Quantum information and relativity theory
Abstract
This article discusses the intimate relationship between quantum mechanics, information theory, and relativity theory. Taken together these are the foundations of presentday theoretical physics, and their interrelationship is an essential part of the theory. The acquisition of information from a quantum system by an observer occurs at the interface of classical and quantum physics. The authors review the essential tools needed to describe this interface, i.e., Kraus matrices and positiveoperatorvalued measures. They then discuss how special relativity imposes severe restrictions on the transfer of information between distant systems and the implications of the fact that quantum entropy is not a Lorentzcovariant concept. This leads to a discussion of how it comes about that Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps. Quantum field theory is, of course, necessary for a consistent description of interactions. Its structure implies a fundamental tradeoff between detector reliability and localizability. Moreover, general relativity produces new and counterintuitive effects, particularly when black holes (or, more generally, event horizons) are involved. In this more general context the authors discuss how most of the current concepts in quantum information theory may require a reassessment.
 Publication:

Reviews of Modern Physics
 Pub Date:
 January 2004
 DOI:
 10.1103/RevModPhys.76.93
 arXiv:
 arXiv:quantph/0212023
 Bibcode:
 2004RvMP...76...93P
 Keywords:

 03.30.+p;
 05.70.Ce;
 02.20.Uw;
 03.65.Fd;
 02.10.Yn;
 01.30.Rr;
 Special relativity;
 Thermodynamic functions and equations of state;
 Quantum groups;
 Algebraic methods;
 Matrix theory;
 Surveys and tutorial papers;
 resource letters;
 Quantum Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 32 pages RevTeX4,4 figures, submitted to RMP. Some parts of the text deleted, many others substantially expanded and updated. One figure and two appendices added. Many new references