Conditional environment overlap
= Conditional environment overlap
{title2=$z=\langle E_1|E_0\rangle$}
For a pure state $a|0\rangle|E_0\rangle+b|1\rangle|E_1\rangle$ with normalized environment states, the upper-right device <reduced density matrix> entry is $ab^*\langle E_1|E_0\rangle$. Distinguishability of the conditional environment states suppresses device coherence. States differing only by a global phase have unit-modulus overlap and do not cause <quantum decoherence>.