Quantum Correlation Coherence Uncertainty ShaoMing Fei 29 June

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

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

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 Quantum channel Kraus operators

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

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

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

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

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. 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