toqito.matrix_props.is_absolutely_k_incoherent¶

Checks if the matrix is absolutely $k$-incoherent.

Module Contents¶

toqito.matrix_props.is_absolutely_k_incoherent.is_absolutely_k_incoherent(mat, k, tol=1e-15)[source]¶

Determine whether a quantum state is absolutely k-incoherent [@Johnston_2022_Absolutely].

Formally, for positive integers (n) and (k), a mixed quantum state is said to be absolutely k-incoherent if (U rho U^* in mathbb{I}_{k, n}) for all unitary matrices (U in text{U}(mathbb{C}^n)).

This function checks if the provided density matrix is absolutely k-incoherent based on the criteria introduced in [@Johnston_2022_Absolutely] and the corresponding QETLAB functionality [@QETLAB_link]. When necessary, an SDP is set up via cvxpy.

The notion of absolute k-incoherence is connected to the notion of quantum state antidistinguishability as discussed in [@Johnston_2025_Tight].

Examples

```python exec=”1” source=”above” import numpy as np from toqito.matrix_props import is_absolutely_k_incoherent mat = np.array([[2, 1, 2],

[1, 2, -1], [2, -1, 5]])

print(is_absolutely_k_incoherent(mat, 4)) ```

!!! See: [is_antidistinguishable()][toqito.state_props.is_antidistinguishable.is_antidistinguishable], [is_k_incoherent()][toqito.matrix_props.is_k_incoherent.is_k_incoherent]

Raises:

ValueError – If the input matrix is not square.

Parameters:

mat (numpy.ndarray) – Matrix to check for absolute k-incoherence.
k (int) – The positive integer indicating the absolute coherence level.
tol (float) – Tolerance for numerical comparisons (default is 1e-15).

Returns:

True if the quantum state is absolutely k-incoherent, False otherwise.

Return type:

bool