DephasingChannel

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</tt> gives the identity channel.

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