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Bound on measurement based on no-signaling

Erika Andersson, Stephen Mark Barnett

Published Jan 1, 2003• 0 citations
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Related papers

Bound on measurement based on the no-signaling condition

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We obtain a tight bound on the measurement which discriminates without error between two nonorthogonal states. The derivation is based on the no-signaling condition, without any reference to generalized measurements.

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Quantum correlations do not allow signaling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signaling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimized by the maximum confidence strategy. We show that this strategy may be derived from the no-signaling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.

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No-signaling theories, which can contain nonlocal correlations stronger than quantum correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In practice, Bell tests are powerful tools to certify nonlocality, but their effectiveness is limited by the detector efficiency. In this work, we provide almost tight detection efficiency bounds for showing the nonlocality of no-signaling theories, by introducing a general class of Bell inequalities. In particular, we provide a tight bound for the bipartite case and an asymptotic tight bound for the multipartite case. The tightness of these bounds shows that they well characterize the structure of no-signaling theories. The bounds also imply that the detector efficiency requirement can be made arbitrarily low in both bipartite and multipartite cases by increasing the number of measurement settings. Furthermore, our work sheds light on the detector efficiency requirement for showing the nonlocality of the quantum theory.

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Testing the No-Signaling Hypothesis

Bruce Holton

•Nov 1, 2019•0 citations
Quantum correlations do not allow signaling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signaling condition limits allowed operations and, in the context of quantum communication, may be used to put bounds on quantum state discrimination. We find that the natural figure of merit to consider is the confidence in identifying a state, which is optimized by the maximum confidence strategy. We show that this strategy may be derived from the no-signaling condition, and demonstrate the relationship between maximum confidence measurements and entanglement concentration.
No-signaling theories, which can contain nonlocal correlations stronger than quantum correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In practice, Bell tests are powerful tools to certify nonlocality, but their effectiveness is limited by the detector efficiency. In this work, we provide almost tight detection efficiency bounds for showing the nonlocality of no-signaling theories, by introducing a general class of Bell inequalities. In particular, we provide a tight bound for the bipartite case and an asymptotic tight bound for the multipartite case. The tightness of these bounds shows that they well characterize the structure of no-signaling theories. The bounds also imply that the detector efficiency requirement can be made arbitrarily low in both bipartite and multipartite cases by increasing the number of measurement settings. Furthermore, our work sheds light on the detector efficiency requirement for showing the nonlocality of the quantum theory.