Difference between revisions of "ChannelDistinguishability"

	ChannelDistinguishability
	Computes the maximum probability of distinguishing two quantum channels
Other toolboxes required	cvx
Related functions	Distinguishability; LocalDistinguishability
Function category	Distinguishing objects

Revision as of 01:55, 28 November 2014

ChannelDistinguishability is a 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

DIST = ChannelDistinguishability(PHI,PSI)
DIST = ChannelDistinguishability(PHI,PSI,P)
DIST = ChannelDistinguishability(PHI,PSI,P,DIM)

Argument descriptions

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

>> n = 4;
>> Phi = SymmetricProjection(n)*2/(n+1);
>> Psi = AntisymmetricProjection(n)*2/(n-1);
>> ChannelDistinguishability(Phi,Psi)

ans =

    1.0000

Source code

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

References

↑ John Watrous. Lecture 20: Channel distinguishability and the completely bounded trace norm, Theory of Quantum Information Lecture Notes, 2011.

[1] John Watrous. Lecture 20: Channel distinguishability and the completely bounded trace norm, Theory of Quantum Information Lecture Notes, 2011.

[1]

@@ Line 5: / Line 5: @@
 |rel=[[Distinguishability]]<br />[[LocalDistinguishability]]
 |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).
@@ Line 21: / Line 20: @@
 ==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
+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;