Unifying Typical Entanglement and Coin Tossing: on Randomization in Probabilistic Theories

Müller, Markus P.; Dahlsten, Oscar; Vedral, Vlatko

doi:10.1007/s00220-012-1605-x

Cited by 32 publications

(35 citation statements)

References 49 publications

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“…Furthermore, consequences of the postulates-such as projectivityseem crucial for thermodynamic reasoning. In fact, weaker versions of postulates 1 and 2, in conjunction with local tomography, are enough to make sense of the general-probabilistic thermodynamics results in [73,74].…”

Section: Discussionmentioning

confidence: 99%

Higher-order interference and single-system postulates characterizing quantum theory

2014

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We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the composition of many systems; and second, it is closer to experiment by having absence of higher-order interference as a postulate, which is currently the subject of experimental investigation. We give three postulates-no higher-order interference, classical decomposability of states, and strong symmetry-and prove that the only non-classical operational probabilistic theories satisfying them are real, complex, and quaternionic quantum theory, together with threelevel octonionic quantum theory and ball state spaces of arbitrary dimension. Then we show that adding observability of energy as a fourth postulate yields complex quantum theory as the unique solution, relating the emergence of the complex numbers to the possibility of Hamiltonian dynamics. We also show that there may be interesting non-quantum theories satisfying only the first two of our postulates, which would allow for higher-order interference in experiments while still respecting the contextuality analogue of the local orthogonality principle.

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Section: Discussionmentioning

confidence: 99%

Higher-order interference and single-system postulates characterizing quantum theory

2014

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“…On the other hand, we show that these postulates already imply many structural properties which are also present in quantum theory, for example self-duality and the existence of analogues of projective measurements, observables, eigenvalues and eigenspaces.In summary, our analysis shows that important structural aspects of quantum and classical theory are already implied by these aspects of thermodynamics, but on the other hand it suggests that there is still some 'elbow room' for modification within these limits dictated by thermodynamics.Thermodynamics in GPTs has been considered in some earlier works. In [35,36], the authors introduced a notion of (Rényi-2-)entanglement entropy, and studied the phenomenon of thermalisation by entanglement [37][38][39] and the black-hole information problem (in particular the Page curve [40]) in generalisations of quantum theory. Hänggi and Wehner [46] have related the uncertainty principle to the second law in the framework of GPTs.…”

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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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“…The possibility of a pure and reversilble description is particularly appealing for the foundations of thermodynamics, as it reconciles the mixedness of thermodynamic ensembles with the pure and reversible picture provided by fundamental physics. In the quantum case, purification is the starting point for all recent proposals to derive thermodynamic ensembles from the typicality of pure entangled states [69][70][71][72][73][74][75], an idea that has been recently explored also in the broader framework of general probabilistic theories [76,77]. Building on the purification principle, we establish the desired duality between entanglement and thermodynamics, showing that the degree of entanglement of a pure bipartite system coincides with the degree of mixedness of its parts.…”

Section: Introductionmentioning

confidence: 92%

“…, and χ is the invariant state. Another example of purity monotone induced by a norm is the notion of purity introduced in [76,77], based on the Schatten two-norm. In the quantum case, this notion of purity coincides with the ordinary notion P Tr 2 ( ) ( ) r r = and therefore coincides with the f-purity with f x x .…”

Section: Measures Of Mixedness and Measures Of Entanglementmentioning

confidence: 99%

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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Unifying Typical Entanglement and Coin Tossing: on Randomization in Probabilistic Theories

Cited by 32 publications

References 49 publications

Higher-order interference and single-system postulates characterizing quantum theory

Higher-order interference and single-system postulates characterizing quantum theory

Thermodynamics and the structure of quantum theory

Entanglement and thermodynamics in general probabilistic theories

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