# DepolarizingChannel

Jump to navigation
Jump to search

DepolarizingChannel | |

Produces a depolarizing channel | |

Other toolboxes required | none |
---|---|

Related functions | DephasingChannel |

Function category | Superoperators |

` DepolarizingChannel` is a function that returns the Choi matrix of the partially depolarizing channel, which acts as follows:

\[\Delta(X) := (1-p)\mathrm{Tr}(X)\frac{I}{d^2} + pX,\]

where $I$ is the identity matrix, $d$ is the local dimension, and $0 \leq p \leq 1$ is a given parameter ($p = 0$ by default).

## Syntax

`DELTA = DepolarizingChannel(DIM)``DELTA = DepolarizingChannel(DIM,P)`

## Argument descriptions

`DIM`: The dimension of the channel. That is, the channel will act on`DIM`-by-`DIM`matrices.`P`(optional, default 0): A parameter (from 0 to 1, inclusive) that specifies which partially depolarizing channel to produce.`P = 0`gives the completely depolarizing channel, and`P = 1`gives the identity channel.

## Examples

### The completely depolarizing channel

The completely depolarizing channel maps every density matrix to the maximally-mixed state:

```
>> ApplyMap(RandomDensityMatrix(3),DepolarizingChannel(3))
ans =
0.3333 0 0
0 0.3333 0
0 0 0.3333
```

## Source code

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