Quantum Correlation, Coherence & Uncertainty

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Presentation transcript:

Quantum Correlation, Coherence & Uncertainty Shao-Ming Fei(费少明) 第九届海峡两岸粒子物理与宇宙学研讨会 29 June to 2 July 2019 1

Superposition principle quantum mechanics Quantum coherence Uncertainty relations Quantum correlations discord, entanglement steerability, nonlocality

黑洞:探测量子引力的窗口! 黑洞熵:面积律 霍金辐射:黑体辐射 信息丢失?

引力的全息性 全息原理:量子引力基本原理 纠缠熵也许是理解引力全息性的关键 (’t Hooft, 1993,L.Susskind,1994) 在一个引力系统中,区域V中的最大熵正比于V的边界面积(Plack单位),而非体积 纠缠熵也许是理解引力全息性的关键

Quantum state Quantum measurement

Quantum states Pure state: vector Mixed state: density matrix Density matrix: Hermitian, Semipositive

Quantum measurement Observable self-adjoint operator Observable O : real eigenvalues eigenvectors probability von Neumann measurement POVM (Positive operator-valued measure) Two or more POVMs: Jointly measurability

Evolution Kraus operators Quantum channel

Quantum coherence Incoherent states Measures of coherence - norm coherence von Neumann entropy Relative entropy of coherence

Robustness of coherence Phys. Rev. Lett. 116, 150502 (2016) Phase discrimination W.Q. Zheng, Z.H. Ma, H.Y. Wang, S.M. Fei, X.H. Peng, Phys. Rev. Lett. 120 (2018) 230504 NMR

Max- relative entropy of coherence : an operational coherence measure Subchannel discrmination K.F. Bu, U. Singh, S.M. Fei, A.K. Pati, J.D. Wu, Phys. Rev. Lett. 119 (2017) 150405

Coherence from Hellinger distance Z.X. Jin, S.M. Fei, Phys. Rev. A 97 (2018) 062342 Z.H. Ma, J. Cui, Z. Cao, S.M. Fei, V. Vedral, T. Byrnes, C. Radhakrishnan, Operational advantage of basis-independent quantum coherence, Euro. Phys. Lett. 125 (2019) 50005

Quantum Coherence and Energy Flow Coherence among non-degenerate energy subspaces (CANES) T. Ma, M.J. Zhao, S.M. Fei, M.H. Yung, Phys. Rev. A 99 (2019) 062303

Quantum correlations Quantum Entanglement Density matrix: Separable! S.Q. Shen, T.R. Xu, S.M. Fei, X. Li-Jost, M. Li, Phys. Rev. A 97 (2018) 032343 M. Li, Z. Wang, J. Wang, S.Q. Shen, S.M. Fei, Euro. Phys. Lett. 129 (2019) 20006

Super-activation of monogamy relations A B C Z.X. Jin, S.M. Fei, Phys. Rev. A 99 (2019) 032343

Operational one-to-one mapping between coherence and entanglement Z.X. Xiong, M.S. Li, Z.J. Zheng, C.J. Zhu, S.M. Fei, Positive-partial-transpose distinguishability for lattice-type maximally entangled states, Phys. Rev. A 99 (2019) 032346 Operational one-to-one mapping between coherence and entanglement H.J. Zhu, Z.H. Ma, Z. Cao, S.M. Fei, V. Vedral, Phys. Rev. A 96 (2017) 032316

Quantum information masking: B. Li, S.H Jiang, X.B. Liang, X. Li-Jost, H. Fan, S.M. Fei, Phys. Rev. A 99 (2019) 052343

Uncertainty Relations(product form) H. P. Robertson, Phys. Rev. 34, 163 (1929) Uncertainty relations based on Shannon entropy Z.H. Chen, Z.H. Ma, Y.L. Xiao, S.M. Fei, Phys. Rev. A 98 (2018) 042305

Heisenberg’s measurement uncertainty relation based on statistical distances W.C. Ma, Z.H. Ma, H.Y. Wang, Y. Liu, Z.H. Chen, F. Kong, Z.K. Li, M.J. Shi, F.Z. Shi, S.M. Fei, J.F. Du, Phys. Rev. Lett. 116 (2016) 160405

Uncertainties of genuinely incompatible triple measurements H.H. Qin, T.G. Zhang, L. Jost, C.P. Sun, X. Li-Jost, S.M. Fei, Phys. Rev. A 99 (2019) 032107

Error-Disturbance Trade-off in Sequential Quantum Measurements a complete set of projective measurements on the meter state

Error and disturbance M. Ozawa, Phys. Rev. A 67, 042105 (2003); Ann. Phys. 311, 350 (2004); Phys. Lett. A 320, 367 (2004).

Y. L. Mao, Z. H. Ma, R. B. Jin, Q. C. Sun, S. M. Fei, Q. Zhang, J Y.L. Mao, Z.H. Ma, R.B. Jin, Q.C. Sun, S.M. Fei, Q. Zhang, J. Fan, J.W. Pan, Phys. Rev. Lett. 122 (2019) 090404

Uncertainty Equality with Quantum Memory Conditional linear entropy Mutually unbiased bases (MUB)

A complete set of d + 1 MUBs H. Wang, Z. Ma, S. Wu, W. Zheng, Z. Cao, Z. Chen, Z. Li, S.M. Fei, X. Peng, J. Du, V. Vedral, NPJ Quant. Inform. 5 (2019) 39

Thanks!