An information-theoretic principle implies that any discrete physical theory is classical

Pfister, Corsin; Wehner, Stephanie

doi:10.1038/ncomms2821

Cited by 40 publications

(49 citation statements)

References 22 publications

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“…Furthermore it implies an analogous generalized no-broadcasting theorem [13]. Similar postulates such as information gain implies disturbance [14] are also sufficient to discount classical degrees of freedom.…”

Section: Proof See Appendixmentioning

confidence: 89%

Entanglement is Necessary for Emergent Classicality in All Physical Theories

2017

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One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of which physical principles give rise to entanglement. Why does quantum theory have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? We demonstrate that without entanglement, non-classical degrees of freedom cannot reversibly interact. We present two postulates, no-cloning / no-broadcasting and local transitivity, either of which are sufficient to imply the existence of entangled states in any non-classical theory with reversible interactions. Therefore we argue that entanglement is an inevitable feature of a non-classical universe.

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Section: Proof See Appendixmentioning

confidence: 89%

Entanglement is Necessary for Emergent Classicality in All Physical Theories

2017

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“…For more detailed explanations of the framework, see e.g. [34,51,52,55,86,87]. The framework contains quantum theory and also the application of probability theory to classical physics, often referred to as classical probability theory, as special cases.…”

Section: The Mathematical Frameworkmentioning

confidence: 99%

Thermodynamics and the structure of quantum theory

et al. 2017

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Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behaviour should arguably satisfy. In the framework of generalised probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin's notion of higher-order interference.information processing, and in this way to gain a deeper understanding of its characteristic properties in terms of computation or communication.In a complementary approach, there has been a wave of attempts to find simple physical principles that single out quantum correlations from the set of all non-signalling correlations in the device-independent formalism [70]. These include non-trivial communication complexity [71], macroscopic locality [72], or information causality [73]. However, none of these principles so far turns out to yield the set of quantum correlations exactly. This led to the discovery of 'almost quantum correlations ' [75] which are more general than those allowed by quantum theory, but satisfy all the aforementioned principles. Almost quantum correlations seem to appear naturally in the context of quantum gravity [77].A relation to other fields of physics can also be drawn from information causality, which can be understood as the requirement that a notion of entropy [66-69] exists which has some natural properties like the dataprocessing inequality [74]. These emergent connections to entropy and quantum gravity are particularly interesting since they point to an area of physics where modifications of quantum theory are well-motivated: Jacobson's results [78] and holographic duality [79] relate thermodynamics, entanglement, and (quantum) gravity, and modifying quantum theory has been discussed as a means to overcome apparent paradoxes in blackhole physics [80].While GPTs provide a way to generalise quantum theory and to study more general correlations and physical theories, they still leave open the question as to which principles should guide us in applying the GPT formalism for this purpose. The considerations above suggest taking, as a guideline for such modifi...

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“…When the measurement dimension and information dimension differ, i.e., when < d d m i , we say that the theory features a dimension mismatch. Before discussing this aspect, we give a brief review of the concepts of GPTs; more comprehensive reviews are available in the literature [5,12,16,42].…”

Section: Dimension Mismatch In Gptsmentioning

confidence: 99%

“…In fact, understanding what features identify quantum mechanics among GPTs is a deep question, which may lead to a reformulation of quantum theory based on more physical axioms, see [5][6][7][8][9][10][11]. Discussing information processing and physical properties of GPTs may give insight to this question [5,[12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Dimension of physical systems, information processing, and thermodynamics

et al. 2014

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We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are different in generalized probabilistic theories. We discuss in detail the case of a theory known as 'boxworld', and show that such a theory features systems with dimension mismatch. This dimension mismatch can be made arbitrarily large using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauerʼs erasure principle and thus the second law.

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An information-theoretic principle implies that any discrete physical theory is classical

Cited by 40 publications

References 22 publications

Entanglement is Necessary for Emergent Classicality in All Physical Theories

Entanglement is Necessary for Emergent Classicality in All Physical Theories

Thermodynamics and the structure of quantum theory

Dimension of physical systems, information processing, and thermodynamics

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