A hidden-variables version of Gisin’s theorem...A hidden-variables version of Gisin’s theorem...
Transcript of A hidden-variables version of Gisin’s theorem...A hidden-variables version of Gisin’s theorem...
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A hidden-variables version of Gisin’s theorem
Koichiro Umetsu (Nihon University)
K. Fujikawa and K. Umetsu, arXiv: 1410.1702 [quant-ph]
Based on
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in collaboration with Kazuo Fujikawa (RIKEN)
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Introduction
ベルの不等式:
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局所実在論と量子力学を明確に区別するcriterion
局所実在論 (local realism) :
文脈依存性のない局所的な隠れた変数理論によって記述
(Non-contextual and local hidden variables models )
局所実在論の予言(CHSH inequality):
量子力学はCHSH inequality の破れを予言する:
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CHSH inequality and Aspect’s experiment
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Aspect et.al., PRL (1982)
この対決の最終的な決着は1982年のAspect et.al. の実験において, この量が2を超えることがあることが実証された.
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Gisin’s Theorem Gisin’s Theorem の対偶:
全ての に対して常にCHSH 不等式が成立するならば,その状態は separable state である.
Gisin, PLA (1991)
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※ CHSH 不等式と量子状態の関係を理解する上で,非常に意義深い.
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A hidden-variables version of Gisin’s Theorem
A hidden-variables version of Gisin’s Theorem
Non-contextual and local hidden variables models の範囲内で満たされる等式.
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この等式の証明は次の要請に基づく(詳細は時間の制限により省略):
d=4 でも成立することを要請
Bell, Rev. Mod. Phys. (1966)
The known concrete hidden-variables models in d=2 satisfy the relation:
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Numerical Test Gisin’s example:
• 測定器の設定:
• 波動関数の設定:
( )
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局所実在論の予言:
• Hidden-variables version of Gisin’s theorem:
• CHSH inequality:
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Results
Case A:
Case B:
Case C:
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Aspect’s Experiment
Notations 1:
• S: 光源 (光子対を放出)
• , : 偏光板 ( は調節可能なパラメータ )
• 同時検出が観測される.
• PM: Photomultiplier
(光子が飛んで来れば+1, 飛んで来なければ -1 の値を取る.)
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Freedman et.al. PRL (1972), Aspect et.al., PRL (1981)
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Hidden-variable version of Gisin’s theorem
9 この実験結果は局所実在論の予言を明確に破る.
Aspect’s experimental values
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CHSH inequality
A. Aspect, et.al., PRL (1981) CHSH inequality
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CHSH inequality
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Summary • Hidden-variables version of Gisin’s theorem を定式化:
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• CHSH inequality と比べ,Hidden-variables version of Gisin’s theorem は量子力学と隠れた変数理論を区別できる領域が広い.
• 実験を行う立場からも,扱うパラメータが少ないため実験の手間は 軽減される.
• このHidden-variables version of Gisin’s theorem はCHSH inequality に代わる量子力学と局所実在論を区別する新しいcriterionになる かもしれない.
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CHSH inequality and Aspect’s experiment
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Aspect et.al., PRL (1982)
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Hidden-variables version of Gisin’s theorem and Aspect’s experiment
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Freedman et.al. PRL (1972), Aspect et.al., PRL (1981)