# MaximumOutputFidelity

 Other toolboxes required MaximumOutputFidelity Computes the maximum output fidelity of two quantum channels CVX DiamondNormFidelity Norms and distance measures no

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 and PSI 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:

>> d = 3;
>> Phi = {eye(d)};
>> Psi = RandomSuperoperator(d);
>> MaximumOutputFidelity(Phi,Psi)

ans =

0.7638