best365平台“博约学术论坛”系列报告 第78期 (2016年第5期)

Title：Separability criteria with angular and Hilbert space averages

报告人：Kazuo Fujikawa（日本理化所）

时   间：5月31日（周二）上午10:00

地   点：中心教学楼612

ABSTRACT
The practically useful criteria of separable states ρ =Σk wkρk in d = 2 × 2 are discussed. The

equality G(a, b) = 4[⟨ψ|P(a)⊗P(b)|ψ⟩−⟨ψ|P(a)⊗1|ψ⟩⟨ψ|1⊗P(b)|ψ⟩] = 0 for any two projection

operators P(a) and P(b) provides a necessary and sufficient separability criterion in the case of a

separable pure state ρ = |ψ⟩⟨ψ|. We propose the separability criteria of mixed states, which aregiven by Trρ{a σ ⊗ b σ} = (1/3)C cos φ for two spin 1/2 systems and 4Trρ{P(a) ⊗ P(b)} =1+(1/2)C cos 2φ for two photon systems, respectively, after taking a geometrical angular average of a and b with fixed cos φ = a b. Here −1 ≤ C ≤ 1, and the difference in the numerical coefficients 1/2 and 1/3 arises from the different rotational properties of the spinor and the transverse photon.If one instead takes an average over the states in the d = 2 Hilbert space, the criterion for two photon systems is replaced by 4Trρ{P(a)⊗P(b)} = 1+(1/3)C cos 2φ. Those separability criteria are shown to be very efficient using the existing experimental data of Aspect et al. in 1981 and Sakai et al. in 2006. When the Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average.

Curriculum Vitae

Fujikawa教授原东京大学教授，现为日本理化所兼职教授，发表SCI论文140余篇，出版专著1部（K. Fujikawa and H. Suzuki, Path Integrals and Quantum Anomalides, (Oxford University Press, 2004).），是国际著名学者，排行为日本理论物理学界前几名，是亚太理论物理中心科学委员会委员。Fujikawa于1965年毕业于东京大学理学部物理学系，1970年在Princeton获得博士学位。多年从事量子物理研究，在量子场论和高精度测量的精确计算上有重要成果。近年来，在测不准关系和非绝热量子现象中有很好的成果。

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