Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory

Wolf, Michael M.; Perez-Garcia, David; Fernandez, Carlos

doi:10.48550/arxiv.0905.2998

Cited by 4 publications

(9 citation statements)

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“…Similar results in terms of operators in case of measurements on states were obtained in [2,8]. Now we will proceed by deriving some conditions on the incompatibility of two-outcome measurements based on the results of Prop.…”

Section: A Compatibility Of Two-outcome Measurementsmentioning

confidence: 54%

“…We will formulate the problem of compatibility of two two-outcome measurements as a problem of linear programming [16] similar to the one obtained in [2]. We will start with the results of Prop.…”

Section: B Linear Programming Problem For Compatibility Of Two-outcom...mentioning

confidence: 99%

“…Incompatibility lies deeply within quantum mechanics and many of the famous and key aspect of quantum theories have been traced to Heisenberg uncertainty principle, no cloning theorem, violations of Bell inequalities and other notions making use of compatibility, see [1] for recent review. In light of these discoveries compatibility in the framework of general probabilistic theories has been studied [2][3][4] in order to show the difference between classical and non-classical probabilistic theories. Also the connection of compatibility and steering in general probabilistic theories have been studied [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…Recently incompatibility of measurements on quantum channels and combs has been in question [7] as it potentially could be used as a resource in quantum theory in a similar ways as an incompatibility of measurements on quantum states [1]. The degree of compatibility (also called robustness of incompatibility) has been studied for measurements on channels and combs [2,7,8].…”

Section: Introductionmentioning

confidence: 99%

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All measurements in a probabilistic theory are compatible if and only if the state space is a simplex

Plávala

2016

Preprint

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We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome measurements to be compatible and we use these conditions to show that there exist incompatible measurements whenever the state space is not a simplex. We also formulate the linear programming problem for the compatibility of two-outcome measurements.

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Section: A Compatibility Of Two-outcome Measurementsmentioning

confidence: 54%

Section: B Linear Programming Problem For Compatibility Of Two-outcom...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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All measurements in a probabilistic theory are compatible if and only if the state space is a simplex

Plávala

2016

Preprint

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“…Several suggestions have been made. Superquantum correlations lead to violations of the Heisenberg uncertainty principle [14,15], which is another seemingly purely quantum result. PR-boxes would allow distributed computation to be performed with only one bit of communication [16], which looks unlikely but doesn't violate any known physical law.…”

Section: Introductionmentioning

confidence: 99%

Tsirelson’s Bound Prohibits Communication through a Disconnected Channel

Carmi

Moskovich

2018

Entropy

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Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality

Plávala¹

2017

Phys. Rev. A

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We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not follow the standard line of thinking stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and Bell nonlocality as entanglement-assisted incompatibility tests. We show that all of the proposed definitions are, in the special case of measurements, the same as the standard definitions, but not all of the known results for measurements generalize to channels. For example, we show that for quantum channels, steering is not a necessary condition for Bell nonlocality. We further investigate the introduced conditions and concepts in the special case of quantum theory and we provide many examples to demonstrate these concepts and their implications.

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Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory

Cited by 4 publications

References 0 publications

All measurements in a probabilistic theory are compatible if and only if the state space is a simplex

All measurements in a probabilistic theory are compatible if and only if the state space is a simplex

Tsirelson’s Bound Prohibits Communication through a Disconnected Channel

Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality

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