Geometry of quantum state space and quantum correlations

Geometry of quantum state space and quantum correlations Quantum state space is endowed with a metric structure, and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by $$2\times 2$$ 2 × 2 density matrices, we determine a particular Riemannian metric for a state $$\rho $$ ρ and show that if $$\rho $$ ρ gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equal to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Geometry of quantum state space and quantum correlations

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Publisher
Springer US
Copyright
Copyright © 2016 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/s11128-015-1227-2
Publisher site
See Article on Publisher Site

Abstract

Quantum state space is endowed with a metric structure, and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by $$2\times 2$$ 2 × 2 density matrices, we determine a particular Riemannian metric for a state $$\rho $$ ρ and show that if $$\rho $$ ρ gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equal to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 12, 2016

References

  • Monotone metrics on matrix spaces
    Petz, D
  • Wigner–Yanase information on quantum state space: the geometric approach
    Gibilisco, P; Isola, T
  • Quantum entanglement
    Horodecki, R; Horodecki, P; Horodecki, M; Horodecki, K

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