toqito.state_props.is_ensemble¶

Checks if a set of quantum states form an ensemble.

Module Contents¶

toqito.state_props.is_ensemble.is_ensemble(states)[source]¶

Determine if a set of states constitute an ensemble.

For more info, see Section: Ensemble Of Quantum States from [@Watrous_2018_TQI].

An ensemble of quantum states is defined by a function

[: eta : Gamma rightarrow text{Pos}(mathcal{X})

]

that satisfies

[: text{Tr}left( sum_{a in Gamma} eta(a) right) = 1.

]

Examples

Consider the following set of matrices

[: eta = left{ rho_0, rho_1 right}

]

where

[: rho_0 = frac{1}{2} begin{pmatrix} 1 & 0 \ 0 & 0 end{pmatrix}, quad rho_1 = frac{1}{2} begin{pmatrix} 0 & 0 \ 0 & 1 end{pmatrix}.

]

The set (eta) constitutes a valid ensemble.

`python exec="1" source="above" from toqito.state_props import is_ensemble import numpy as np rho_0 = np.array([[0.5, 0], [0, 0]]) rho_1 = np.array([[0, 0], [0, 0.5]]) states = [rho_0, rho_1] print(is_ensemble(states)) `

Parameters:: states (list[numpy.ndarray]) – The list of states to check.
Returns:: True if states form an ensemble and False otherwise.
Return type:: bool