toqito.states.domino

toqito.states.domino(idx)

Produce a domino state [CBDOM99], [UPB99].

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)
[[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)
[[0.        ],
 [0.        ],
 [0.        ],
 [0.        ],
 [0.        ],
 [0.        ],
 [0.        ],
 [0.70710678],
 [0.70710678]]

References

[CBDOM99]

Bennett, Charles H., et al. Quantum nonlocality without entanglement. Phys. Rev. A, 59:1070–1091, Feb 1999. https://arxiv.org/abs/quant-ph/9804053

[UPB99]

Bennett, Charles H., et al. “Unextendible product bases and bound entanglement.” Physical Review Letters 82.26 (1999): 5385. https://arxiv.org/abs/quant-ph/9808030

Raises:

ValueError – Invalid value for idx.

Parameters:

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

Returns:

Domino state of index idx.