toqito.states.max_entangled

toqito.states.max_entangled(dim, is_sparse=False, is_normalized=True)[source]

Produce a maximally entangled bipartite pure state [WikEnt].

Produces a maximally entangled pure state as above that is sparse if is_sparse = True and is full if is_sparse = False. The pure state is normalized to have Euclidean norm 1 if is_normalized = True, and it is unnormalized (i.e. each entry in the vector is 0 or 1 and the Euclidean norm of the vector is sqrt(dim) if is_normalized = False.

Examples

We can generate the canonical \(2\)-dimensional maximally entangled state

\[u = \frac{1}{\sqrt{2}} \left( |00 \rangle + |11 \rangle \right)\]

using toqito as follows.

>>> from toqito.states import max_entangled
>>> max_entangled(2)
[[0.70710678],
 [0.        ],
 [0.        ],
 [0.70710678]]

By default, the state returned in normalized, however we can generate the unnormalized state

\[v = |00\rangle + |11 \rangle\]

using toqito as follows.

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

References

Parameters:

  • dim – Dimension of the entangled state.

  • is_sparse – True if vector is spare and False otherwise.

  • is_normalized – True if vector is normalized and False otherwise.

Returns:

The maximally entangled state of dimension dim.