toqito.states.bell

Bell states represent the simplest examples of quantum entanglement of two qubits.

Also known as EPR pairs, Bell states comprise of four quantum states in a superposition of 0 and 1.

Module Contents

toqito.states.bell.bell(idx)

Produce a Bell state [@WikiBellSt].

Returns one of the following four Bell states depending on the value of idx:

[

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}

]

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.

`python exec="1" source="above" from toqito.states import bell import numpy as np print(bell(0)) `

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