libCreme: An optimization library for evaluating convex-roof entanglement measures

• Published in: Computer physics communications Vol. 183; no. 1; pp. 155 - 165
• Main Authors: Röthlisberger, Beat, Lehmann, Jörg, Loss, Daniel
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 2012
• Subjects: Algorithms; Computer programs; Convex roof; Entanglement; Entanglement measure; Libraries; Matlab; Octaves; Optimization; Running; Convex roof; Entanglement measure
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2011.08.012

We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focusing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems. Program title: libCreme Catalogue identifier: AEKD_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKD_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU GPL version 3 No. of lines in distributed program, including test data, etc.: 4323 No. of bytes in distributed program, including test data, etc.: 70 542 Distribution format: tar.gz Programming language: Matlab/Octave and C/C++ Computer: All systems running Matlab or Octave Operating system: All systems running Matlab or Octave Classification: 4.9, 4.15 Nature of problem: Evaluate convex-roof entanglement measures. This involves solving a non-linear (unitary) optimization problem. Solution method: Two algorithms are provided: A conjugate-gradient method using a differential-geometric approach and a quasi-Newton method together with a mapping to Euclidean space. Running time: Typically seconds to minutes for a density matrix of a few low-dimensional systems and a decent implementation of the pure-state entanglement measure. ► We present two independent algorithms to evaluate convex-roof entanglement measures. ► One algorithm is a conjugate-gradient method operating on the constraint manifold. ► The other one is a quasi-Newton method in combination with a mapping to Euclidean space. ► Both algorithms can be applied to convex-roof extensions of any pure-state measure.