MaximumOutputFidelity

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.