  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.
