Quantum information processing and relativistic quantum fields

• Published in: Classical and quantum gravity Vol. 31; no. 7; pp. 75007 - 75020
• Main Authors: Benincasa, Dionigi M T, Borsten, Leron, Buck, Michel, Dowker, Fay
• Format: Journal Article
• Language: English
• Published: IOP Publishing 07.04.2014
• Subjects: Couples; Detectors; Frames; Holes; Mathematical analysis; measurement; quantum fields; Quantum gravity; relativistic quantum information; Signalling; Transformations
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/0264-9381/31/7/075007

It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom-qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light-crossing time of the cavity.