states.max_mixed
¶
Maximally mixed state.
Module Contents¶
Functions¶
|
Produce the maximally mixed state [1]. |
- states.max_mixed.max_mixed(dim, is_sparse=False)¶
Produce the maximally mixed state [1].
Produces the maximally mixed state on of
dim
dimensions. The maximally mixed state is defined as\[\begin{split}\omega = \frac{1}{d} \begin{pmatrix} 1 & 0 & \ldots & 0 \\ 0 & 1 & \ldots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \ldots & 1 \end{pmatrix},\end{split}\]or equivalently, it is defined as
\[\omega = \frac{\mathbb{I}}{\text{dim}(\mathcal{X})}\]for some complex Euclidean space \(\mathcal{X}\). The maximally mixed state is sometimes also referred to as the tracial state.
The maximally mixed state is returned as a sparse matrix if
is_sparse = True
and is full ifis_sparse = False
.Examples
Using
toqito
, we can generate the \(2\)-dimensional maximally mixed state\[\begin{split}\omega_2 = \frac{1}{2} \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\end{split}\]as follows.
>>> from toqito.states import max_mixed >>> max_mixed(2, is_sparse=False) array([[0.5, 0. ], [0. , 0.5]])
One may also generate a maximally mixed state returned as a sparse matrix
>>> from toqito.states import max_mixed >>> max_mixed(2, is_sparse=True) <2x2 sparse matrix of type '<class 'numpy.float64'>' with 2 stored elements (1 diagonals) in DIAgonal format>
References
- Parameters:
dim (int) – Dimension of the entangled state.
is_sparse (bool) – True if vector is spare and False otherwise.
- Returns:
The maximally mixed state of dimension dim.
- Return type:
[numpy.ndarray, scipy.sparse.dia_matrix]