toqito.state_props.is_mixed

toqito.state_props.is_mixed(state)

Determine if a given quantum state is mixed [WikMix].

A mixed state by definition is a state that is not pure.

Examples

Consider the following density matrix:

\[\begin{split}\rho = \begin{pmatrix} \frac{3}{4} & 0 \\ 0 & \frac{1}{4} \end{pmatrix} \in \text{D}(\mathcal{X}).\end{split}\]

Calculating the rank of \(\rho\) yields that the \(\rho\) is a mixed state. This can be confirmed in toqito as follows:

>>> from toqito.states import basis
>>> from toqito.state_props import is_mixed
>>> e_0, e_1 = basis(2, 0), basis(2, 1)
>>> rho = 3 / 4 * e_0 * e_0.conj().T + 1 / 4 * e_1 * e_1.conj().T
>>> is_mixed(rho)
True

References

[WikMix]

Wikipedia: Quantum state - Mixed states https://en.wikipedia.org/wiki/Quantum_state#Mixed_states

Parameters:

state – The density matrix representing the quantum state.

Returns:

True if state is mixed and False otherwise.