Dimension of physical systems, information processing, and thermodynamics

Brunner, Nicolás; Kaplan, Marc; Leverrier, Anthony; Skrzypczyk, Paul

doi:10.1088/1367-2630/16/12/123050

Cited by 30 publications

(35 citation statements)

References 54 publications

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“…This suggests that the exclusivity principle, which has so far been considered only in the realm of contextuality, may be thermodynamically relevant. This observation is also closely related to the notion of 'dimension mismatch' described in [82], and to orthomodularity in quantum logic (see for example [23]).…”

Section: Why the 'Gbit' Is Ruled Outmentioning

confidence: 54%

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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Section: Why the 'Gbit' Is Ruled Outmentioning

confidence: 54%

Thermodynamics and the structure of quantum theory

et al. 2017

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“…[13]), despite being simplicial. Furthermore, it is interesting to notice that simplicial theories have no dimension mismatch [14] and satisfy the Information Content Principle [15]. Indeed, these properties are not sensitive to the parallel composition rule, making all the simplicial theories equivalent on the basis of their simplicial structure.…”

Section: Discussionmentioning

confidence: 99%

Classical theories with entanglement

2020

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We consider theories where the set of states for every system is a simplex. A special case of such theories is that of classical theories, i.e. those whose pure states are jointly perfectly discriminable. The standard classical theory is the one satisfying local discriminability. However, simplicial theories-including the classical ones-can violate local discriminability, thus admitting entangled states. After proving that simplicial theories are necessarily causal, we provide necessary and sufficient conditions for them to exhibit entanglement, and classify their system-composition rules.

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“…In all these theories the logarithm of the dimension is exactly equal to the measurement entropy of the maximally mixed state. Thanks to this fact, erasure cost defined in [99] coincides with the worst case erasure cost defined above.…”

Section: Duality Between Information Erasure and Entanglement Generationmentioning

confidence: 75%

Entanglement and thermodynamics in general probabilistic theories

Chiribella

Scandolo

2015

New J. Phys.

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Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement. The correspondence is then used to define entanglement measures in the general probabilistic framework. Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).

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Dimension of physical systems, information processing, and thermodynamics

Cited by 30 publications

References 54 publications

Thermodynamics and the structure of quantum theory

Thermodynamics and the structure of quantum theory

Classical theories with entanglement

Entanglement and thermodynamics in general probabilistic theories

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