# 環境誘導超選擇

## 定義

1. 環境誘導退相干（退相干）：系統內的量子相干性會被表觀地與有效地消滅殆盡，也就是說，無法觀測到量子態疊加效應等等量子現象。
2. 超選擇：對於每一種觀測設置，環境會對系統選擇出一組耐久不變的優化態；這樣，可以按照量子動力學理論定義出系統的可觀測到的物理量。

## 概述

${\displaystyle |\psi _{1}\rangle |E_{0}\rangle \to |\psi _{1}\rangle |E_{1}\rangle }$
${\displaystyle |\psi _{2}\rangle |E_{0}\rangle \to |\psi _{2}\rangle |E_{2}\rangle }$

${\displaystyle |\psi _{+}\rangle ={\frac {1}{\sqrt {2}}}(|\psi _{1}\rangle +|\psi _{2}\rangle )}$
${\displaystyle |\psi _{-}\rangle ={\frac {1}{\sqrt {2}}}(|\psi _{1}\rangle -|\psi _{2}\rangle )}$

${\displaystyle |\psi _{\pm }\rangle |E_{0}\rangle \to {\frac {1}{\sqrt {2}}}(|\psi _{1}\rangle |E_{1}\rangle \pm |\psi _{2}\rangle |E_{2}\rangle )}$

${\displaystyle |\psi _{\pm }\rangle ={\frac {1}{\sqrt {2}}}(|\psi _{1}\rangle \pm |\psi _{2}\rangle )|E_{1}\rangle }$

${\displaystyle |\alpha \rangle ={\frac {1}{\sqrt {2}}}(\alpha _{+}|\psi _{+}\rangle +\alpha _{-}|\psi _{-}\rangle )}$

{\displaystyle {\begin{aligned}|\alpha \rangle |E_{0}\rangle &={\frac {1}{\sqrt {2}}}(\alpha _{+}|\psi _{+}\rangle |E_{0}\rangle +\alpha _{-}|\psi _{-}\rangle |E_{0}\rangle )\\&\to {\frac {1}{2}}[(\alpha _{+}+\alpha _{-})|\psi _{1}\rangle |E_{1}\rangle +(\alpha _{+}-\alpha _{-})|\psi _{2}\rangle |E_{2}\rangle ]\\\end{aligned}}}

## 範例

${\displaystyle |\psi _{1}\rangle |D_{0}\rangle \to |\psi _{1}\rangle |D_{1}\rangle }$
${\displaystyle |\psi _{2}\rangle |D_{0}\rangle \to |\psi _{2}\rangle |D_{2}\rangle }$

${\displaystyle |\psi _{+}\rangle ={\frac {1}{\sqrt {2}}}(|\psi _{1}\rangle +|\psi _{2}\rangle )}$

${\displaystyle |\psi _{+}\rangle |D_{0}\rangle \to {\frac {1}{\sqrt {2}}}(|\psi _{1}\rangle |D_{1}\rangle +|\psi _{2}\rangle |D_{2}\rangle )}$

## 參考文獻

1. Maximilian A. Schlosshauer. Decoherence And the Quantum-To-Classical Transition. Springer Science & Business Media. 1 January 2007. ISBN 978-3-540-35773-5.
2. Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 2003, 75, 715