toqito.states.brauer

toqito.states.brauer(dim, p_val)[source]

Produce all Brauer states [WikBrauer].

Produce a matrix whose columns are all of the (unnormalized) “Brauer” states: states that are the p_val-fold tensor product of the standard maximally-entangled pure state on dim local dimensions. There are many such states, since there are many different ways to group the 2 * p_val parties into p_val pairs (with each pair corresponding to one maximally-entangled state).

The exact number of such states is:

``` import numpy as np

np.factorial(2 * p_val) / (np.factorial(p_val) * 2**p_val) ```

which is the number of columns of the returned matrix.

This function has been adapted from QETLAB.

Examples

Generate a matrix whose columns are all Brauer states on 4 qubits.

>>> from toqito.states import brauer
>>> brauer(2, 2)
[[1. 1. 1.]
 [0. 0. 0.]
 [0. 0. 0.]
 [1. 0. 0.]
 [0. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]
 [0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 1.]
 [0. 1. 0.]
 [0. 0. 0.]
 [1. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]
 [1. 1. 1.]]

References

Parameters:

  • dim – Dimension of each local subsystem

  • p_val – Half of the number of parties (i.e., the state that this function computes will live in \((\mathbb{C}^D)^{\otimes 2 P})\)

Returns:

Matrix whose columns are all of the unnormalized Brauer states.