# MaximumOutputFidelity

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MaximumOutputFidelity | |

Computes the maximum output fidelity of two quantum channels | |

Other toolboxes required | CVX |
---|---|

Related functions | DiamondNorm Fidelity |

Function category | Norms and distance measures |

Usable within CVX? | 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
```

## Source code

Click here to view this function's source code on github.