Quantifying quantum correlation via quantum coherence
Guang-Yong Zhou, Lin-Jian Huang, Jun-Ya Pan, Li-Yun Hu, Jie-Hui Huang
Quantifying quantum correlation via quantum coherence
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.
resource theory / quantum correlation / quantum coherence
[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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