通过非广延熵对定域实在论 Peres 判据的推广
量子物理
2007-05-23 v1
摘要
已知一个二粒子自旋-1/2 系统处于 Einstein-Podolsky-Rosen 纠缠态 ∣ Ψ − ⟩ ≡ 1 2 ( ∣ ↑ ⟩ A ∣ ↓ ⟩ B − ∣ ↓ ⟩ A ∣ ↑ ⟩ B ) |\Psi^-\rangle \equiv \frac{1}{\sqrt 2}(|\uparrow\rangle_A|\downarrow\rangle_B - |\downarrow\rangle_A|\uparrow\rangle_B) ∣ Ψ − ⟩ ≡ 2 1 ( ∣ ↑ ⟩ A ∣ ↓ ⟩ B − ∣ ↓ ⟩ A ∣ ↑ ⟩ B ) 1 + 3 x 4 \frac{1+3x}{4} 4 1 + 3 x 3 ( 1 − x ) 4 \frac{3(1-x)}{4} 4 3 ( 1 − x ) x < 1 / 3 x<1/3 x < 1/3 ∣ Φ ± ⟩ ≡ 1 2 ( ∣ ↑ ⟩ A ∣ ↑ ⟩ B ± ∣ ↓ ⟩ A ∣ ↓ ⟩ B ) |\Phi^{\pm}\rangle \equiv \frac{1}{\sqrt 2}(|\uparrow\rangle_A|\uparrow\rangle_B \pm |\downarrow\rangle_A|\downarrow\rangle_B) ∣ Φ ± ⟩ ≡ 2 1 ( ∣ ↑ ⟩ A ∣ ↑ ⟩ B ± ∣ ↓ ⟩ A ∣ ↓ ⟩ B ) ∣ Ψ ± ⟩ ≡ 1 2 ( ∣ ↑ ⟩ A ∣ ↓ ⟩ B ± ∣ ↓ ⟩ A ∣ ↑ ⟩ B ) |\Psi^{\pm}\rangle \equiv \frac{1}{\sqrt 2}(|\uparrow\rangle_A|\downarrow\rangle_B \pm |\downarrow\rangle_A|\uparrow\rangle_B) ∣ Ψ ± ⟩ ≡ 2 1 ( ∣ ↑ ⟩ A ∣ ↓ ⟩ B ± ∣ ↓ ⟩ A ∣ ↑ ⟩ B ) 1 − x 4 \frac{1-x}{4} 4 1 − x 1 − y 4 \frac{1-y}{4} 4 1 − y 1 − z 4 \frac{1-z}{4} 4 1 − z 1 + x + y + z 4 \frac{1+x+y+z}{4} 4 1 + x + y + z S q ≡ 1 − T r ρ q q − 1 ( q ∈ R ; S 1 = − T r ρ ln ρ ) S_q \equiv \frac{1- Tr \rho^q}{q-1} (q \in \cal{R}; S_1 = - Tr \rho \ln \rho) S q ≡ q − 1 1 − T r ρ q ( q ∈ R ; S 1 = − T r ρ ln ρ ) ( x , y , z ) (x,y,z) ( x , y , z ) x + y + z < 1 x+y+z<1 x + y + z < 1 x = y = z x=y=z x = y = z
引用
@article{arxiv.quant-ph/0007112,
title = {Generalization of the Peres criterion for local realism through nonextensive entropy},
author = {Constantino Tsallis and Seth Lloyd and Michel Baranger},
journal= {arXiv preprint arXiv:quant-ph/0007112},
year = {2007}
}
备注
Figures 1a, 1b, 2 and 3