Quantum information and relativity theory

Abstract

Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its description are Kraus matrices and positive operator valued measures (POVMs). Special relativity imposes severe restrictions on the transfer of information between distant systems. Quantum entropy is not a Lorentz covariant concept. Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps. Quantum field theory, which is necessary for a consistent description of interactions, implies a fundamental trade-off between detector reliability and localizability. General relativity produces new, counterintuitive effects, in particular when black holes (or more generally, event horizons) are involved. Most of the current concepts in quantum information theory may then require a reassessment.

Violating Bell’s inequalities in vacuum

“…In this limit, the effects of both detector pair-creation, and the "leakage" of each detector's wavefunction to the outside of its localization region, become exponentially small, of the order of ∼ exp(− 2cMR ) [10,11]. Note, that this ensures that the overlap between the detectors' wavefunctions is negligible.…”

Sudden change in quantum and classical correlations and the Unruh effect

“…[17] for a recent review). This is not only interesting in its own right but may also have practical importance because of new trends of implementing quantum-information protocols at global scales through the use of satellite systems [18][19][20][21][22].…”

Classical correlation and quantum discord sharing of Dirac fields in noninertial frames

“…The integration of the quantum information and another fundamental part of modern physics theories-relativity theory gives birth to the theory of the relativistic quantum information [1][2][3]. It is believed that the investigation of the quantum correlation in a relativistic framework is not only helpful to understand some key questions in the quantum information theory, but also plays an important role in the study of the entropy and information paradox [4,5] of the black hole.…”