Deriving Quantum Theory from Its Local Structure and Reversibility

Torre, Gonzalo de la; Masanes, Lluís; Short, Anthony; Müller, Markus P.

doi:10.1103/physrevlett.109.090403

Cited by 45 publications

(81 citation statements)

References 10 publications

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“…In fact quantum theory obeys a much stronger principle than reversibility: any set of perfectly distinguishable states of a system can be mapped via unitary evolution to any other set of the same size. The importance of reversibility in quantum theory is suggested by the prevalent usage of it (or stronger versions of it) as an axiom in numerous information-theoretic derivations of quantum theory [2,4,10,13,16,17].…”

Section: Discussionmentioning

confidence: 99%

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Reversible dynamics in strongly non-local Boxworld systems

Al-Safi¹,

Short

2014

J. Phys. A: Math. Theor.

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In order to better understand the structure of quantum theory, or speculate about theories that may supercede it, it can be helpful to consider alternative physical theories. "Boxworld" describes one such theory, in which all non-signaling correlations are achievable. In a limited class of multipartite Boxworld systems -wherein all subsystems are identical and all measurements have the same number of outcomes -it has been demonstrated that the set of reversible dynamics is 'trivial', generated solely by local relabellings and permutations of subsystems. We develop the convex formalism of Boxworld to give an alternative proof of this result, then extend this proof to all multipartite Boxworld systems, and discuss the potential relevance to other theories. These results lend further support to the idea that the rich reversible dynamics in quantum theory may be the key to understanding its structure and its informational capabilities.

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Section: Discussionmentioning

confidence: 99%

“…A common example of this is reversibility (or transitivity) [2,[10][11][12][13], which demands that any two pure states are linked by a reversible transformation.…”

Section: Introductionmentioning

confidence: 99%

Reversible dynamics in strongly non-local Boxworld systems

Al-Safi¹,

Short

2014

J. Phys. A: Math. Theor.

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“…Since this gives rise to a constructive derivation of the explicit architecture of qubit quantum theory, it involves a large number of individual steps compared to the rather abstract reconstructions [3][4][5][6][7][8][9][10]. However, this is also rewarding as it offers novel informational explanations for typical features of quantum theory, and so many reconstruction steps are actually quite instructive.…”

Section: Synopsis Of the Reconstruction Steps And Key Resultsmentioning

confidence: 99%

“…In particular, the goal should be to find an operational justification for the textbook axioms, i.e., ultimately for complex Hilbert spaces, unitary dynamics, tensor product structure for composite systems, Born rule, and so on. The result would be a reconstruction of quantum theory from operational axioms [1][2][3][4][5][6][7][8][9][10] and should ideally yield a better understanding of what quantum theory tells us about Nature; and why it is the way it is.…”

Section: Introductionmentioning

confidence: 99%

Quantum Theory from Rules on Information Acquisition

Hoehn

2017

Entropy

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Abstract:We summarize a recent reconstruction of the quantum theory of qubits from rules constraining an observer's acquisition of information about physical systems. This review is accessible and fairly self-contained, focusing on the main ideas and results and not the technical details. The reconstruction offers an informational explanation for the architecture of the theory and specifically for its correlation structure. In particular, it explains entanglement, monogamy and non-locality compellingly from limited accessible information and complementarity. As a by-product, it also unravels new 'conserved informational charges' from complementarity relations that characterize the unitary group and the set of pure states.

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“…In fact, there actually exist a number of successful reconstructions of finite dimensional quantum theory from operational axioms, most of which have been performed within the frameworks of generalized or operational probability theories [9,[23][24][25][26][27][28][29][30][31][32] (see also [33] which is adapted to a space-time language and the more mathematical reconstructions [34,35]). Despite the beauty and great technical achievements of some of these reconstructions, they arguably come short of providing a fully satisfactory physical and conceptual picture of quantum theory.…”

Section: Introductionmentioning

confidence: 99%

Quantum theory from questions

2017

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We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S's state as O's 'catalogue of knowledge' about S. From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C 2 N ; (b) states evolve unitarily under the group PSU(2 N ) according to the von Neumann evolution equation; and (c) O's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels new structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a 'charge of quantum theory' and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in [1].

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Deriving Quantum Theory from Its Local Structure and Reversibility

Cited by 45 publications

References 10 publications

Reversible dynamics in strongly non-local Boxworld systems

Reversible dynamics in strongly non-local Boxworld systems

Quantum Theory from Rules on Information Acquisition

Quantum theory from questions

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