MaximumOutputFidelity

MaximumOutputFidelity is a function that computes the maximum output fidelity between two quantum channels $\Phi$ and $\Psi$, defined as follows:
 * $$F_{max}(\Phi,\Psi) := \max_{\rho,\sigma}\big\{F(\Phi(\rho),\Psi(\sigma)) : \rho,\sigma \text{ are density matrices}\big\},$$

where $F(\cdot,\cdot)$ is the usual fidelity between quantum states.

Syntax

 * MOF = MaximumOutputFidelity(PHI,PSI)
 * MOF = MaximumOutputFidelity(PHI,PSI,DIM_PHI)
 * MOF = MaximumOutputFidelity(PHI,PSI,DIM_PHI,DIM_PSI)

Argument descriptions

 * PHI,PSI: Quantum channels, represented as either Choi matrices or cells of Kraus operators.
 * DIM_PHI,DIM_PSI (optional): 1-by-2 vectors containing the input and output dimensions of PHI and PSI, respectively. These arguments must be provided if and only if PHI</tt> and PSI</tt> are provided as Choi matrices and they have unequal input and output dimensions.

Examples
The following code computes the minimum output fidelity of a random qutrit channel $\Psi$ with the identity channel: