Difference between revisions of "Purity"

	Purity
	Computes the purity of a quantum state
Other toolboxes required	none
Function category	Miscellaneous

Revision as of 13:57, 15 October 2014

Purity is a function that computes the purity of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.

Syntax

GAMMA = Purity(RHO)

Argument descriptions

RHO: A density matrix to have its purity computed.

Examples

Purity of pure states

Pure states have purity equal to 1, as illustrated by the following code:

>> phi = RandomStateVector(3);
>> Purity(phi*phi')

ans =

    1.0000

>> Purity(RandomDensityMatrix(3,0,1))

ans =

    1.0000

Purity of mixed states

If $\rho \in M_d$ is mixed then its purity is strictly less than 1. Its purity attains its minimum value of $1/d$ if and only if $\rho$ is the maximally-mixed state (i.e., the scaled identity operator).

>> Purity(WernerState(2,1/4)) % the state WernerState(2,1/4) acts on 4-dimensional space

ans =

    0.2653

>> Purity(eye(4)/4)

ans =

    0.2500

Source code

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

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 |desc=Computes the purity of a quantum state
 |cat=[[List of functions#Miscellaneous|Miscellaneous]]
-|upd=July 18, 2013
+|upd=October 15, 2014
-|v=1.00}}
+|v=0.50}}
 <tt>'''Purity'''</tt> is a [[List of functions|function]] that computes the [[purity_(concept)|purity]] of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$.