Two-spinors, oscillator algebras, and qubits: aspects of manifestly covariant approach to relativistic quantum information

Marek Czachor

doi:10.1007/s11128-010-0163-4

Two-spinors, oscillator algebras, and qubits: aspects of manifestly covariant approach to relativistic quantum information

Abstract

The first part of the paper reviews applications of 2-spinor methods to relativistic qubits (analogies between tetrads in Minkowski space and 2-qubit states, qubits defined by means of null directions and their role for elimination of the Peres-Scudo-Terno phenomenon, advantages and disadvantages of relativistic polarization operators defined by the Pauli-Lubanski vector, manifestly covariant approach to unitary representations of inhomogeneous SL(2,C)). The second part deals with electromagnetic fields quantized by means of harmonic oscillator Lie algebras (not necessarily taken in irreducible representations). As opposed to non-relativistic singlets one has to distinguish between maximally symmetric and EPR states. The distinction is one of the sources of 'strange' relativistic properties of EPR correlations. As an example, EPR averages are explicitly computed for linear polarizations in states that are antisymmetric in both helicities and momenta. The result takes the familiar form ±p cos 2(α −β) independently of the choice of representation of harmonic oscillator algebra. Parameter p is determined by spectral properties of detectors and the choice of EPR state, but is unrelated to detector efficiencies. Brief analysis of entanglement with vacuum and vacuum violation of Bell's inequality is given. The effects are related to inequivalent notions of vacuum states. Technical appendices discuss details of the representation I employ in field quantization. In particular, M-shaped delta-sequences are used to define Dirac deltas regular at zero.

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Marek Czachor prof. dr hab.

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Publication version: Accepted or Published Version
DOI:: Digital Object Identifier (open in new tab) 10.1007/s11128-010-0163-4
License: Copyright (2010 Springer Science+Business Media, LLC)

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: Quantum Information Processing no. 9, pages 171 - 232,
ISSN: 1570-0755
Language:: English
Publication year:: 2010
Bibliographic description:: Czachor M.: Two-spinors, oscillator algebras, and qubits: aspects of manifestly covariant approach to relativistic quantum information// Quantum Information Processing. -Vol. 9, nr. Iss. 2 (2010), s.171-232
DOI:: Digital Object Identifier (open in new tab) 10.1007/s11128-010-0163-4
Verified by:: Gdańsk University of Technology