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Optimized Measures of Bipartite Quantum Correlation · Around

2019

Optimized Measures of Bipartite Quantum Correlation

Levin, Joshua, Smith, Graeme

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How can we characterize different types of correlation between quantum systems? Since correlations cannot be generated locally, we take any real function of a multipartite state which cannot increase under local operations to measure a correlation.

Correlation measures that can be expressed as an optimization of a linear combination of entropies are particularly useful, since they can often be interpreted operationally.
We systematically study such optimized linear entropic functions, and by enforcing monotonicity under local processing we identify four cones of correlation measures for bipartite quantum states.
This yields two new optimized measures of bipartite quantum correlation that are particularly simple, which have the additional property of being additive.

Built on

E. H. Lieb and M. B. Ruskai, “Proof of the strong subadditivity of quantum‐mechanical entropy,” Journal of Mathematical Physics
1973
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C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, “Entanglement-assisted capacity of a quantum channel and the reverse shannon theorem,” IEEE Transactions on Information Theory
2002
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B. M. Terhal, M. Horodecki, D. W. Leung, and D. P. DiVincenzo, “The entanglement of purification,” Journal of Mathematical Physics
2002
Earlier work this paper cites.

Similar

N. Pippenger, “The inequalities of quantum information theory,” IEEE Transactions on Information Theory
2003
Cited alongside, same era.
M. Christandl and A. Winter, ““squashed entanglement”: An additive entanglement measure,” Journal of Mathematical Physics
2004
Cited alongside, same era.
M. Christandl and A. Winter, “Uncertainty, monogamy, and locking of quantum correlations,” IEEE Transactions on Information Theory
2006
Cited alongside, same era.

Then

J. Chen and A. Winter, “Non-additivity of the entanglement of purification (beyond reasonable doubt),” arXiv preprint arXiv:1206.1307
Original
2012
Later among the works it cites.
A. Cross, K. Li, and G. Smith, “Uniform additivity in classical and quantum information,” Phys. Rev. Lett
2017
Later among the works it cites.
M. Alhejji and G. Smith, “Monotonicity under local operations: Linear entropic formulas,” arXiv preprint arXiv:1811.08000
Original
2018
Later among the works it cites.

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