Quantum Information Processing and Relativistic Quantum Fields

TL;DR

This paper demonstrates that certain idealized measurements and unitary operations on relativistic quantum fields can enable superluminal signalling, challenging causality assumptions and prompting reconsideration of measurement models.

Contribution

It reveals that ideal measurements and specific unitary transformations in relativistic quantum fields can lead to superluminal signalling, highlighting limitations of current measurement models.

Findings

Ideal wave packet measurements enable superluminal signalling.

Unitary transformations between orthogonal states can also cause superluminal effects.

Detector models coupling to finite frequencies may violate causality.

Abstract

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.