toqito.state_props.purity

Calcultes the purity of a quantum state.

Module Contents

toqito.state_props.purity.purity(rho)

Compute the purity of a quantum state [@WikiPurity].

The negativity of a subsystem can be defined in terms of a density matrix (rho): The purity of a quantum state (rho) is defined as

[

text{Tr}(rho^2),

]

where (text{Tr}) is the trace function.

Examples

Consider the following scaled state defined as the scaled identity matrix

[

rho = frac{1}{4} begin{pmatrix}

1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1

end{pmatrix} in text{D}(mathcal{X}).

]

Calculating the purity of (rho) yields (frac{1}{4}). This can be observed using |toqito⟩ as follows.

`python exec="1" source="above" session="purity_example" from toqito.state_props import purity import numpy as np print(purity(np.identity(4) / 4)) `

Calculate the purity of the Werner state:

`python exec="1" source="above" session="purity_example" from toqito.states import werner rho = werner(2, 1 / 4) print(purity(rho)) `

Raises:

ValueError – If matrix is not density operator.

Parameters:

rho (numpy.ndarray) – A density matrix of a pure state vector.

Returns:

A value between 0 and 1 that corresponds to the purity of (rho).

Return type:

float