ChannelDistinguishability - Revision history

Rmmateri at 16:32, 13 June 2018

2018-06-13T16:32:21Z

← Older revision		Revision as of 16:32, 13 June 2018
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	\|name=ChannelDistinguishability		\|name=ChannelDistinguishability
	\|desc=Computes the maximum probability of distinguishing two quantum channels		\|desc=Computes the maximum probability of distinguishing two quantum channels
	\|req=[http://cvxr.com/cvx/ ~~cvx~~]		\|req=[http://cvxr.com/cvx/ CVX]
	\|rel=[[Distinguishability]]<br />[[LocalDistinguishability]]		\|rel=[[Distinguishability]]<br />[[LocalDistinguishability]]
	\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]		\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]

Nathaniel: Updated to use superoperator_dims function

2014-11-28T01:55:40Z

Updated to use superoperator_dims function

← Older revision		Revision as of 01:55, 28 November 2014
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	\|rel=[[Distinguishability]]<br />[[LocalDistinguishability]]		\|rel=[[Distinguishability]]<br />[[LocalDistinguishability]]
	\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]		\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]
	\|upd=~~October 10~~, 2014		\|upd=November 27, 2014}}
	~~\|v=0.50~~}}
	<tt>'''ChannelDistinguishability'''</tt> is a [[List of functions\|function]] that computes the maximum probability of distinguishing two quantum channels. That is, this function computes the maximum probability of winning the following game: You are given a complete description of two quantum channels $\Phi$ and $\Psi$, and then are given one of those two channels, and asked to determine which channel was given to you (by supplying some input state to the channel and then measuring the output).		<tt>'''ChannelDistinguishability'''</tt> is a [[List of functions\|function]] that computes the maximum probability of distinguishing two quantum channels. That is, this function computes the maximum probability of winning the following game: You are given a complete description of two quantum channels $\Phi$ and $\Psi$, and then are given one of those two channels, and asked to determine which channel was given to you (by supplying some input state to the channel and then measuring the output).

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	==Examples==		==Examples==
	===Perfectly distinguishable channels===		===Perfectly distinguishable channels===
	The following code demonstrates that the simple example of two channels that can be perfectly distinguished from <ref>John Watrous. [https://cs.uwaterloo.ca/~watrous/CS766/LectureNotes/20.pdf Lecture 20: Channel distinguishability and the completely bounded trace norm], ''Theory of Quantum Information Lecture Notes'', 2011.</ref> can indeed be perfectly distinguished		The following code demonstrates that the simple example of two channels that can be perfectly distinguished from <ref>John Watrous. [https://cs.uwaterloo.ca/~watrous/CS766/LectureNotes/20.pdf Lecture 20: Channel distinguishability and the completely bounded trace norm], ''Theory of Quantum Information Lecture Notes'', 2011.</ref> can indeed be perfectly distinguished:
	<syntaxhighlight>		<syntaxhighlight>
	>> n = 4;		>> n = 4;

Nathaniel: Created page with "{{Function |name=ChannelDistinguishability |desc=Computes the maximum probability of distinguishing two quantum channels |req=[http://cvxr.com/cvx/ cvx] |rel=Distinguishabil..."

2014-10-15T14:34:55Z

Created page with "{{Function |name=ChannelDistinguishability |desc=Computes the maximum probability of distinguishing two quantum channels |req=[http://cvxr.com/cvx/ cvx] |rel=Distinguishabil..."

New page

{{Function
|name=ChannelDistinguishability
|desc=Computes the maximum probability of distinguishing two quantum channels
|req=[http://cvxr.com/cvx/ cvx]
|rel=[[Distinguishability]]<br />[[LocalDistinguishability]]
|cat=[[List of functions#Distinguishing_objects|Distinguishing objects]]
|upd=October 10, 2014
|v=0.50}}
<tt>'''ChannelDistinguishability'''</tt> is a [[List of functions|function]] that computes the maximum probability of distinguishing two quantum channels. That is, this function computes the maximum probability of winning the following game: You are given a complete description of two quantum channels $\Phi$ and $\Psi$, and then are given one of those two channels, and asked to determine which channel was given to you (by supplying some input state to the channel and then measuring the output).

==Syntax==
* <tt>DIST = ChannelDistinguishability(PHI,PSI)</tt>
* <tt>DIST = ChannelDistinguishability(PHI,PSI,P)</tt>
* <tt>DIST = ChannelDistinguishability(PHI,PSI,P,DIM)</tt>

==Argument descriptions==
* <tt>PHI,PSI</tt>: The quantum channels to be distinguished. They can either be input as Choi matrices or as cells of Kraus operators.
* <tt>P</tt> (optional, default <tt>[1/2, 1/2]</tt>): A vector that specifies that <tt>PHI</tt> and <tt>PSI</tt> are chosen with probability <tt>P(1)</tt> and <tt>P(2)</tt>, respectively.
* <tt>DIM</tt> (optional, by default tries to guess the input and output dimensions): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt> and <tt>PSI</tt>. <tt>DIM</tt> is required if and only if both <tt>PHI</tt> and <tt>PSI</tt> are provided as Choi matrices and the input and output dimensions are different.

==Examples==
===Perfectly distinguishable channels===
The following code demonstrates that the simple example of two channels that can be perfectly distinguished from <ref>John Watrous. [https://cs.uwaterloo.ca/~watrous/CS766/LectureNotes/20.pdf Lecture 20: Channel distinguishability and the completely bounded trace norm], ''Theory of Quantum Information Lecture Notes'', 2011.</ref> can indeed be perfectly distinguished
<syntaxhighlight>
>> n = 4;
>> Phi = SymmetricProjection(n)*2/(n+1);
>> Psi = AntisymmetricProjection(n)*2/(n-1);
>> ChannelDistinguishability(Phi,Psi)

ans =

1.0000
</syntaxhighlight>

{{SourceCode|name=ChannelDistinguishability}}

==References==
<references />