# IsAbsPPT

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IsAbsPPT | |

Determines whether or not a density matrix is absolutely PPT | |

Other toolboxes required | none |
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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

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