toqito.states.brauer¶

Brauer states are the p_val-fold tensor product of the standard maximally-entangled pure states.

Module Contents¶

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

Produce all Brauer states [@WikiBrauer].

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:

`python exec="1" source="above" import math import numpy as np p_val = 2 print(math.factorial(2 * p_val) / (math.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.

`python exec="1" source="above" from toqito.states import brauer print(brauer(2, 2)) `

Parameters:

dim (int) – Dimension of each local subsystem
p_val (int) – Half of the number of parties (i.e., the state that this function computes will live in

Return type:

numpy.ndarray

:param : :type : (mathbb{C}^D)^{otimes 2 P})

Returns:

Matrix whose columns are all of the unnormalized Brauer states.

Parameters:

dim (int)
p_val (int)

Return type:

numpy.ndarray