arXiv:quant-ph/0401112 · Physical Review A

Proposed direct test of a certain type of noncontextuality in quantum mechanics

Karl Svozil

Published Oct 9, 2009• 20 citations

Abstract

The noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are ``interlinked'' by common observables.

DOI: 10.1103/physreva.80.040102

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arXiv:quant-ph/0401112 · Physical Review A

Proposed direct test of a certain type of noncontextuality in quantum mechanics

Karl Svozil

Published Oct 9, 2009• 20 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.80.040102

Related papers

Proposed Direct Test of Quantum Contextuality

Karl Svozil

Feb 1, 20091 citation

Testing quantum contextuality

Karl Svozil

Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables {J 2 1,J 2 2,J 2 3} and { ¯ J 2 1, ¯ J 2 2,J 2 3} with [J 2 1, ¯ J 2 1] ̸= 0 are measured. The outcomes of measurements of J 2 3 (via J 2 1,J 2 2) and J 2 3 (via ¯ J 2 1, ¯ J 2 2) are compared. Although formally J 2 3 is associated with the same projection operator, quantum contextuality requires that the outcome depends on the complete disposition of the measurement apparatus, in particular whether J 2 1 or ¯ J 2 1 is measured alongside. Besides complementarity, contextuality [1, 2, 3, 4, 5] is another, more subtle nonclassical feature of quantum mechanics. That is, one and the same physical observable may appear different, depending on the context of measurement; i.e., depending on the particular way it was inferred. Stated differently, the outcome of a physical measurement may depend also on other physical measurements which are coperformed. In Bell’s own words [1, section 5], “The result of anTwo entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables {J 2 1,J 2 2,J 2 3} and { ¯ J 2 1, ¯ J 2 2,J 2 3} with [J 2 1, ¯ J 2 1] ̸= 0 are measured. The outcomes of measurements of J 2 3 (via J 2 1,J 2 2) and J 2 3 (via ¯ J 2 1, ¯ J 2 2) are compared. Although formally J 2 3 is associated with the same projection operator, quantum contextuality requires that the outcome depends on the complete disposition of the measurement apparatus, in particular whether J 2 1 or ¯ J 2 1 is measured alongside. Besides complementarity, contextuality [1, 2, 3, 4, 5] is another, more subtle nonclassical feature of quantum mechanics. That is, one and the same physical observable may appear different, depending on the context of measurement; i.e., depending on the particular way it was inferred. Stated differently, the outcome of a physical measurement may depend also on other physical measurements which are coperformed. In Bell’s own words [1, section 5], “The result of an

Jul 5, 19990 citations

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Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables $\{J_1^2,J_2^2,J_3^2\}$ and $\{\bar J_1^2, \bar J_2^2,J_3^2\}$ with $[J_1^2,\bar J_1^2]\neq 0$ are measured. The outcomes of measurements of $J_3^2$ (via $J_1^2,J_2^2$ ) and $J_3^2$ (via $\bar J_1^2,\bar J_2^2$ ) are compared. Although formally $J_3^2$ is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether $J_1^2$ or $\bar J_1^2$ is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables $\{J_1^2,J_2^2,J_3^2\}$ and $\{\bar J_1^2, \bar J_2^2,J_3^2\}$ with $[J_1^2,\bar J_1^2]\neq 0$ are measured. The outcomes of measurements of $J_3^2$ (via $J_1^2,J_2^2$) and $J_3^2$ (via $\bar J_1^2,\bar J_2^2$) are compared. Although formally $J_3^2$ is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether $J_1^2$ or $\bar J_1^2$ is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.

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Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables

\{J_1^2,J_2^2,J_3^2\}

and

\{\bar J_1^2, \bar J_2^2,J_3^2\}

with

[J_1^2,\bar J_1^2]\neq 0

are measured. The outcomes of measurements of

J_3^2

(via

J_1^2,J_2^2

) and

J_3^2

(via

\bar J_1^2,\bar J_2^2

) are compared. Although formally

J_3^2

is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether

J_1^2

\bar J_1^2

is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.