This MATLAB package is built for quantum entanglement detection and constructing positive maps which are not completely positive.
PnCP has been tested on Ubuntu and MacOS.
To use PnCP, add the entire matlab archive to path. The 'demo.m' file demonstrates the two main commands.
To generate a (rational) positive map use the
Gen_PnCP command, e.g.,
Phi = Gen_PnCP(3,3,'mosek','CNR',2,2,rationalize=1);
Details for the input arguments can be learnt using
help('Gen_PnCP')
Given a quantum state along with its density matrix
, to generate a rational pncp map which can detect the entanglement of
, use the command
Ent_PnCP, e.g.
output = Ent_PnCP(M,N,m,P,attempts);
Phi = output{1,1};
ampliation = output{1,2};
where are the dimensions of the composite systems for
,
is the dimension of the codomain of the desired
and
attemps is the number of trials to conduct.
Details for the input arguments can be learnt using
help('Ent_PnCP')
If only a floating point map is required, there is a similar command
EntF_PnCP.
For a list of entangled quantum states which are identified via PnCP, and their identifying pcnp map, see the "Catalogue of Examples.ipynb" file.
PnCP is released under the conditions of the GNU General Public License 3.0
Performance standards, examples and details of PnCP can be found in the article
[1] Practical construction of positive maps which are not completely positive.
If you use PnCP, please cite the above article for its use.
The construction used in PnCP is from the article
[2] There are many more positive maps than completely positive maps.
Abhishek Bhardwaj : Abhishek 'dot' Bhardwaj 'dot' Maths 'at' gmail 'dot' com