state_props.is_mixed

Checks if a quantum state is mixed.

Functions

is_mixed(state)

Determine if a given quantum state is mixed [1].

Module Contents

state_props.is_mixed.is_mixed(state)

Determine if a given quantum state is mixed [1].

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

[1] (1,2)

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

Parameters:

state (numpy.ndarray) – The density matrix representing the quantum state.

Returns:

True if state is mixed and False otherwise.

Return type:

bool