Difference between revisions of "Purity"
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| − | <tt>'''Purity'''</tt> is a [[List of functions|function]] that computes the purity of a quantum state $\rho$ (i.e., it computes the quantity ${\rm Tr}(\rho^2)$. | + | <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== | ||
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.