Quantum-Bayesian coherence

Fuchs, Christopher A.; Schack, Rüdiger

doi:10.1103/revmodphys.85.1693

Cited by 267 publications

(339 citation statements)

References 146 publications

(233 reference statements)

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“…A similar principle applies to statements regarding the wave function. This is true even in a Bayesian approach [47], where quantum states are interpreted as gambling commitments (the fact that gambling commitments are not, in practice, expressed in terms of arbitrarily large integers means that state space has to be coarse-grained in this approach). It follows that a so-called state-dependent definition of error or disturbance is really a state-independent one for which the region R is very small.…”

Section: The Operator Approachmentioning

confidence: 99%

Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

Appleby

2016

Entropy

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Busch, Lahti and Werner (BLW) have recently criticized the operator approach to the description of quantum errors and disturbances. Their criticisms are justified to the extent that the physical meaning of the operator definitions has not hitherto been adequately explained. We rectify that omission. We then examine BLW's criticisms in the light of our analysis. We argue that, although the BLW approach favour (based on the Wasserstein two-deviation) has its uses, there are important physical situations where an operator approach is preferable. We also discuss the reason why the error-disturbance relation is still giving rise to controversies almost a century after Heisenberg first stated his microscope argument. We argue that the source of the difficulties is the problem of interpretation, which is not so wholly disconnected from experimental practicalities as is sometimes supposed.

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Section: The Operator Approachmentioning

confidence: 99%

Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

Appleby

2016

Entropy

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“…For the purpose of foundational studies-particularly ones of the quantum Bayesian variety [15][16][17][23][24][25]-it is worthwhile recording what this convex set looks like from this perspective.…”

Section: Equality Is Obtained If and Only If G = DImentioning

confidence: 99%

“…These properties make no direct use of the original defining symmetry for SICs, and instead imply them. It is our hope that a better understanding of SIC-sets will lead to new and powerful tool for studying the structure of quantum mechanics [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States

Appleby

Dang

Fuchs

2014

Entropy

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Abstract:Recently there has been much effort in the quantum information community to prove (or disprove) the existence of symmetric informationally complete (SIC) sets of quantum states in arbitrary finite dimension. This paper strengthens the urgency of this question by showing that if SIC-sets exist: (1) by a natural measure of orthonormality, they are as close to being an orthonormal basis for the space of density operators as possible; and (2) in prime dimensions, the standard construction for complete sets of mutually unbiased bases and Weyl-Heisenberg covariant SIC-sets are intimately related: The latter represent minimum uncertainty states for the former in the sense of Wootters and Sussman. Finally, we contribute to the question of existence by conjecturing a quadratic redundancy in the equations for Weyl-Heisenberg SIC-sets.

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“…Recent developments in quantum information have seen a more general discussion of quantum mechanics as a statistical theory [3,4]. In the spirit of these discussions, it may be worthwhile to reconsider the concept of joint probability based on the general operator algebra of quantum statistics.…”

Section: Introductionmentioning

confidence: 99%

Reasonable conditions for joint probabilities of non-commuting observables

Hofmann

2014

Quantum Stud.: Math. Found.

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In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d 2 independent elements, where d is the number of possible outcomes for a precise measurement of an observable. In principle, it is therefore possible to express the density operator by a joint probability of two observables that cannot actually be measured jointly because they do not have any common eigenstates. However, such joint probabilities do not refer to an actual measurement outcome, so their definition cannot be based on a set of possible events. Here, I consider the criteria that could specify a unique mathematical form of joint probabilities in the quantum formalism. It is shown that a reasonable set of conditions results in the definition of joint probabilities by ordered products of the corresponding projection operators. It is pointed out that this joint probability corresponds to the quasi probabilities that have recently been observed experimentally in weak measurements.

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Quantum-Bayesian coherence

Cited by 267 publications

References 146 publications

Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States

Reasonable conditions for joint probabilities of non-commuting observables

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