states.domino

Produce a domino state.

Functions

domino(idx)

Produce a domino state [1][2].

Module Contents

states.domino.domino(idx)

Produce a domino state [1][2].

The orthonormal product basis of domino states is given as

\[\begin{split}\begin{equation} \begin{aligned} |\phi_0\rangle = |1\rangle |1 \rangle, \qquad |\phi_1\rangle = |0 \rangle \left(\frac{|0 \rangle + |1 \rangle}{\sqrt{2}} \right), & \qquad |\phi_2\rangle = |0\rangle \left(\frac{|0\rangle - |1\rangle}{\sqrt{2}}\right), \\ |\phi_3\rangle = |2\rangle \left(\frac{|0\rangle + |1\rangle}{\sqrt{2}}\right), \qquad |\phi_4\rangle = |2\rangle \left(\frac{|0\rangle - |1\rangle}{\sqrt{2}}\right), & \qquad |\phi_5\rangle = \left(\frac{|0\rangle + |1\rangle}{\sqrt{2}}\right) |0\rangle, \\ |\phi_6\rangle = \left(\frac{|0\rangle - |1\rangle}{\sqrt{2}}\right) |0\rangle, \qquad |\phi_7\rangle = \left(\frac{|0\rangle + |1\rangle}{\sqrt{2}}\right) |2\rangle, & \qquad |\phi_8\rangle = \left(\frac{|0\rangle - |1\rangle}{\sqrt{2}}\right) |2\rangle. \end{aligned} \end{equation}\end{split}\]

Returns one of the following nine domino states depending on the value of idx.

Examples

When idx = 0, this produces the following Domino state

\[|\phi_0 \rangle = |11 \rangle |11 \rangle.\]

Using |toqito⟩, we can see that this yields the proper state.

from toqito.states import domino
domino(0)

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

When idx = 3, this produces the following Domino state

\[|\phi_3\rangle = |2\rangle \left(\frac{|0\rangle + |1\rangle} {\sqrt{2}}\right)\]

Using |toqito⟩, we can see that this yields the proper state.

from toqito.states import domino
domino(3)

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

References

[1] (1,2)

Charles H. Bennett, David P. DiVincenzo, Christopher A. Fuchs, Tal Mor, Eric Rains, Peter W. Shor, John A. Smolin, and William K. Wootters. Quantum nonlocality without entanglement. Physical Review A, 59(2):1070–1091, Feb 1999. URL: http://dx.doi.org/10.1103/PhysRevA.59.1070, doi:10.1103/physreva.59.1070.

[2] (1,2)

Charles H. Bennett, David P. DiVincenzo, Tal Mor, Peter W. Shor, John A. Smolin, and Barbara M. Terhal. Unextendible product bases and bound entanglement. Physical Review Letters, 82(26):5385–5388, Jun 1999. URL: http://dx.doi.org/10.1103/PhysRevLett.82.5385, doi:10.1103/physrevlett.82.5385.

Raises:

ValueError – Invalid value for idx.

Parameters:

idx (int) – A parameter in [0, 1, 2, 3, 4, 5, 6, 7, 8]

Returns:

Domino state of index idx.

Return type:

numpy.ndarray