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
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