states.bb84

BB84 basis states.

Module Contents

Functions

bb84()

Obtain the BB84 basis states [1].
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]])]]

Note

We use #doctest to verify our examples work as expected.

# doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE is used here to make sure doctest matches the calculated output to be close to the expected output instead of making sure both match exactly.

References

[1] (1,2)

Wikipedia. Bb84. https://en.wikipedia.org/wiki/BB84.

Returns:

The four BB84 basis states.

Return type:

numpy.ndarray