= Entanglement fidelity bound by state fidelity
{title2=$F_e(\rho,\Lambda)\leq F(\rho,\Lambda(\rho))^2$}
In the <unsquared quantum fidelity> convention, the fidelity between a purification and its channel output is the square root of <entanglement fidelity>. Tracing out the purifying reference leaves the input and output marginals. <Monotonicity of quantum fidelity under partial trace> therefore gives the bound. Preserving an input marginal is a weaker requirement than preserving its correlations with a reference.
Back to article page
