Home // International Journal On Advances in Security, volume 3, numbers 1 and 2, 2010 // View article

Information Geometrical Approximation of Quantum Channel Security

Authors:
Laszlo Gyongyosi
Sandor Imre

Keywords: quantum cryptography; quantum cloning; quantum informational distance

Abstract:
The problem of quantum cloning is closely connected to quantum cryptography. While an eavesdropper on a quantum channel cannot copy perfectly the sent quantum states, in many cases a cloning machine is known to be the most powerful eavesdropping strategy with which to counter quantum cryptographic protocols. In this paper, effective computational geometrical methods are used to analyze cloning activity on a quantum channel. A geometric approach is demonstrated which analyzes the security of the quantum channel, based on quantum relative entropy and Delaunay triangulation on the Bloch sphere. In the security analysis, an approximation algorithm derived from classical computational geometry is used to determine the smallest enclosing ball of balls using core-sets. An improved version is presented which is able to obtain a more effective approximation algorithm in quantum space, while the performances of the proposed geometric algorithms are compared.

Pages: 52 to 67

Copyright: Copyright (c) to authors, 2010. Used with permission.

Publication date: September 5, 2010

Published in: journal

ISSN: 1942-2636