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Title: Interplay between computable measures of entanglement and other quantum correlations

Abstract

Composite quantum systems can be in generic states characterized not only by entanglement but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue, focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D{sub G}. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship D{sub G}{>=}N{sup 2} holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner, and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, which we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems.

Authors:
;  [1]
  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
Publication Date:
OSTI Identifier:
22093457
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 5; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; FOCUSING; GEOMETRY; INDICATORS; MIXED STATE; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; QUANTUM MECHANICS

Citation Formats

Girolami, Davide, and Adesso, Gerardo. Interplay between computable measures of entanglement and other quantum correlations. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.052110.
Girolami, Davide, & Adesso, Gerardo. Interplay between computable measures of entanglement and other quantum correlations. United States. https://doi.org/10.1103/PHYSREVA.84.052110
Girolami, Davide, and Adesso, Gerardo. Tue . "Interplay between computable measures of entanglement and other quantum correlations". United States. https://doi.org/10.1103/PHYSREVA.84.052110.
@article{osti_22093457,
title = {Interplay between computable measures of entanglement and other quantum correlations},
author = {Girolami, Davide and Adesso, Gerardo},
abstractNote = {Composite quantum systems can be in generic states characterized not only by entanglement but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue, focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D{sub G}. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship D{sub G}{>=}N{sup 2} holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner, and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, which we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems.},
doi = {10.1103/PHYSREVA.84.052110},
url = {https://www.osti.gov/biblio/22093457}, journal = {Physical Review. A},
issn = {1050-2947},
number = 5,
volume = 84,
place = {United States},
year = {2011},
month = {11}
}