IsAbsPPT

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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 [1].

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.

References

  1. R. Hildebrand. Positive partial transpose from spectra. Phys. Rev. A, 76:052325, 2007. E-print: arXiv:quant-ph/0502170