Is Absolute Separability Determined by the Partial Transpose?

A small collection of MATLAB scripts that supplement the content in the following paper:

[AJR14] S. Arunachalam, N. Johnston, V. Russo Is Absolute Separability Determined by the Partial Transpose? arXiv:1405.5853

See Lemma 2 and Lemma 5 in [AJR14] for more information in regards to the MATLAB scripts.

Tested with MATLAB 7.10.0 (R2010a)

Requires:

• CVX -- www.cvxr.com
• QETLAB -- http://www.qetlab.com

Usage

In ChoiExample.m, the script determines the eigenvalue range described in Lemma 5 for the Choi Map by using EigenInterval.m, and also runs the semidefinite program (SDP) described in Eq. (4) of 1 in EigenRangeSDP.m. A second example of using the reduction map is also given.

In IsWernerAbsPPTCheck.m the script cycles through all Werner -1/(n-1) states and determines if the constraint matrices generated are absolutely PPT. For n = 1...140 this has been checked to be true. Checking for higher values of n is computationally taxing.