Miscellaneous in Quantum Theory and Information

Andrew Whitaker

Xian Shi

Abstract Finite tight frames play an important role in miscellaneous areas, including quantum information theory. Here we apply a class of tight frames, equiangular tight frames, to address the problem of detecting the entanglement of bipartite states. Here we derive some entanglement criteria based on positive operator-valued measurements built from equiangular tight frames. We also present a class of entanglement witnesses based on the equiangular tight frames. At last, we generalize the entanglement criterion for bipartite systems to multipartite systems.

M. Kibler

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity.We motivate why such algebras are interesting for fractional supersymmetric quantum mechanics, angular momentum theory and quantum information.More precisely, quon algebras are used for (i) a realization of a generalized Weyl-Heisenberg algebra from which it is possible to associate a fractional supersymmetric dynamical system, (ii) a polar decomposition of SU 2 and (iii) a construction of mutually unbiased bases in Hilbert spaces of prime dimension.We also briefly discuss (symmetric informationally complete) positive operator valued measures in the spirit of (iii).

Teodor Strömberg

Vlatko Vedral

Abstract In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.