states.chessboard

Chessboard state represent the state of a chessboard used in quantum chess.

In a quantum chessboard, each chess piece is quantum having a superposition of channel states, giving rise to a unique chess piece.

Functions

chessboard(mat_params[, s_param, t_param])

Produce a chessboard state [1].

Module Contents

states.chessboard.chessboard(mat_params, s_param=None, t_param=None)

Produce a chessboard state [1].

Generates the chessboard state defined in [1]. Note that, for certain choices of s_param and t_param, this state will not have positive partial transpose, and thus may not be bound entangled.

Examples

The standard chessboard state can be invoked using toqito as

>>> from toqito.states import chessboard
>>> chessboard([1, 2, 3, 4, 5, 6], 7, 8)
array([[ 0.22592593,  0.        ,  0.12962963,  0.        ,  0.        ,
         0.        ,  0.17777778,  0.        ,  0.        ],
       [ 0.        ,  0.01851852,  0.        ,  0.        ,  0.        ,
         0.01111111,  0.        ,  0.02962963,  0.        ],
       [ 0.12962963,  0.        ,  0.18148148,  0.        ,  0.15555556,
         0.        ,  0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.01851852,  0.        ,
         0.02222222,  0.        , -0.01481481,  0.        ],
       [ 0.        ,  0.        ,  0.15555556,  0.        ,  0.22592593,
         0.        , -0.14814815,  0.        ,  0.        ],
       [ 0.        ,  0.01111111,  0.        ,  0.02222222,  0.        ,
         0.03333333,  0.        ,  0.        ,  0.        ],
       [ 0.17777778,  0.        ,  0.        ,  0.        , -0.14814815,
         0.        ,  0.23703704,  0.        ,  0.        ],
       [ 0.        ,  0.02962963,  0.        , -0.01481481,  0.        ,
         0.        ,  0.        ,  0.05925926,  0.        ],
       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,
         0.        ,  0.        ,  0.        ,  0.        ]])

References

[1] (1,2,3,4)

Dagmar Bruß and Asher Peres. Construction of quantum states with bound entanglement. Phys. Rev. A, 61:030301, Feb 2000. URL: https://link.aps.org/doi/10.1103/PhysRevA.61.030301, doi:10.1103/PhysRevA.61.030301.

Parameters:

  • mat_params (list[float]) – Parameters of the chessboard state as defined in [1].

  • s_param (float) – Default is np.conj(mat_params[2]) / np.conj(mat_params[5]).

  • t_param (float) – Default is t_param = mat_params[0] * mat_params[3] / mat_params[4].

Returns:

A chessboard state.

Return type:

numpy.ndarray