Nathaniel: Created page with "{{Function |name=DephasingChannel |desc=Produces a dephasing channel |rel=DepolarizingChannel |cat=Superoperators |upd=January 22, 201..."

2015-01-22T17:36:29Z

Created page with "{{Function |name=DephasingChannel |desc=Produces a dephasing channel |rel=DepolarizingChannel |cat=Superoperators |upd=January 22, 201..."

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{{Function
|name=DephasingChannel
|desc=Produces a dephasing channel
|rel=[[DepolarizingChannel]]
|cat=[[List of functions#Superoperators|Superoperators]]
|upd=January 22, 2015}}
<tt>'''DephasingChannel'''</tt> is a [[List of functions|function]] that returns the Choi matrix of the partially dephasing channel, which acts as follows:

: <math>\Delta(X) := (1-p)\mathrm{diag}(X) + pX,</math>

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==
* <tt>DELTA = DephasingChannel(DIM)</tt>
* <tt>DELTA = DephasingChannel(DIM,P)</tt>

==Argument descriptions==
* <tt>DIM</tt>: The dimension of the channel. That is, the channel will act on <tt>DIM</tt>-by-<tt>DIM</tt> matrices.
* <tt>P</tt> (optional, default 0): A parameter (from 0 to 1, inclusive) that specifies which partially dephasing channel to produce. <tt>P = 0</tt> gives the completely dephasing channel, and <tt>P = 1</tt> gives the identity channel.

==Examples==
===The completely dephasing channel===
The completely dephasing channel maps every density matrix to its diagonal:
<syntaxhighlight>
>> 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
</syntaxhighlight>

{{SourceCode|name=DephasingChannel}}

DephasingChannel - Revision history

Nathaniel: Created page with "{{Function |name=DephasingChannel |desc=Produces a dephasing channel |rel=DepolarizingChannel |cat=Superoperators |upd=January 22, 201..."