states.bell
¶
Bell state.
Module Contents¶
Functions¶
|
Produce a Bell state [1]. |
- states.bell.bell(idx)¶
Produce a Bell state [1].
Returns one of the following four Bell states depending on the value of
idx
:\[\begin{split}\begin{equation} \begin{aligned} u_0 = \frac{1}{\sqrt{2}} \left( |00 \rangle + |11 \rangle \right), & \qquad & u_1 = \frac{1}{\sqrt{2}} \left( |00 \rangle - |11 \rangle \right), \\ u_2 = \frac{1}{\sqrt{2}} \left( |01 \rangle + |10 \rangle \right), & \qquad & u_3 = \frac{1}{\sqrt{2}} \left( |01 \rangle - |10 \rangle \right). \end{aligned} \end{equation}\end{split}\]Examples
When
idx = 0
, this produces the following Bell state:\[u_0 = \frac{1}{\sqrt{2}} \left( |00 \rangle + |11 \rangle \right).\]Using
toqito
, we can see that this yields the proper state.>>> from toqito.states import bell >>> import numpy as np >>> bell(0) array([[0.70710678], [0. ], [0. ], [0.70710678]])
References
- Raises:
ValueError – If
idx
is not an integer.- Parameters:
idx (int) – A parameter in [0, 1, 2, 3]
- Returns:
Bell state with index
idx
.- Return type:
numpy.ndarray