Super-quantum correlation and geometry for Bell-diagonal states with weak measurements

Super-quantum correlation and geometry for Bell-diagonal states with weak measurements We propose “weak one-way deficit” by weak measurements as the generalization of one-way deficit defined for standard projective measurements. The weak one-way deficit for Werner state is obtained analytically. We find that weak one-way deficit is smaller than the standard one-way deficit, which contrasts with a straightforward expectation based on the known fact that super-quantum discord by weak measurement is always larger than the quantum discord defined by projective measurement. On the other hand, by tuning the weak measurement continuously to the projective measurement, both weak one-way deficit and super-quantum discord converge to the same value, which is either the one-way deficit or the quantum discord both quantifying quantum correlation. In this sense, weak measurement does not necessarily capture more quantumness of correlations. We also give the geometry of super-quantum discord of the Bell-diagonal states with explicit geometrical figures. As an application, the dynamic behavior of super-quantum correlation including super-quantum discord and weak one-way deficit under decoherence is investigated. We find that the order relation of the super-quantum correlation and the quantum correlation remained unchanged under the phase flipping channel for the Bell-diagonal states and the Werner states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Super-quantum correlation and geometry for Bell-diagonal states with weak measurements

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Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0649-y
Publisher site
See Article on Publisher Site

Abstract

We propose “weak one-way deficit” by weak measurements as the generalization of one-way deficit defined for standard projective measurements. The weak one-way deficit for Werner state is obtained analytically. We find that weak one-way deficit is smaller than the standard one-way deficit, which contrasts with a straightforward expectation based on the known fact that super-quantum discord by weak measurement is always larger than the quantum discord defined by projective measurement. On the other hand, by tuning the weak measurement continuously to the projective measurement, both weak one-way deficit and super-quantum discord converge to the same value, which is either the one-way deficit or the quantum discord both quantifying quantum correlation. In this sense, weak measurement does not necessarily capture more quantumness of correlations. We also give the geometry of super-quantum discord of the Bell-diagonal states with explicit geometrical figures. As an application, the dynamic behavior of super-quantum correlation including super-quantum discord and weak one-way deficit under decoherence is investigated. We find that the order relation of the super-quantum correlation and the quantum correlation remained unchanged under the phase flipping channel for the Bell-diagonal states and the Werner states.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 8, 2013

References

  • Weak measurements with a qubit meter
    Wu, SJ; Mölmer, K
  • Weak values in nonideal spin measurements: An exact treatment beyond the asymptotic regime
    Pan, AK; Matzkin, A
  • Einselection and decoherence from an information theory perspective
    Zurek, WH
  • Geometric measure of quantum discord
    Luo, S; Fu, S
  • Quantum computing: The power of discord
    Merali, Z
  • Bounds on localizable information via semidefinite programming
    Synak, B; Horodecki, K; Horodecki, M

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