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}} | ||
<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)) | |||
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 0.3333Source code
Click here to view this function's source code on github.