DepolarizingChannel: Difference between revisions

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Created page with "{{Function |name=DepolarizingChannel |desc=Produces a depolarizing channel |cat=Superoperators |upd=March 4, 2014 |v=0.50}} <tt>'''Depolar..."
 
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|name=DepolarizingChannel
|name=DepolarizingChannel
|desc=Produces a depolarizing channel
|desc=Produces a depolarizing channel
|rel=[[DephasingChannel]]
|cat=[[List of functions#Superoperators|Superoperators]]
|cat=[[List of functions#Superoperators|Superoperators]]
|upd=March 4, 2014
|upd=March 4, 2014}}
|v=0.50}}
<tt>'''DepolarizingChannel'''</tt> is a [[List of functions|function]] that returns the Choi matrix of the partially depolarizing channel, which acts as follows:
<tt>'''DepolarizingChannel'''</tt> is a [[List of functions|function]] that returns the Choi matrix of the partially depolarizing channel, which acts as follows:


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The completely depolarizing channel maps every density matrix to the maximally-mixed state:
The completely depolarizing channel maps every density matrix to the maximally-mixed state:
<syntaxhighlight>
<syntaxhighlight>
>> >> ApplyMap(RandomDensityMatrix(3),DepolarizingChannel(3))
>> ApplyMap(RandomDensityMatrix(3),DepolarizingChannel(3))


ans =
ans =

Latest revision as of 17:37, 22 January 2015

DepolarizingChannel
Produces a depolarizing channel

Other toolboxes required none
Related functions DephasingChannel
Function category Superoperators

DepolarizingChannel is a function that returns the Choi matrix of the partially depolarizing channel, which acts as follows:

<math>\Delta(X) := (1-p)\mathrm{Tr}(X)\frac{I}{d^2} + pX,</math>

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

Source code

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