# DephasingChannel

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DephasingChannel | |

Produces a dephasing channel | |

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

Related functions | DepolarizingChannel |

Function category | Superoperators |

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

\[\Delta(X) := (1-p)\mathrm{diag}(X) + pX,\]

where $\mathrm{diag}$ is the map that erases everything off the diagonal of its input, and $0 \leq p \leq 1$ is a given parameter ($p = 0$ by default).

## Syntax

`DELTA = DephasingChannel(DIM)``DELTA = DephasingChannel(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 dephasing channel to produce.`P = 0`gives the completely dephasing channel, and`P = 1`gives the identity channel.

## Examples

### The completely dephasing channel

The completely dephasing channel maps every density matrix to its diagonal:

```
>> rho = RandomDensityMatrix(3)
rho =
0.2575 -0.1464 + 0.0460i 0.0869 - 0.1260i
-0.1464 - 0.0460i 0.5016 -0.0074 + 0.1864i
0.0869 + 0.1260i -0.0074 - 0.1864i 0.2409
>> ApplyMap(rho,DephasingChannel(3))
ans =
0.2575 0 0
0 0.5016 0
0 0 0.2409
```

## Source code

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