|Produces a chessboard state|
|Other toolboxes required||none|
|Related functions|| BreuerState|
|Function category||Special states, vectors, and operators|
- RHO = ChessboardState(A,B,C,D,M,N)
- RHO = ChessboardState(A,B,C,D,M,N,S,T)
- A,B,C,D,M,N: Six parameters that define chessboard states, as in , with S = A*conj(C)/conj(N) and T = A*D/M. If C*M*conj(N) does not equal A*B*conj(C) then RHO is entangled. If each of A,B,C,D,M,N are real then RHO has positive partial transpose, and is hence bound entangled.
- S,T: Additional (optional) parameters of the chessboard states, also as in . Note that, for certain choices of S and T, this state will not have positive partial transpose, and thus may not be bound entangled – a warning will be produced in these cases.
Generating bound entangled states
Chessboard states are useful because they form a wide family of bound entangled states. The following code generates a random chessboard state and verifies that it is entangled yet positive-partial-transpose (and hence bound entangled).
>> rho = ChessboardState(randn(1),randn(1),randn(1),randn(1),randn(1),randn(1)); >> IsSeparable(rho) Determined to be entangled via the Filter Covariance Matrix Criterion. Reference: O. Gittsovich, O. Gühne, P. Hyllus, and J. Eisert. Unifying several separability conditions using the covariance matrix criterion. Phys. Rev. A, 78:052319, 2008. ans = 0 >> IsPPT(rho) ans = 1
When specifying S and T
If you specify S and T manually, it is possible that the resulting state will not have positive partial transpose – a warning is produced in these cases.
>> rho = ChessboardState(1,2,3,4,5,6,7,8); Warning: The specified chessboard state does not have positive partial transpose. > In ChessboardState at 45
Click on "expand" to the right to view the MATLAB source code for this function.
- D. Bruss and A. Peres. Construction of quantum states with bound entanglement. Phys. Rev. A, 61:30301(R), 2000. E-print: arXiv:quant-ph/9911056