Processing math: 100%

Detecting entanglement of quantum channels

Chaojian Li,Bang-Hai Wang,Bujiao Wu,Xiao Yuan

Table 1. Quantum game with

${W}_{\mathrm{CNOT},1}$ for the noisy CNOT gate.

α	${\rho }_{A}^{{\rm{T}}}$	${\rho }_{B}^{{\rm{T}}}$	${O}_{A^{\prime} }$	${O}_{B^{\prime} }$	α	${\rho }_{A}^{{\rm{T}}}$	${\rho }_{B}^{{\rm{T}}}$	${O}_{A^{\prime} }$	${O}_{B^{\prime} }$
1	${\mathbb{I}}$	${\mathbb{I}}$	${\mathbb{I}}$	${\mathbb{I}}$	1	${\mathbb{I}}$	${\sigma }_{x}$	${\mathbb{I}}$	${\sigma }_{x}$
1	${\mathbb{I}}$	${\sigma }_{y}$	${\sigma }_{z}$	${\sigma }_{y}$	−1	${\mathbb{I}}$	${\sigma }_{z}$	${\sigma }_{z}$	${\sigma }_{z}$
−1	${\sigma }_{x}$	${\sigma }_{x}$	${\sigma }_{x}$	${\mathbb{I}}$	−1	${\sigma }_{x}$	${\mathbb{I}}$	${\sigma }_{x}$	${\sigma }_{x}$
1	${\sigma }_{x}$	${\sigma }_{z}$	${\sigma }_{y}$	${\sigma }_{y}$	1	${\sigma }_{x}$	${\sigma }_{y}$	${\sigma }_{y}$	${\sigma }_{z}$
1	${\sigma }_{y}$	${\sigma }_{z}$	${\sigma }_{x}$	${\sigma }_{y}$	1	${\sigma }_{y}$	${\sigma }_{y}$	${\sigma }_{x}$	${\sigma }_{z}$
1	${\sigma }_{y}$	${\sigma }_{x}$	${\sigma }_{y}$	${\mathbb{I}}$	1	${\sigma }_{y}$	${\mathbb{I}}$	${\sigma }_{y}$	${\sigma }_{x}$
1	${\sigma }_{z}$	${\sigma }_{y}$	${\mathbb{I}}$	${\sigma }_{y}$	−1	${\sigma }_{z}$	${\sigma }_{z}$	${\mathbb{I}}$	${\sigma }_{z}$
1	${\sigma }_{z}$	${\mathbb{I}}$	${\sigma }_{z}$	${\mathbb{I}}$	1	${\sigma }_{z}$	${\sigma }_{x}$	${\sigma }_{z}$	${\sigma }_{x}$