Quantifying quantum correlation via quantum coherence

Guang-Yong Zhou, Lin-Jian Huang, Jun-Ya Pan, Li-Yun Hu, Jie-Hui Huang

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Front. Phys. ›› 2018, Vol. 13 ›› Issue (4) : 130701. DOI: 10.1007/s11467-018-0804-0
RESEARCH ARTICLE
RESEARCH ARTICLE

Quantifying quantum correlation via quantum coherence

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Abstract

Resource theory is applied to quantify the quantum correlation of a bipartite state and a computable measure is proposed. Since this measure is based on quantum coherence, we present another possible physical meaning for quantum correlation, i.e., the minimum quantum coherence achieved under local unitary transformations. This measure satisfies the basic requirements for quantifying quantum correlation and coincides with concurrence for pure states. Since no optimization is involved in the final definition, this measure is easy to compute irrespective of the Hilbert space dimension of the bipartite state.

Keywords

resource theory / quantum correlation / quantum coherence

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Guang-Yong Zhou, Lin-Jian Huang, Jun-Ya Pan, Li-Yun Hu, Jie-Hui Huang. Quantifying quantum correlation via quantum coherence. Front. Phys., 2018, 13(4): 130701 https://doi.org/10.1007/s11467-018-0804-0

References

[1]
E. Knill and R. Laflamme, Power of one bit of quantum information, Phys. Rev. Lett. 81(25), 5672 (1998)
CrossRef ADS Google scholar
[2]
A. Datta, A. Shaji, and C. M. Caves, Quantum discord and the power of one qubit, Phys. Rev. Lett. 100(5), 050502 (2008)
CrossRef ADS Google scholar
[3]
B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, Experimental quantum computing without entanglement, Phys. Rev. Lett. 101(20), 200501 (2008)
CrossRef ADS Google scholar
[4]
H. Ollivier and W. H. Zurek, Quantum discord: A measure of the quantumness of correlations, Phys. Rev. Lett. 88(1), 017901 (2001)
CrossRef ADS Google scholar
[5]
G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: Manipulations and monotones, New J. Phys. 10(3), 033023 (2008)
CrossRef ADS Google scholar
[6]
F. G. S. L. Brandão and G. Gour, Reversible framework for quantum resource theories, Phys. Rev. Lett. 115(7), 070503 (2015)
CrossRef ADS Google scholar
[7]
B. Coecke, T. Fritz, and R. W. Spekkens, A mathematical theory of resources, Inf. Comput. 250, 59 (2016)
CrossRef ADS Google scholar
[8]
R. Demkowicz-Dobrzański and L. Maccone, Using entanglement against noise in quantum metrology, Phys. Rev. Lett. 113(25), 250801 (2014)
CrossRef ADS Google scholar
[9]
J. Åberg, Catalytic coherence, Phys. Rev. Lett. 113(15), 150402 (2014)
CrossRef ADS Google scholar
[10]
V. Narasimhachar and G. Gour, Low-temperature thermodynamics with quantum coherence, Nat. Commun. 6(1), 7689 (2015)
CrossRef ADS Google scholar
[11]
P. Ćwikliński, M. Studziński, M. Horodecki, and J. Oppenheim, Limitations on the evolution of quantum coherences: Towards fully quantum second laws of thermodynamics, Phys. Rev. Lett. 115(21), 210403 (2015)
CrossRef ADS Google scholar
[12]
M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6(1), 6383 (2015)
CrossRef ADS Google scholar
[13]
M. Lostaglio, K. Korzekwa, D. Jennings, and T. Rudolph, Quantum coherence, time-translation symmetry, and thermodynamics, Phys. Rev. X 5(2), 021001 (2015)
CrossRef ADS Google scholar
[14]
I. Marvian and R. W. Spekkens, Extending Noether’s theorem by quantifying the asymmetry of quantum states, Nat. Commun. 5(1), 3821 (2014)
CrossRef ADS Google scholar
[15]
F. Levi and F. Mintert, A quantitative theory of coherent delocalization, New J. Phys. 16(3), 033007 (2014)
CrossRef ADS Google scholar
[16]
L. M. Yang, B. Chen, S. M. Fei, and Z. X. Wang, Dynamics of coherence-induced state ordering under Markovian channels, Front. Phys. 13(5), 130310 (2018)
CrossRef ADS Google scholar
[17]
T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113(14), 140401 (2014)
CrossRef ADS Google scholar
[18]
X. D. Yu, D. J. Zhang, G. F. Xu, and D. M. Tong, Alternative framework for quantifying coherence,Phys. Rev. A 94(6), 060302(R) (2016)
[19]
X. Yuan, H. Zhou, Z. Cao, and X. Ma, Intrinsic randomness as a measure of quantum coherence, Phys. Rev. A 92(2), 022124 (2015)
CrossRef ADS Google scholar
[20]
A. Winter and D. Yang, Operational resource theory of coherence, Phys. Rev. Lett. 116(12), 120404 (2016)
CrossRef ADS Google scholar
[21]
Y. Yao, X. Xiao, L. Ge, and C. P. Sun, Quantum coherence in multipartite systems, Phys. Rev. A 92(2), 022112 (2015)
CrossRef ADS Google scholar
[22]
Z. Xi, Y. Li, and H. Fan, Quantum coherence and correlations in quantum system, Sci. Rep. 5(1), 10922 (2015)
CrossRef ADS Google scholar
[23]
J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116(16), 160407 (2016)
CrossRef ADS Google scholar
[24]
C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, and T. Byrnes, Distribution of quantum coherence in multipartite systems, Phys. Rev. Lett. 116(15), 150504 (2016)
CrossRef ADS Google scholar
[25]
T. R. Bromley, M. Cianciaruso, and G. Adesso, Frozen quantum coherence, Phys. Rev. Lett. 114(21), 210401 (2015)
CrossRef ADS Google scholar
[26]
X. D. Yu, D. J. Zhang, C. L. Liu, and D. M. Tong, Measure-independent freezing of quantum coherence, Phys. Rev. A 93(6), 060303 (2016)
CrossRef ADS Google scholar
[27]
E. Chitambar, A. Streltsov, S. Rana, M. N. Bera, G. Adesso, and M. Lewenstein, Assisted distillation of quantum coherence, Phys. Rev. Lett. 116(7), 070402 (2016)
CrossRef ADS Google scholar
[28]
R. A. Horn and C. R. Johnson, Matrix Analysis, Chaps. 2, 5 and 7, New York: Cambridge University Press, 1985
CrossRef ADS Google scholar
[29]
A. Brodutch and K. Modi, Criteria for measures of quantum correlations, Quantum Inf. Comput. 12, 721 (2012)
[30]
W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80(10), 2245 (1998)
CrossRef ADS Google scholar
[31]
P. Rungta, V. Bužek, C. M. Caves, M. Hillery, and G. J. Milburn, Universal state inversion and concurrence in arbitrary dimensions, Phys. Rev. A 64(4), 042315 (2001)
CrossRef ADS Google scholar
[32]
E. Chitambar and M. H. Hsieh, Relating the resource theories of entanglement and quantum coherence, Phys. Rev. Lett. 117(2), 020402 (2016)
CrossRef ADS Google scholar
[33]
A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Measuring quantum coherence with entanglement, Phys. Rev. Lett. 115(2), 020403 (2015)
CrossRef ADS Google scholar
[34]
J. J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116(16), 160407 (2016)
CrossRef ADS Google scholar
[35]
B. Dakić, V. Vedral, and Ç. Brukner, Necessary and sufficient condition for nonzero quantum discord, Phys. Rev. Lett. 105(19), 190502 (2010)
CrossRef ADS Google scholar
[36]
J. H. Huang, L. Wang, and S. Y. Zhu, A new criterion for zero quantum discord,New J. Phys. 13(6), 063045 (2011)
CrossRef ADS Google scholar
[37]
L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80(2), 517 (2008)
CrossRef ADS Google scholar
[38]
R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81(2), 865 (2009)
CrossRef ADS Google scholar
[39]
K. Modi, T. Paterek, W. Son, V. Vedral, and M. Williamson, Unified view of quantum and classical correlations, Phys. Rev. Lett. 104(8), 080501 (2010)
CrossRef ADS Google scholar
[40]
C. C. Rulli and M. S. Sarandy, Global quantum discord in multipartite systems, Phys. Rev. A 84(4), 042109 (2011)
CrossRef ADS Google scholar
[41]
J. Batle, A. Farouk, O. Tarawneh, and S. Abdalla, Multipartite quantum correlations among atoms in QED cavities, Front. Phys. 13(1), 130305 (2018)
CrossRef ADS Google scholar

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