物理學院“博約學術論壇”系列報告第34期     (2013年第1期)

題  目：Quantum Discord, CHSH Inequality and Hidden Variables
              --- Critical reassessment of hidden-variables models---
報告人：Professor Kazuo Fujikawa
                Visiting scientist at RIKEN in Japan
時  間：2013年3月1日(星期五)上午10:00
地  點：中心教學樓610

    應物理學院葛墨林院士邀請，K.Fujikawa教授自2013年2月21日開始在北京理工大學物理學院進行為期一個月的訪問和交流。Fujikawa教授是物理學院擬引進的兼職教授，近3年中將每年在北京理工大學進行為期3個月以上的科研和教學工作。

ABSTRACT
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.

簡歷：
1965年畢業(yè)于東京大學理學部物理學系。
1970年在Princeton得到博士學位。
1983年任廣島大學理論物理學研究所教授，然后又在京都大學基礎物理學研究所和東京大學理學部物理學系任教授，2004年4月開始任日本大學教授

聯系方式：物理學院辦公室（68913163）
網    址： http://physics.bit.edu.cn/

(審核：姜艷)