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.

Functions

max_entangled(dim[, is_sparse, is_normalized])

Produce a maximally entangled bipartite pure state [1].

Module Contents

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

Produce a maximally entangled bipartite pure state [1].

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)
array([[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)
array([[1.],
       [0.],
       [0.],
       [1.]])

References

[1] (1,2)

Wikipedia. Quantum entanglement. URL: https://en.wikipedia.org/wiki/Quantum_entanglement.

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.dia_array]