# DephasingChannel

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 Other toolboxes required DephasingChannel Produces a dephasing channel none DepolarizingChannel 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