channel_ops.kraus_to_choi¶

Computes the Choi matrix of a list of Kraus operators.

Functions¶

kraus_to_choi(kraus_ops[, sys])

Compute the Choi matrix of a list of Kraus operators.

Module Contents¶

channel_ops.kraus_to_choi.kraus_to_choi(kraus_ops, sys=2)¶

Compute the Choi matrix of a list of Kraus operators.

(Section: Kraus Representations of [1]).

The Choi matrix of the list of Kraus operators, kraus_ops. The default convention is that the Choi matrix is the result of applying the map to the second subsystem of the standard maximally entangled (unnormalized) state. The Kraus operators are expected to be input as a list of numpy arrays (i.e. [[A_1, B_1],…,[A_n, B_n]]). In case the map is CP (completely positive), it suffices to input a flat list of operators omitting their conjugate transpose (i.e. [\(K_1\),…, \(K_n\)]).

This function was adapted from the QETLAB package.

Examples

The transpose map:

The Choi matrix of the transpose map is the swap operator. Notice that the transpose map is not completely positive.

>>> import numpy as np
>>> from toqito.channel_ops import kraus_to_choi
>>> kraus_1 = np.array([[1, 0], [0, 0]])
>>> kraus_2 = np.array([[1, 0], [0, 0]]).conj().T
>>> kraus_3 = np.array([[0, 1], [0, 0]])
>>> kraus_4 = np.array([[0, 1], [0, 0]]).conj().T
>>> kraus_5 = np.array([[0, 0], [1, 0]])
>>> kraus_6 = np.array([[0, 0], [1, 0]]).conj().T
>>> kraus_7 = np.array([[0, 0], [0, 1]])
>>> kraus_8 = np.array([[0, 0], [0, 1]]).conj().T
>>>
>>> kraus_ops = [[kraus_1, kraus_2], [kraus_3, kraus_4], [kraus_5, kraus_6], [kraus_7, kraus_8]]
>>> kraus_to_choi(kraus_ops)
array([[1., 0., 0., 0.],
       [0., 0., 1., 0.],
       [0., 1., 0., 0.],
       [0., 0., 0., 1.]])