# cirq.kraus

Returns a list of matrices describing the channel for the given value.

### Used in the notebooks

Used in the tutorials

These matrices are the terms in the operator sum representation of a quantum channel. If the returned matrices are $${A_0,A_1,..., A_{r-1} }$$, then this describes the channel:

$$\rho \rightarrow \sum_{k=0}^{r-1} A_k \rho A_k^\dagger$$


These matrices are required to satisfy the trace preserving condition

$$\sum_{k=0}^{r-1} A_k^\dagger A_k = I$$


where $$I$$ is the identity matrix. The matrices $$A_k$$ are sometimes called Kraus or noise operators.

val The value to describe by a channel.
default Determines the fallback behavior when val doesn't have a channel. If default is not set, a TypeError is raised. If default is set to a value, that value is returned.

If val has a _kraus_ method and its result is not NotImplemented, that result is returned. Otherwise, if val has a _mixture_ method and its results is not NotImplement a tuple made up of channel corresponding to that mixture being a probabilistic mixture of unitaries is returned. Otherwise, if val has a _unitary_ method and its result is not NotImplemented a tuple made up of that result is returned. Otherwise, if a default value was specified, the default value is returned.

TypeError val doesn't have a kraus or unitary method (or that method returned NotImplemented) and also no default value was specified.

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