Difference between revisions of "Purity"
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(Created page with "{{Function |name=Purity |desc=Computes the purity of a quantum state |upd=July 18, 2013 |v=1.00}} <tt>'''Purity'''</tt> is a function that computes the [...") |
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|name=Purity | |name=Purity | ||
|desc=Computes the purity of a quantum state | |desc=Computes the purity of a quantum state | ||
| − | |upd= | + | |cat=[[List of functions#Miscellaneous|Miscellaneous]] |
| − | |v= | + | |upd=October 15, 2014 |
| − | <tt>'''Purity'''</tt> is a [[List of functions|function]] that computes the | + | |v=0.50}} |
| + | <tt>'''Purity'''</tt> is a [[List of functions|function]] that computes the purity of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$). | ||
==Syntax== | ==Syntax== | ||
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===Purity of pure states=== | ===Purity of pure states=== | ||
Pure states have purity equal to 1, as illustrated by the following code: | Pure states have purity equal to 1, as illustrated by the following code: | ||
| − | < | + | <syntaxhighlight> |
| − | >> phi = | + | >> phi = RandomStateVector(3); |
>> Purity(phi*phi') | >> Purity(phi*phi') | ||
| Line 23: | Line 24: | ||
1.0000 | 1.0000 | ||
| − | >> Purity( | + | >> Purity(RandomDensityMatrix(3,0,1)) |
ans = | ans = | ||
1.0000 | 1.0000 | ||
| − | </ | + | </syntaxhighlight> |
===Purity of mixed states=== | ===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). | 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). | ||
| − | < | + | <syntaxhighlight> |
| − | >> Purity( | + | >> Purity(WernerState(2,1/4)) % the state WernerState(2,1/4) acts on 4-dimensional space |
ans = | ans = | ||
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0.2500 | 0.2500 | ||
| − | </ | + | </syntaxhighlight> |
| + | |||
| + | {{SourceCode|name=Purity}} | ||
Latest revision as of 01:40, 13 May 2018
| Purity | |
| Computes the purity of a quantum state | |
| Other toolboxes required | none |
|---|---|
| Function category | Miscellaneous |
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 =
1.0000Purity 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 =
0.2500Source code
Click here to view this function's source code on github.