MaximumOutputFidelity

	MaximumOutputFidelity
	Computes the maximum output fidelity of two quantum channels
Other toolboxes required	none
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:

<math>F_{max}(\Phi,\Psi) := \max_{\rho,\sigma}\big\{F(\Phi(\rho),\Psi(\sigma)) : \rho,\sigma \text{ are density matrices}\big\},</math>

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

Syntax

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.

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

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