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.
B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, Experimental quantum computing without entanglement, Phys. Rev. Lett. 101(20), 200501 (2008) https://doi.org/10.1103/PhysRevLett.101.200501
G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: Manipulations and monotones, New J. Phys. 10(3), 033023 (2008) https://doi.org/10.1088/1367-2630/10/3/033023
R. Demkowicz-Dobrzański and L. Maccone, Using entanglement against noise in quantum metrology, Phys. Rev. Lett. 113(25), 250801 (2014) https://doi.org/10.1103/PhysRevLett.113.250801
V. Narasimhachar and G. Gour, Low-temperature thermodynamics with quantum coherence, Nat. Commun. 6(1), 7689 (2015) https://doi.org/10.1038/ncomms8689
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) https://doi.org/10.1103/PhysRevLett.115.210403
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) https://doi.org/10.1038/ncomms7383
13
M. Lostaglio, K. Korzekwa, D. Jennings, and T. Rudolph, Quantum coherence, time-translation symmetry, and thermodynamics, Phys. Rev. X 5(2), 021001 (2015) https://doi.org/10.1103/PhysRevX.5.021001
14
I. Marvian and R. W. Spekkens, Extending Noether’s theorem by quantifying the asymmetry of quantum states, Nat. Commun. 5(1), 3821 (2014) https://doi.org/10.1038/ncomms4821
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) https://doi.org/10.1007/s11467-018-0780-4
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) https://doi.org/10.1103/PhysRevA.92.022124
Z. Xi, Y. Li, and H. Fan, Quantum coherence and correlations in quantum system, Sci. Rep. 5(1), 10922 (2015) https://doi.org/10.1038/srep10922
23
J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116(16), 160407 (2016) https://doi.org/10.1103/PhysRevLett.116.160407
24
C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, and T. Byrnes, Distribution of quantum coherence in multipartite systems, Phys. Rev. Lett. 116(15), 150504 (2016) https://doi.org/10.1103/PhysRevLett.116.150504
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) https://doi.org/10.1103/PhysRevA.93.060303
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) https://doi.org/10.1103/PhysRevLett.116.070402
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) https://doi.org/10.1103/PhysRevA.64.042315
32
E. Chitambar and M. H. Hsieh, Relating the resource theories of entanglement and quantum coherence, Phys. Rev. Lett. 117(2), 020402 (2016) https://doi.org/10.1103/PhysRevLett.117.020402
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) https://doi.org/10.1103/PhysRevLett.115.020403
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) https://doi.org/10.1103/PhysRevLett.116.160407
35
B. Dakić, V. Vedral, and Ç. Brukner, Necessary and sufficient condition for nonzero quantum discord, Phys. Rev. Lett. 105(19), 190502 (2010) https://doi.org/10.1103/PhysRevLett.105.190502
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) https://doi.org/10.1103/PhysRevLett.104.080501
J. Batle, A. Farouk, O. Tarawneh, and S. Abdalla, Multipartite quantum correlations among atoms in QED cavities, Front. Phys. 13(1), 130305 (2018) https://doi.org/10.1007/s11467-017-0711-9