axioms pertaining to some mathematical theory (e.g. the theory of natural numbers and arithmetic) and automatically searches for proofs of theorems. Typically, a lot of hard, manual labour goes into identifying the "right" set of axioms to feed to a theorem prover, however researchers at Edinburgh have recently developed a technique they call "conjecture synthesis" for doing this automatically. Naive approaches (i.e. generate all "possible" axioms and check them) quickly become computationally unfeasible, but this conjecture synthesis technique cleverly incorporates axioms that have already been verified into the search routine to get impressive results. The existing work treats a type of mathematical theory called a "term theory", where one is primarily concerned with showing that two terms are equal (e.g. x * (y + z) = x*y + x*z). This poster explores how the techniques of conjecture synthesis can be extended to so-called "graphical theories", where, instead of terms, we are concerned with the equality of diagrams (e.g. quantum circuits, or Penrose-style tensor diagrams). We then suggest how this extension can be used to explore problems in multipartite quantum entanglement.

Cyril Branciard, University of Queensland
Simulation of multipartite quantum correlations with classical communication
Quantum correlations can be nonlocal, and violate some Bell inequalities. The simulation of quantum correlations with alternative nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality, as well as interesting insights on their peculiarities. For bipartite correlations, Toner and Bacon showed that a single bit of communication allowed to reproduce any correlation obtained by performing Von Neumann measurements on a singlet state. Very little is known however on multipartite correlations: is it also possible to simulate these classically with a finite number of bits?

Dina Genkina, Perimeter Institute
Optimal Probabilistic Teleportation from Multiple Input Copies
We consider the maximum probability of successfully teleporting a quantum state without using a classical communication channel.  We show that, when multiple copies of the state are available, the probability of successful teleportation increases, asymptotically attaining the inverse of the Hilbert space dimension. Such a limit value is determined by the amount of classical information that the EPR channel can send back from the future into the past without violating causality.

Patrick Coles, Carnegie Mellon University
The principle behind the uncertainty principle
Expressions of the uncertainty principle in terms of entropy – entropic uncertainty relations – are gathering increasing interest, particularly ones that allow for quantum memory or quantum side information since they are very strong and are useful for cryptography [Berta et al. Nature Physics 6, 659 (2010)]. Entropic uncertainty relations come in a variety of forms and are proven in a variety of ways. But is there a common principle responsible for all of these relations? We show that several entropic uncertainty relations, including quantum memory ones, are ultimately due to the monotonicity of the relative entropy. This suggests the uncertainty principle can be viewed as a data-processing inequality, expressing the notion that information cannot increase due to evolution in time. Furthermore, finding minimum uncertainty states (i.e. states that satisfy the uncertainty relation with equality) is intimately connected to the question of whether the particular measurement process is reversible, or whether information is irreversibly lost in the process.

Laura Mancinska, University of Waterloo, IQC
Kochen-Specker sets, Pseudo-telepathy Games and Coding Games
We investigate the relationships between Kochen-Specker (KS) sets, pseudo-telepathy (PT) games and coding games. It is known that certain types of PT games can be turned into KS sets and vice versa (Renner and Wolf, 2004). Recently it has been showed that entanglement can increase the number of messages that can be sent over a classical channel with zero-error probability (Cubitt, Leung, Matthews, Winter, 2010). We call such scenarios PT coding games. It turns out that a relationship similar to the one found by Renner and Wolf exists between KS sets and PT coding games. The connections between KS sets, PT games and coding games raises the question of whether these three objects are in fact just different aspects of the same phenomenon.

Fabio Costa, University of Vienna
Quantum correlations with no causal order
We pose the question whether causal ordering between events is a necessary element in quantum theory. In order to address the problem we develop a formalism for multipartite quatum correlations that does not assume any underlying space-time or causal structure, but only that local agents are free to perform arbitrary quantum operations. All known situations, including non-signalling correlations between space-like separated observers, signalling ones between observers connected by a channel and probabilistic mixtures of them, can be expressed in this formalism. We find that there exist more general possibilities that are incompatible with any underlying causal structure.

Armin Nikkhah Shirazi, University of Michigan
A Dimensional Theory of Quantum Mechanics
Ever since quantum mechanics was first developed, it has been unclear what it really tells us about reality. A novel framework, based on 5 axioms, is presented here which offers an interpretation of quantum mechanics unlike any considered thus far: It is postulated that physical objects can exist in one of two distinct modes, based on whether they have an intrinsic actual spacetime history or not. If they do, their mode of existence is actual and they can be described by classical physics. If they do not, then their mode of existence is called actualizable and they must be described in terms of a linear superposition of all possible actualizable (not actual) histories. The reason for the distinction is based on the axiom that there exists a limit in which spacetime reduces to a one-dimension reduced version, called areatime, and that objects which merely actualizably exist in spacetime actually exist in areatime. The operational comparison of the passage of time for such objects to the passage of time for a spacetime observer is postulated to be made possible by what is called an angular dual bilateral symmetry. This symmetry is isomorphic to the trivial group of order one but due to additional specification of the identity operation can be decomposed into the superposition of two imaginary phase angles of opposite sign. To mathematically describe the spacetime manifestation of objects which actually exist in areatime,  each actualizable history is associated with an actualizable path, which in turn is associated with the imaginary phases. For a single free particle, the complex exponent is identified with term proportional to its relativistic action, thus recovering the path integral formulation of quantum mechanics.

Daniel Cavalcanti, CQT
Activation of nonlocality in quantum networks
The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility known as quantum nonlocality represents a milestone in the foundations of quantum theory. Quantum nonlocality is also a valuable resource for information processing tasks e.g. quantum communication quantum key distribution quantum state estimation or randomness extraction. Still deciding if a quantum state is nonlocal remains a challenging problem. We introduce a novel approach to this question: we study the nonlocal properties of quantum states when distributed and measured in networks. Using our framework we show how any one-way entanglement distillable state leads to nonlocal correlations. Then we prove that nonlocality is a non-additive resource which can be activated. There exist states local at the single-copy level that become nonlocal when taking several copies of it. Our results imply that the nonlocality of quantum states strongly depends on the measurement context.Reference: D. Cavalcanti M.L. Almeida V. Scarani A. Acin. Nature Communications 2 184 (2011).

Vlad Gheroghiu, Carnegie Mellon University
Information-theoretical study of collisional decoherence of chiral molecules in a gas
We present a microscopic decoherence model for a chiral molecule immersed in a buffer gas in terms of a two-level system interacting with a two-qubit environment. Our model allows a simple derivation of a master equation computed first by J. Trost and K. Hornberger [PRL 103 023202 (2009)]. We employ information-theoretical concepts to explain the stability of the chiral states by collisional decoherence in terms of information about chirality flowing out to the environment. This is a prototypical system that illustrates the modern principles of decoherence and the quantum-to-classical transition.

Jonathan Poritz, Colorado State University - Pueblo
TBA

Denis Rosset, Universit de Genve - GAP Optique
Bilocality : characterizing the effects of the topology of local variables
When considering tripartite quantum experiments sharing two pairs of local variables the quantum physicist can ask (i) if local correlations are really described by an hidden local variable shared by the three parties or (ii) if the distribution of local variables should be restricted to the topology of the quantum state whose correlations they try to reproduce.We note that this question is relevant for N-partite systems with N>2. We will see that the set of correlations obeying ii) is non-convex and can be characterized in some subspaces by nonlinear equivalents of Bell inequalities.