Quantum Field Theory based Quantum Information: Measurements and Correlations

TL;DR

This paper develops a relativistic quantum information framework using quantum field theory, combining measurement formalism and causal evolution, with applications to detector models and quantum correlations.

Contribution

It introduces a novel combination of Quantum Temporal Probabilities and Closed-Time-Path formalisms for relativistic quantum measurements and correlations in quantum field theory.

Findings

Derived new formulas for measurement probabilities in QTP formalism.

Demonstrated relations between QTP and CTP formalisms.

Showed how detector models and photodetection theories emerge as special cases.

Abstract

This is the first in a series of papers aiming to develop a relativistic quantum information theory in terms of unequal-time correlation functions in quantum field theory. In this work, we highlight two formalisms which together can provide a useful theoretical platform suitable for further developments: 1) Quantum field measurements using the Quantum Temporal Probabilities (QTP) method; 2) Closed-Time-Path (CTP) formalism for causal time evolutions. QTP incorporates the detector into the quantum description, while emphasising that the records of measurement are macroscopic, and they can be expressed in terms of classical spacetime coordinates. We first present a new, elementary derivation of the QTP formulas for the probabilities of n measurement events. We then demonstrate the relation of QTP with the Closed-Time-Path formalism, by writing an explicit formula that relates the associated generating functionals. We exploit the path integral representation of the CTP formalism, in order to express the measured probabilities in terms of path integrals. After this, we provide some simple applications of the QTP formalism. In particular, we show how Unruh-DeWitt detector models and Glauber's photodetection theory appear as limiting cases . Finally, with quantum correlation being the pivotal notion in relativistic quantum information and measurements, we highlight the role played by the CTP two-particle irreducible effective action which enables one to tap into the resources of non-equilibrium quantum field theory for our stated purpose.