IsAbsPPT

IsAbsPPT
Determines whether or not a density matrix is absolutely PPT
Other toolboxes required	none
Related functions	AbsPPTConstraints InSeparableBall
Function category	Ball of separability

IsAbsPPT is a function that determines whether or not a density matrix $\rho$ is "absolutely PPT" (that is, whether or not $U\rho U^\dagger$ has positive partial transpose for all unitary matrices $U$). The conditions that determine whether or not a state is absolutely PPT were derived in .

This function returns 1 if $\rho$ is absolutely PPT, 0 if it is not absolutely PPT, and -1 if it was unable to determine whether or not $\rho$ is absolutely PPT within a reasonable amount of time.

Syntax

• IAPPT = IsAbsPPT(RHO)
• IAPPT = IsAbsPPT(RHO,DIM)

Argument descriptions

• RHO: A bipartite density matrix (or any bipartite positive semidefinite operator).
• DIM (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the two subsystems that X acts on.

Examples

The maximally-mixed state is the simplest example of an absolutely PPT state:

>> d = 5;
>> rho = eye(d^2);
>> IsAbsPPT(rho)

ans =

     1

Notes

• This function always gives an answer of either 0 or 1 if at least one of the local dimensions is 6 or less. If both local dimensions are 7 or higher, than sometimes an answer of -1 is returned, indicating that the script was unable to determine whether or not RHO is absolutely PPT within a reasonable amount of time (but these situations are still relatively rare).

• Absolutely PPT states are sometimes said to be "PPT from spectrum".

Source code

Click here to view this function's source code on github.