# Computable measure of quantum correlation

Computable measure of quantum correlation A general state of an $$m\otimes n$$ m ⊗ n system is a classical-quantum state if and only if its associated $$A$$ A -correlation matrix (a matrix constructed from the coherence vector of the party $$A$$ A , the correlation matrix of the state, and a function of the local coherence vector of the subsystem $$B$$ B ), has rank no larger than $$m-1$$ m - 1 . Using the general Schatten $$p$$ p -norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $$p$$ p -norms and any function of the local coherence vector of the unmeasured subsystem, leading to a class of computable quantities which can be used to capture the quantumness of correlations due to the subsystem $$A$$ A . We introduce two special members of these quantifiers: The first one coincides with the tight lower bound on the geometric measure of discord, so that such lower bound fully captures the quantum correlation of a bipartite system. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord. The second quantifier has the property that it is invariant under a local and reversible operation performed on the unmeasured subsystem, so that it can be regarded as a computable well-defined measure of the quantum correlations. The approach presented in this paper provides a way to circumvent the problem with the geometric discord. We provide some examples to exemplify this measure. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Computable measure of quantum correlation

21 pages

Loading next page...

/lp/springer-journals/computable-measure-of-quantum-correlation-A62EptLYgY
Publisher site
See Article on Publisher Site

### Abstract

A general state of an $$m\otimes n$$ m ⊗ n system is a classical-quantum state if and only if its associated $$A$$ A -correlation matrix (a matrix constructed from the coherence vector of the party $$A$$ A , the correlation matrix of the state, and a function of the local coherence vector of the subsystem $$B$$ B ), has rank no larger than $$m-1$$ m - 1 . Using the general Schatten $$p$$ p -norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $$p$$ p -norms and any function of the local coherence vector of the unmeasured subsystem, leading to a class of computable quantities which can be used to capture the quantumness of correlations due to the subsystem $$A$$ A . We introduce two special members of these quantifiers: The first one coincides with the tight lower bound on the geometric measure of discord, so that such lower bound fully captures the quantum correlation of a bipartite system. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord. The second quantifier has the property that it is invariant under a local and reversible operation performed on the unmeasured subsystem, so that it can be regarded as a computable well-defined measure of the quantum correlations. The approach presented in this paper provides a way to circumvent the problem with the geometric discord. We provide some examples to exemplify this measure.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 7, 2014

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off