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SeCQC: An open-source program code for the numerical Search for the classical Capacity of Quantum Channels


Jiangwei Shang, Kean Loon Lee, and Berthold-Georg Englert

Abstract

SeCQC is an open-source program code which implements a Numerical Search for the classical Capacity of Quantum Channels (SeCQC) by using an iterative method. Given a quantum channel, SeCQC finds the statistical operators and POVM outcomes that maximize the accessible information, and thus determines the classical capacity of the quantum channel. The optimization procedure is realized by using a steepest-ascent method that follows the gradient in the POVM space, and also uses conjugate gradients for speed-up.

License Agreement

SeCQC is an open-source program that, given a quantum channel, implements a Numerical Search for the classical Capacity of Quantum Channels. It is a derivative of the open-source program code SOMIM (see Ref. [1]). Copyright © 2010 J.W. Shang, K.L. Lee and B.-G. Englert.

SeCQC is a free software: You can redistribute it and/or modify it under the terms of the GNU General Public License Version 3 as published by the Free Software Foundation.

SeCQC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of FITNESS or MERCHANTABILITY FOR PARTICULAR PURPOSE. See the GNU General Public License at http://www.gnu.org/licenses/ for details.

What can SeCQC be used for?

Given a certain quantum channel, SeCQC finds the statistical operators as well as POVM outcomes that maximize the accessible information (AI), and thus determines the classical capacity of the quantum channel.

The calculation is performed using a combination of the steepest-ascent method (see Ref. [2] and Section 11.5 in Ref. [3]) and the conjugate-gradients (CG) method [4]. The percentage chance to calculate with one method or the other can be specified by the user. The implementation in SeCQC also makes use of the golden-section search method.

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Contact information

Please send your comments, suggestions, or bug reports to the following email account: secqc@quantumlah.org.

References

[1] K. L. Lee, J. W. Shang, W. K. Chua, S. Y. Looi, and B.-G. Englert, SOMIM: An open-source program code for the numerical Search for Optimal Measurements by an Iterative Method, arXiv:0805.2847 (http://arxiv.org/abs/0805.2847), SOMIM web site.
[2] J. Rehacek, B.-G. Englert, and D. Kaszlikowski, Iterative procedure for computing accessible information in quantum communication, Phys. Rev. A 71, 054303 (2005); eprint available at http://arxiv.org/pdf/quant-ph/0408134.
[3] J. Suzuki, S. M. Assad, and B.-G. Englert, "Accessible information about quantum states: An open optimization problem", Chapter 11 in Mathematics of Quantum Computation and Quantum Technology, edited by G. Chen, S. J. Lomonaco, and L. Kauffman (Chapman & Hall/CRC, Boca Raton 2007), pp. 309-348; also available at http://physics.nus.edu.sg/~phyebg/Papers/135.pdf.
[4] W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, "Minimization or Maximazation of Functions", Chapter 10 in Numerical Recipes in C: The Art of Scientific Computating, (Cambridge University Press, 2nd edition 1992), pp. 394-455.



Latest update: SeCQC version 1.0 28/07/2011