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物理学院“博约学术论坛”系列报告第34期

发布日期:2013年02月27日

题 目:Quantum Discord, CHSH Inequality and Hidden Variables
               --- Critical reassessment of hidden-variables models---

报告人:Professor Kazuo Fujikawa
                 Visiting scientist at RIKEN in Japan

时 间:2013年3月1日(星期五)上午10:00

地 点:中心教学楼610

应物理学院葛墨林院士邀请,K.Fujikawa教授自2013年2月21日开始在新葡萄京娱乐场8455进行为期一个月的访问和交流。Fujikawa教授是物理学院的兼职教授,近3年中将每年在新葡萄京娱乐场8455进行为期3个月以上的科研和教学工作。

ABSCTRACT:
The notion of quantum discord is expected to carry information characteristic to quantum mechanics. It is then interesting to examine it in the context of the hidden-variable models such as the ones due to Bell and Kochen-Specker in the Hilbert space with dimensions d=2. We may then be able to distinguish the quantum mechanical aspects and classical deterministic aspects of quantum discord. To perform this analysis, it turns out to be essential to define the conditional measurement. Surprisingly, the known d=2 hidden-variable models such as the ones by Bell and Kochen-Specker, which have been believed to be consistent so far,   are in fact inconsistent and excluded by this analysis. No consistent non-contextual hidden-variable model exists even in d=2if one requires the uniqueness of the dispersion-free representation in hidden variable space, and thus no non-contextual hidden variable models in any dimensions.
 
Somewhat related to this property, it is shown that the well-known prediction of CHSH inequality |B|≦2, for the CHSH operator B introduced by Cirel’son, is not unique. This non-uniqueness arises from the failure of linearity condition of quantum mechanics in the non-contextual hidden-variable model in d=4 used by Bell and CHSH, in agreement with Gleason’s theorem which excludes d=4 non-contextual hidden-variable models. If one imposes the linearity condition, their model is converted to a factored product of two d=2 models which describes quantum mechanical separable states but does not give a non-contextual d=4 model. The experimental refutation of CHSH inequality is thus interpreted that the full contents of quantum mechanics even for a far-apart system cannot be described by separable quantum mechanical states only. But the non-contextual hidden-variable model in d=4 used by them to derive the inequality is inconsistent and does not exist. This observation is consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to hidden variables.

简历:
 1965年毕业于东京大学理学部物理学系。
 1970年在Princeton得到博士学位。
 1983年任广岛大学理论物理学研究所教授,然后又在京都大学基础物理学研究所和东京大学理学部物理学系任教授,2004年4月开始任日本大学教授。

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