state_props.negativity

Calculates the negativity property of a quantum state.

Functions

negativity(rho[, dim])

Compute the negativity of a bipartite quantum state [1].

Module Contents

state_props.negativity.negativity(rho, dim=None)

Compute the negativity of a bipartite quantum state [1].

The negativity of a subsystem can be defined in terms of a density matrix \(\rho\):

\[\mathcal{N}(\rho) \equiv \frac{||\rho^{\Gamma_A}||_1-1}{2}.\]

Calculate the negativity of the quantum state \(\rho\), assuming that the two subsystems on which \(\rho\) acts are of equal dimension (if the local dimensions are unequal, specify them in the optional dim argument). The negativity of \(\rho\) is the sum of the absolute value of the negative eigenvalues of the partial transpose of \(\rho\).

Examples

Example of the negativity of density matrix of Bell state.

>>> from toqito.states import bell
>>> from toqito.state_props import negativity
>>> rho = bell(0) @ bell(0).conj().T
>>> negativity(rho)
np.float64(0.4999999999999998)

See also

log_negativity

References

[1] (1,2)

Wikipedia. Negativity. URL: https://en.wikipedia.org/wiki/Negativity_(quantum_mechanics).

Raises:

ValueError – If dimension of matrix is invalid.

Parameters:

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

• dim (list[int] | int) – The default has both subsystems of equal dimension.

Returns:

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

Return type:

float