1. 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

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

5. 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？

6. 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

7. Quantum state
Quantum measurement

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

9. 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

10. Evolution
Kraus operators
Quantum channel

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

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

13. 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)

14. Coherence from Hellinger distance
Z.X. Jin, S.M. Fei, Phys. Rev. A 97 (2018)
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 (2019) 50005

15. 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)

16. 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)
M. Li, Z. Wang, J. Wang, S.Q. Shen, S.M. Fei,
Euro. Phys. Lett. 129 (2019) 20006

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

18. 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)
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)

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

20. 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)

21. 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)

22. 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)

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

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

25. 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)

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

27. 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

30. Thanks！