toqito.state_props.log_negativity¶

Calculates the logarithmic negativity property of a quantum state.

Module Contents¶

toqito.state_props.log_negativity.log_negativity(rho, dim=None)[source]¶

Compute the log-negativity of a bipartite quantum state [@WikiNeg].

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

[: E_mathcal{N}(rho) equiv text{log}_2left( ||rho^{Gamma_A}||_1 right).

]

Calculate the log-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).

Examples

Example of the log-negativity of density matrix of Bell state.

`python exec="1" source="above" from toqito.states import bell from toqito.state_props import log_negativity rho = bell(0) @ bell(0).conj().T print(log_negativity(rho)) `

!!!See Also: [negativity()][toqito.state_props.negativity.negativity]

Raises:

ValueError – If the input matrix is not a density matrix.

Parameters:

rho (numpy.ndarray) – A density matrix of a pure state vector.
dim (list[int] | int | None) – The default has both subsystems of equal dimension.

Returns:

A positive value that corresponds to the logarithmic negativity of (rho).

Return type:

float