Computable measure of the quantum correlation
| Autor: | Akhtarshenas, S. Javad, Mohammadi, Hamidreza, Karimi, Saman, Azmi, Zahra |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Quantum Inf Process 14, 247-267 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11128-014-0839-2 |
| Popis: | A general state of an $m\otimes n$ system is a classical-quantum state if and only if its associated $A$-correlation matrix (a matrix constructed from the coherence vector of the party $A$, the correlation matrix of the state, and a function of the local coherence vector of the subsystem $B$), has rank no larger than $m-1$. Using the general Schatten $p$-norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $p$-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 $A$. 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. Comment: 14 pages, Title and Abstract are changed, Sections I, III are modified, Two figures are added, Appendices A and B are added, Conclusion is refined |
| Databáze: | arXiv |
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