# IsAbsPPT

 Other toolboxes required IsAbsPPT Determines whether or not a density matrix is absolutely PPT none AbsPPTConstraintsInSeparableBall 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