toqito.states.max_entangled

Maximally entangled states are states where the qubits are completely dependent on each other.

In these states, when a measurement is taken on one of the qubits, the state of the other qubits is automatically known.

Module Contents

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

Produce a maximally entangled bipartite pure state [@WikiMaxEnt].

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.

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

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

[

v = |00rangle + |11 rangle

]

using |toqito⟩ as follows.

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

Parameters:

• dim (int) – Dimension of the entangled state.

• is_sparse (bool) – True if vector is sparse and False otherwise.

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

Returns:

The maximally entangled state of dimension dim.

Return type:

numpy.ndarray | scipy.sparse.coo_array