# DepolarizingChannel

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 Other toolboxes required DepolarizingChannel Produces a depolarizing channel none DephasingChannel 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