helper.channel_dim

Channel dimensions coputes and returns the input, output and environment dimensions of a channel.

Functions

channel_dim(phi[, allow_rect, dim, compute_env_dim])

Compute the input, output, and environment dimensions of a channel.

_expand_dim(dim)

Module Contents

helper.channel_dim.channel_dim(phi, allow_rect=True, dim=None, compute_env_dim=True)

Compute the input, output, and environment dimensions of a channel.

This function returns the dimensions of the input, output, and environment spaces of input channel, in that order. Input and output dimensions are both 1-by-2 vectors containing the row and column dimensions of their spaces. The enviroment dimension is always a scalar, and it is equal to the number of Kraus operators of PHI (if PHI is provided as a Choi matrix then enviroment dimension is the minimal number of Kraus operators of any representation of PHI).

Input DIM should provided if and only if PHI is a Choi matrix with unequal input and output dimensions (since it is impossible to determine the input and output dimensions from the Choi matrix alone). If ALLOW_RECT is false and PHI acts on non-square matrix spaces, an error will be produced. If PHI maps M_{r,c} to M_{x,y} then DIM should be the 2-by-2 matrix [[r,x], [c,y]]. If PHI maps M_m to M_n, then DIM can simply be the vector [m,n]. If ALLOW_RECT is false then returned input and output dimensions will be scalars instead of vectors. If COMPUTE_ENV_DIM is false and the PHI is a Choi matrix we avoid computing the rank of the Choi matrix.

This functions was adapted from QETLAB [1].

References

[1]

Nathaniel Johnston. QETLAB: A MATLAB toolbox for quantum entanglement. URL: https://github.com/nathanieljohnston/QETLAB, doi:10.5281/zenodo.44637.

Parameters:

  • phi (numpy.ndarray | list[numpy.ndarray] | list[list[numpy.ndarray]]) – A superoperator. It should be provided either as a Choi matrix, or as a (1d or 2d) list of numpy arrays whose entries are its Kraus operators.

  • allow_rect (bool) – A flag indicating that the input and output spaces of PHI can be non-square (default True).

  • dim (int | list[int] | numpy.ndarray) – A scalar, vector or matrix containing the input and output dimensions of PHI.

  • compute_env_dim (bool) – A flag indicating whether we compute the enviroment dimension.

Returns:

The input, output, and environment dimensions of a channel.

Return type:

tuple[numpy.ndarray | int]

helper.channel_dim._expand_dim(dim)