qics.quantum.random.degradable_channel

qics.quantum.random.degradable_channel(nin, nout=None, nenv=None, iscomplex=False)

Generate random degradable channel \(\mathcal{N}\), represented as a Stinespring isometry \(V\) such that

\[\mathcal{N}(X) = \text{tr}_2[V X V^\dagger]\]

Also returns Stinespring isometry \(W\) corresponding to the complementary channel \(\mathcal{N}_\text{c}\) such that

\[\mathcal{N}_\text{c}(X) = \text{tr}_1[V X V^\dagger] = \text{tr}_2[W \mathcal{N}(X) W^\dagger].\]

Parameters:

ninint

Dimension of the input system.

noutint, optional

Dimension of the output system. The default is nin.

nenvint, optional

Dimension of the environment system. The default is nout.

iscomplexbool, optional

Whether the Stinespring operators are real (False) or complex (True). The default is False.

Returns:

ndarray

Stinespring operator \(V\) of dimension (nout*nenv, nin) corresponding to \(\mathcal{N}(X)=\text{tr}_2[V X V^\dagger]\).

ndarray

Stinespring operator \(W\) of dimension (nin*nenv, nout) corresponding to \(\mathcal{N}_\text{c}(X)= \text{tr}_2[W \mathcal{N}(X) W^\dagger]\).

Notes

See [1] for additional details.

[1]

Cubitt, Toby S., Mary Beth Ruskai, and Graeme Smith. “The structure of degradable quantum channels.” Journal of Mathematical Physics 49.10 (2008).