ChessboardState

ChessboardState is a function that produces a two-qutrit "chessboard state", as defined in. These states are of interest because they are bound entangled.

Syntax

 * RHO = ChessboardState(A,B,C,D,M,N)
 * RHO = ChessboardState(A,B,C,D,M,N,S,T)

Argument descriptions

 * 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</tt> is entangled. If each of A,B,C,D,M,N</tt> are real then RHO</tt> has positive partial transpose, and is hence bound entangled.
 * S,T</tt>: Additional (optional) parameters of the chessboard states, also as in . Note that, for certain choices of S</tt> and T</tt>, 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).

When specifying S</tt> and T</tt>
If you specify S</tt> and T</tt> manually, it is possible that the resulting state will not have positive partial transpose – a warning is produced in these cases.