toqito.state_props.l1_norm_coherence

Computes the l1-norm of coherence of a quantum state.

Module Contents

toqito.state_props.l1_norm_coherence.l1_norm_coherence(rho)

Compute the l1-norm of coherence of a quantum state [@Rana_2017_Log].

The (ell_1)-norm of coherence of a quantum state (rho) is defined as

[

C_{ell_1}(rho) = sum_{i not= j} left|rho_{i,j}right|,

]

where (rho_{i,j}) is the ((i,j)^{th})-entry of (rho) in the standard basis.

The (ell_1)-norm of coherence is the sum of the absolute values of the sum of the absolute values of the off-diagonal entries of the density matrix rho in the standard basis.

This function was adapted from QETLAB.

Examples

The largest possible value of the (ell_1)-norm of coherence on (d)-dimensional states is (d-1), and is attained exactly by the “maximally coherent states”: pure states whose entries all have the same absolute value.

`python exec="1" source="above" from toqito.state_props import l1_norm_coherence import numpy as np # Maximally coherent state. v = np.ones((3,1))/np.sqrt(3) print(l1_norm_coherence(v)) `

Parameters:

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

Returns:

The l1-norm coherence of rho.

Return type:

float