Quantifying quantum correlation via quantum coherence

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

Front. Phys. ›› 2018, Vol. 13 ›› Issue (4) : 130701

PDF (132KB)
Front. Phys. ›› 2018, Vol. 13 ›› Issue (4) : 130701 DOI: 10.1007/s11467-018-0804-0
RESEARCH ARTICLE

Quantifying quantum correlation via quantum coherence

Author information +
History +
PDF (132KB)

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

Cite this article

Download citation ▾
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 DOI:10.1007/s11467-018-0804-0

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

E. Knill and R. Laflamme, Power of one bit of quantum information, Phys. Rev. Lett. 81(25), 5672 (1998)

[2]

A. Datta, A. Shaji, and C. M. Caves, Quantum discord and the power of one qubit, Phys. Rev. Lett. 100(5), 050502 (2008)

[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)

[4]

H. Ollivier and W. H. Zurek, Quantum discord: A measure of the quantumness of correlations, Phys. Rev. Lett. 88(1), 017901 (2001)

[5]

G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: Manipulations and monotones, New J. Phys. 10(3), 033023 (2008)

[6]

F. G. S. L. Brandão and G. Gour, Reversible framework for quantum resource theories, Phys. Rev. Lett. 115(7), 070503 (2015)

[7]

B. Coecke, T. Fritz, and R. W. Spekkens, A mathematical theory of resources, Inf. Comput. 250, 59 (2016)

[8]

R. Demkowicz-Dobrzański and L. Maccone, Using entanglement against noise in quantum metrology, Phys. Rev. Lett. 113(25), 250801 (2014)

[9]

J. Åberg, Catalytic coherence, Phys. Rev. Lett. 113(15), 150402 (2014)

[10]

V. Narasimhachar and G. Gour, Low-temperature thermodynamics with quantum coherence, Nat. Commun. 6(1), 7689 (2015)

[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)

[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)

[13]

M. Lostaglio, K. Korzekwa, D. Jennings, and T. Rudolph, Quantum coherence, time-translation symmetry, and thermodynamics, Phys. Rev. X 5(2), 021001 (2015)

[14]

I. Marvian and R. W. Spekkens, Extending Noether’s theorem by quantifying the asymmetry of quantum states, Nat. Commun. 5(1), 3821 (2014)

[15]

F. Levi and F. Mintert, A quantitative theory of coherent delocalization, New J. Phys. 16(3), 033007 (2014)

[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)

[17]

T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113(14), 140401 (2014)

[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)

[20]

A. Winter and D. Yang, Operational resource theory of coherence, Phys. Rev. Lett. 116(12), 120404 (2016)

[21]

Y. Yao, X. Xiao, L. Ge, and C. P. Sun, Quantum coherence in multipartite systems, Phys. Rev. A 92(2), 022112 (2015)

[22]

Z. Xi, Y. Li, and H. Fan, Quantum coherence and correlations in quantum system, Sci. Rep. 5(1), 10922 (2015)

[23]

J. Ma, B. Yadin, D. Girolami, V. Vedral, and M. Gu, Converting coherence to quantum correlations, Phys. Rev. Lett. 116(16), 160407 (2016)

[24]

C. Radhakrishnan, M. Parthasarathy, S. Jambulingam, and T. Byrnes, Distribution of quantum coherence in multipartite systems, Phys. Rev. Lett. 116(15), 150504 (2016)

[25]

T. R. Bromley, M. Cianciaruso, and G. Adesso, Frozen quantum coherence, Phys. Rev. Lett. 114(21), 210401 (2015)

[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)

[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)

[28]

R. A. Horn and C. R. Johnson, Matrix Analysis, Chaps. 2, 5 and 7, New York: Cambridge University Press, 1985

[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)

[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)

[32]

E. Chitambar and M. H. Hsieh, Relating the resource theories of entanglement and quantum coherence, Phys. Rev. Lett. 117(2), 020402 (2016)

[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)

[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)

[35]

B. Dakić, V. Vedral, and Ç. Brukner, Necessary and sufficient condition for nonzero quantum discord, Phys. Rev. Lett. 105(19), 190502 (2010)

[36]

J. H. Huang, L. Wang, and S. Y. Zhu, A new criterion for zero quantum discord,New J. Phys. 13(6), 063045 (2011)

[37]

L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80(2), 517 (2008)

[38]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81(2), 865 (2009)

[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)

[40]

C. C. Rulli and M. S. Sarandy, Global quantum discord in multipartite systems, Phys. Rev. A 84(4), 042109 (2011)

[41]

J. Batle, A. Farouk, O. Tarawneh, and S. Abdalla, Multipartite quantum correlations among atoms in QED cavities, Front. Phys. 13(1), 130305 (2018)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

AI Summary AI Mindmap
PDF (132KB)

946

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/