# Difference between revisions of "ChannelDistinguishability"

 Other toolboxes required ChannelDistinguishability Computes the maximum probability of distinguishing two quantum channels CVX DistinguishabilityLocalDistinguishability Distinguishing objects

ChannelDistinguishability is a function that computes the maximum probability of distinguishing two quantum channels. That is, this function computes the maximum probability of winning the following game: You are given a complete description of two quantum channels \$\Phi\$ and \$\Psi\$, and then are given one of those two channels, and asked to determine which channel was given to you (by supplying some input state to the channel and then measuring the output).

## Syntax

• DIST = ChannelDistinguishability(PHI,PSI)
• DIST = ChannelDistinguishability(PHI,PSI,P)
• DIST = ChannelDistinguishability(PHI,PSI,P,DIM)

## Argument descriptions

• PHI,PSI: The quantum channels to be distinguished. They can either be input as Choi matrices or as cells of Kraus operators.
• P (optional, default [1/2, 1/2]): A vector that specifies that PHI and PSI are chosen with probability P(1) and P(2), respectively.
• DIM (optional, by default tries to guess the input and output dimensions): A 1-by-2 vector containing the input and output dimensions of PHI and PSI. DIM is required if and only if both PHI and PSI are provided as Choi matrices and the input and output dimensions are different.

## Examples

### Perfectly distinguishable channels

The following code demonstrates that the simple example of two channels that can be perfectly distinguished from  can indeed be perfectly distinguished:

```>> n = 4;
>> Phi = SymmetricProjection(n)*2/(n+1);
>> Psi = AntisymmetricProjection(n)*2/(n-1);
>> ChannelDistinguishability(Phi,Psi)

ans =

1.0000```

## Source code

Click on "expand" to the right to view the MATLAB source code for this function.