I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the non-unique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distribution is generic), and a no-cloning theorem. Two particular theories are then investigated in detail, for the sake of comparison with the classical and quantum cases. One of these includes states that can give rise to arbitrary non-signalling correlations, including the super-quantum correlations that have become known in the literature as Nonlocal Machines or Popescu-Rohrlich boxes. By investigating these correlations in the context of a theory with well-defined dynamics, I hope to make further progress with a question raised by Popescu and Rohrlich, which is, why does quantum theory not allow these strongly nonlocal correlations? The existence of such correlations forces much of the dynamics in this theory to be, in a certain sense, classical, with consequences for teleportation, cryptography and computation. I also investigate another theory in which all states are local. Finally, I raise the question of what further axiom(s) could be added to the framework in order uniquely to identify quantum theory, and hypothesize that quantum theory is optimal for computation.

Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.

It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are non-local, in the sense that a Bell inequality is violated. They cannot, however, be used for super-luminal signalling. It is also known that it is possible to write down sets of "super-quantum" correlations that are more non-local than is allowed by quantum mechanics, yet are still non-signalling. Viewed as an information theoretic resource, super-quantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signalling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signalling polytope in the case that two observers each choose from two possible measurements with d outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory.At the heart of much debate concerning quantum theory lies the quantum state. Does the wave function correspond directly to some kind of physical wave? If so, it is an odd kind of wave, since it is defined on an abstract configuration space, rather than the three-dimensional space we live in. Nonetheless, quantum interference, as exhibited in the famous two-slit experiment, appears most readily understood by the idea that it is a real wave that is interfering. Many physicists and chemists concerned with pragmatic applications of quantum theory successfully treat the quantum state in this way.Many others have suggested that the quantum state is something less than real [1][2][3][4][5][6][7][8]. In particular, it is often argued that the quantum state does not correspond directly to reality, but represents an experimenter's knowledge or information about some aspect of reality. This view is motivated by, amongst other things, the collapse of the quantum state on measurement. If the quantum state is a real physical state, then collapse is a mysterious physical process, whose precise time of occurrence is not well-defined. From the 'state of knowledge' view, the argument goes, collapse need be no more mysterious than the instantaneous Bayesian updating of a probability distribution upon obtaining new information.The importance of these questions was eloquently stated by Jaynes:But our present [quantum mechanical] formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature -all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that the unscrambling is a prerequisite for any further advance in basic physical theory. For, if we cannot separate the subjective and objective aspects of the formalism, * m@physics.orgwe cannot know what we are talking about; it is just that simple.[9]Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a "real physical state" -not necessarily completely described by quantum theory, but objective and independent of the observer. This assu...

We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.

n a multipartite setting, it is possible to distinguish quantum states that are genuinely n-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely n-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of n-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of three-way nonlocality. Numerical evidence suggests that all three-way entangled pure quantum states can produce three-way nonlocal correlations

Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach's principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C, then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach's principle to a formalism for quantum causal models, and provide examples of how the formalism works.Contents arXiv:1609.09487v2 [quant-ph]

We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes and use it to give a simple proof that the maximally entangled state of two d-dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental program to obtain as good an upper bound as possible on the fraction of local states and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in d d dimensions. We also prove that the quantum correlations violating the inequality are monogamous among nonsignaling correlations and, hence, can be used for quantum key distribution secure against postquantum (but nonsignaling) eavesdroppers. Quantum theory predicts that measurements on separated entangled systems will produce outcome correlations that, in Bell's terminology [1], are not locally causal or, in what has become standard terminology, are nonlocal. In particular, if a Bell inequality is violated, then one cannot consistently assume that the outcomes of measurements on each system are predetermined and independent of the measurements carried out on the other system(s). Violation of Bell inequalities has been confirmed in numerous experiments [2].Violation of Bell inequalities not only tells us something fundamental about nature but also has practical applications. For example, the nonlocality of quantum correlations allows communication complexity problems to be solved using an amount of communication that is smaller than is possible classically [3]. Barrett-Hardy-Kent (BHK) recently showed that testing particular nonlocal quantum correlations allows two parties to distribute a secret key securely, in such a way that the security is guaranteed by the no-signaling principle alone [4] (i.e., without relying on the validity of quantum theory).In this Letter, we extend the chained Bell inequality to an inequality with an arbitrary number of measurement outcomes, which can thus be applied to states in arbitrary dimensions. In the limit of a large number of measurement settings, quantum mechanics predicts correlations for a maximally entangled bipartite state that resemble those of the tripartite Greenberger-Horne-Zeilinger (GHZ) state in that, with probability tending to one, the predictions of any local hidden variable model contradict those of quantum mechanics for at least one pair of measurements. We use this to give a constructive proof of a result originally due to Elitzur, Popescu, and Rohrlich (EPR) [5]: If the quantum correlations of a maximally entangled state of two qubits are written as a convex combination of local and nonlocal correlations, then the local fraction must be zero. Our proof extends EPR's result to maximally entangled states in any dimension and also removes the need for a technical assumption required for EPR's original proof [6]. Mor...