Informational derivation of quantum theory

Chiribella, Giulio; D’Ariano, Giacomo Mauro; Perinotti, Paolo

doi:10.1103/physreva.84.012311

Cited by 549 publications

(940 citation statements)

References 35 publications

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“…4 We can also consider mixtures of two or more mixed states. If M 1 and M 2 are two subspaces of V associated with two states, then M 1 ∨ M 2 is the subspace associated with a mixture of the two.…”

Section: Mixed States In Mqtmentioning

confidence: 99%

“…The most celebrated example of this approach was Bell's analysis [2], which showed that entangled quantum systems have statistical properties unlike any hypothetical local hidden variable model. More recently, there have been several efforts to give quantum theory an operational axiomatic foundation [3,4,5]. In these efforts, a general abstract framework is posited to describe system preparations, choices of measurement, observed results of measurement, and probabilities.…”

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confidence: 99%

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Modal Quantum Theory

Schumacher

Westmoreland

2012

Found Phys

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The remarkable features of quantum theory are best appreciated by comparing the theory to other possible theories-what Spekkens calls "foil" theories [1]. The most celebrated example of this approach was Bell's analysis [2], which showed that entangled quantum systems have statistical properties unlike any hypothetical local hidden variable model. More recently, there have been several efforts to give quantum theory an operational axiomatic foundation [3,4,5]. In these efforts, a general abstract framework is posited to describe system preparations, choices of measurement, observed results of measurement, and probabilities. Many possible theories can be expressed in the framework. The axioms embody fundamental aspects of quantum theory that uniquely identify it among them. A striking lesson of this work is that familiar quantum theory can be characterized by axioms that seem to have little to do with the traditional quantum machinery of states and observables in Hilbert space. The Hilbert space structure is "derived" from the operational axioms.These approaches are based on two distinct concepts of generalization. First, we generalize within quantum theory to give the theory its most general form. For example, we generalize state vectors to density operators as a

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Section: Mixed States In Mqtmentioning

confidence: 99%

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confidence: 99%

Modal Quantum Theory

Schumacher

Westmoreland

2012

Found Phys

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“…In the recent past, there have been several attempts to derive (finite-dimensional) quantum theory within a framework of probabilistic theories 12,28,29 . The idea is the following.…”

Section: Article Nature Communicationsmentioning

confidence: 99%

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

Pfister

Wehner

2013

Nat Commun

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It has been suggested that nature could be discrete in the sense that the underlying state space of a physical system has only a finite number of pure states. Here we present a strong physical argument for the quantum theoretical property that every state space has infinitely many pure states. We propose a simple physical postulate that dictates that the only possible discrete theory is classical theory. More specifically, we postulate that no information gain implies no disturbance or, read in the contrapositive, that disturbance leads to some form of information gain. Furthermore, we show that non-classical discrete theories are still ruled out even if we relax the postulate to hold only approximately in the sense that no information gain only causes a small amount of disturbance. Our postulate also rules out popular generalizations such as the Popescu-Rohrlich-box that allows non-local correlations beyond the limits of quantum theory.

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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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Informational derivation of quantum theory

Cited by 549 publications

References 35 publications

Modal Quantum Theory

Modal Quantum Theory

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

Quantum theory from questions

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