states.bb84¶

BB84 states represent the BB84 basis states, which are based on BB84, a quantum key distribution scheme.

In the BB884 scheme, each qubit is encoded with one of the 4 polarization states: 0, 1, +45° or -45°.

Functions¶

bb84()

Obtain the BB84 basis states [1].

Module Contents¶

states.bb84.bb84()¶

Obtain the BB84 basis states [1].

The BB84 basis states are defined as

\[\begin{split}|0\rangle := \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \quad \\ |1\rangle := \begin{pmatrix} 0 \\ 1 \end{pmatrix}, \quad \\ |+\rangle := \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ 1 \end{pmatrix}, \quad \\ |-\rangle := \frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ -1 \end{pmatrix}.\end{split}\]

Examples

The BB84 basis states can be obtained in |toqito⟩ as follows in the form of a list of arrays.

from toqito.states import bb84
bb84()

[[array([[1.],
         [0.]]),
  array([[0.],
         [1.]])],
 [array([[0.70710678],
         [0.70710678]]),
  array([[ 0.70710678],
         [-0.70710678]])]]

References

Returns:: The four BB84 basis states.
Return type:: numpy.ndarray