"""Computes the Choi matrix of a list of Kraus operators."""
import numpy as np
from toqito.channel_ops import partial_channel
from toqito.channel_props.channel_dim import channel_dim
from toqito.states import max_entangled
[docs]
def kraus_to_choi(kraus_ops: list[np.ndarray] | list[list[np.ndarray]], sys: int = 2) -> np.ndarray:
r"""Compute the Choi matrix of a list of Kraus operators.
(Section: Kraus Representations of [@Watrous_2018_TQI]).
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.
```python exec="1" source="above"
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]]
choi_op = kraus_to_choi(kraus_ops)
print(choi_op)
```
!!! See Also
[choi_to_kraus][toqito.channel_ops.choi_to_kraus.choi_to_kraus]
Args:
kraus_ops: A list of Kraus operators.
sys: The subsystem on which the channel acts (default is 2).
Returns:
The corresponding Choi matrix of the provided Kraus operators.
"""
if sys < 0:
raise ValueError("The `sys` parameter must be non-negative.")
dim_in, _, _ = channel_dim(kraus_ops)
dim_op_1, dim_op_2 = dim_in
choi_mat = partial_channel(
max_entangled(dim_op_1, False, False) @ max_entangled(dim_op_2, False, False).conj().T,
kraus_ops,
sys,
np.array([[dim_op_1, dim_op_1], [dim_op_2, dim_op_2]]),
)
return choi_mat