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InSeparableBall |cat=List of functions#Ball_..."

2014-11-15T04:01:49Z

Created page with "{{Function |name=IsAbsPPT |desc=Determines whether or not a density matrix is absolutely PPT |rel=AbsPPTConstraints<br />InSeparableBall |cat=List of functions#Ball_..."

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{{Function
|name=IsAbsPPT
|desc=Determines whether or not a density matrix is absolutely PPT
|rel=[[AbsPPTConstraints]]<br />[[InSeparableBall]]
|cat=[[List of functions#Ball_of_separability|Ball of separability]]
|upd=November 14, 2014
|v=0.60}}
<tt>'''IsAbsPPT'''</tt> is a [[List of functions|function]] that determines whether or not a density matrix $\rho$ is "absolutely PPT" (that is, whether or not $U\rho U^\dagger$ has [[IsPPT|positive partial transpose]] for all unitary matrices $U$). The conditions that determine whether or not a state is absolutely PPT were derived in <ref name="Hil07">R. Hildebrand. Positive partial transpose from spectra. ''Phys. Rev. A'', 76:052325, 2007. E-print: [http://arxiv.org/abs/quant-ph/0502170 arXiv:quant-ph/0502170]</ref>.

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==
* <tt>IAPPT = IsAbsPPT(RHO)</tt>
* <tt>IAPPT = IsAbsPPT(RHO,DIM)</tt>

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

==Examples==
The maximally-mixed state is the simplest example of an absolutely PPT state:
<syntaxhighlight>
>> d = 5;
>> rho = eye(d^2);
>> IsAbsPPT(rho)

ans =

1
</syntaxhighlight>

==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 <tt>RHO</tt> 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".

{{SourceCode|name=IsAbsPPT}}

==References==
<references />

IsAbsPPT - Revision history

Nathaniel: Created page with "{{Function |name=IsAbsPPT |desc=Determines whether or not a density matrix is absolutely PPT |rel=AbsPPTConstraintsInSeparableBall |cat=List of functions#Ball_..."

Nathaniel: Created page with "{{Function |name=IsAbsPPT |desc=Determines whether or not a density matrix is absolutely PPT |rel=AbsPPTConstraints
InSeparableBall |cat=List of functions#Ball_..."