toqito.state_props.entanglement_of_formation

Computes the entanglement of formation of a bipartite quantum state.

Module Contents

toqito.state_props.entanglement_of_formation.entanglement_of_formation(rho, dim=None)

Compute entanglement-of-formation of a bipartite quantum state [@Quantiki_EOF].

Entanglement-of-formation is the entropy of formation of the bipartite quantum state rho. Note that this function currently only supports rho being a pure state or a 2-qubit state: it is not known how to compute the entanglement-of-formation of higher-dimensional mixed states.

This function was adapted from QETLAB.

Examples

Compute the entanglement-of-formation of a Bell state.

Let (u = frac{1}{sqrt{2}} left(|00rangle + |11rangle right)) and let

[

rho = uu^* = frac{1}{2}begin{pmatrix}

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

end{pmatrix}.

]

The entanglement-of-formation of (rho) is equal to 1.

`python exec="1" source="above" import numpy as np from toqito.state_props import entanglement_of_formation from toqito.states import bell u_vec = bell(0) rho = u_vec @ u_vec.conj().T print(entanglement_of_formation(rho)) `

Raises:

ValueError – If matrices have improper dimension.

Parameters:

• rho (numpy.ndarray) – A matrix or vector.

• dim (list[int] | int | None) – The default has both subsystems of equal dimension.

Returns:

A value between 0 and 1 that corresponds to the entanglement-of-formation of rho.

Return type:

float