Abstract We present our program for the development of quantum informational concepts in relativistic systems in terms of the unequal-time correlation functions of quantum fields. We employ two formalisms that provide the basis for further developments. (i) The Quantum Temporal Probabilities (QTP) Method for quantum field measurements and (ii) the Closed-Time-Path (CTP) formalism for causal time evolutions. We present the main ideas of QTP and we show how it relates to the CTP formalism, allowing us to express concepts of measurement theory in terms of path-integrals. We also present many links of our program to non-equilibrium quantum field theories. Details can be found in a recent paper by the authors [1].
Abstract We present our program for the development of quantum informational concepts in relativistic systems in terms of the unequal-time correlation functions of quantum fields. We employ two formalisms that provide the basis for further developments. (i) The Quantum Temporal Probabilities (QTP) Method for quantum field measurements and (ii) the Closed-Time-Path (CTP) formalism for causal time evolutions. We present the main ideas of QTP and we show how it relates to the CTP formalism, allowing us to express concepts of measurement theory in terms of path-integrals. We also present many links of our program to non-equilibrium quantum field theories. Details can be found in a recent paper by the authors [1].
Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest.
This paper continues on the program of developing a relativistic quantum information theory in terms of unequal-time correlation functions in quantum field theory (QFT) (Anastopoulos et al., 2023). Here, we focus on the definition of quantum resources from the irreducibly quantum behavior contained in the correlation functions of a QFT. We explain how set-ups with N particle detectors probe the information in the high order field correlation functions. Our main object is the associated hierarchy of probability densities of N -detector events. We show that classical probabilistic hierarchies are subject to two conditions: Kolmogorov additivity and measurement independence. QFT violates those conditions, and the degree of violation enables us to define novel quantum resources. We give specific examples in set-ups where the main observables are the times of particle detection events. The new resources capture instances of irreducibly quantum behavior that differs from the quantum behavior encapsulated in Bell inequalities. An interesting byproduct of our analysis is a relativistic state reduction rule for particles detected through scattering.
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential relativistic principles of locality, causality, and Lorentz covariance, and are therefore inadequate for quantum field theoretic settings. While most existing work focuses on scalar fields, realistic particles possess spin, polarization, and internal degrees of freedom that introduce new conceptual and operational challenges. To this end, we employ the Quantum Temporal Probabilities (QTP) framework for relativistic measurements to describe electromagnetic, Dirac, and internally structured scalar fields. Our results include probabilities for the time-of-arrival that take spin/polarization into account, generalized photodetection formulas beyond Glauber's theory, an unambiguous derivation of the particle oscillation formula together with its limitations, and a first-principles analysis of relativistic qudits.
We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several other approaches: indefinite causal structures, consistent histories, generalised quantum games, out-of-time-order correlations(OTOCs), and path integrals. We establish close relationships among these space-time approaches in non-relativistic quantum theory, resulting in a unified picture. With the exception of amplitude-weighted correlations in the path integral formalism, in a given experiment, temporal correlations in the different approaches are the same or operationally equivalent.
We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of the detector. We explicitly construct the probabilities associated to n measurement events, while treating the spacetime coordinates of the events are random variables. These probabilities define a linear functional of a 2n unequal time correlation function of the field, and thus, they are Poincaré covariant. The probability assignment depends on the properties of the measurement apparatuses, their state of motion, intrinsics dynamics, initial states and couplings to the measured field. For each apparatus, this information is contained in a function, the detector kernel, that enters into the probability assignment. In a companion paper, we construct the detector kernel for different types of measurement.
Requiring causality on measurements in quantum field theory seems to impose strong conditions on a self-adjoint operator to be really measurable. This may seem limiting and artificial in the operator language of algebraic quantum field theory (AQFT), but is essential for a truly relativistic theory. Recent publications attempt to deal with this issue by including the apparatus into the formalism, connecting AQFT with measurement theory, but other options have been suggested. In this essay, I discuss the causality conditions on self-adjoint operators both in the language of AQFT and in the language of quantum information theory. I then present measurement theory in AQFT, modelling the apparatus as a quantum field with coupling to the measured system restricted to a region of spacetime. I highlight how this approach leads to a causally well behaved theory. Finally, I attempt to formulate the causality conditions on measurements in the Feynman path integral approach, using the concept of decoherent histories. I claim that the path integral approach has problems with causality similar to the operator based approaches and that even here causality is an a posteriori condition.