toqito.states.chessboard

toqito.states.chessboard(mat_params, s_param=None, t_param=None)[source]

Produce a chessboard state [BP00].

Generates the chessboard state defined in [BP00]. 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)
[[ 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

[BP00] (1,2,3)

Three qubits can be entangled in two inequivalent ways. D. Bruss and A. Peres Phys. Rev. A, 61:30301(R), 2000 arXiv: 991.1056

Parameters:

mat_params – Parameters of the chessboard state as defined in [BP00].
s_param – Default is np.conj(mat_params[2]) / np.conj(mat_params[5]).
t_param – Default is t_param = mat_params[0] * mat_params[3] / mat_params[4].

Returns:

A chessboard state.