This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.
This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.
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.
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 analyze potential violations of causality in Unruh DeWitt-type detector models in relativistic quantum information. We proceed by first studying the relation between faster-than-light signaling and the causal factorization of the dynamics for multiple detector-field interactions. We show in what way spatially extended nonrelativistic detector models predict superluminal propagation of the field's initial conditions. We draw parallels between this characteristic of detector models, stemming from their nonrelativistic dynamics, and Sorkin's ``impossible measurements on quantum fields'' [R. D. Sorkin, in Directions in General Relativity: Proceedings of the 1993 International Symposium, Maryland (Cambridge University Press, 1993), Vol. 2, pp. 293--305.]. Based on these features, we discuss the validity of measurements in quantum field theory when performed with nonrelativistic particle detectors.
Pointlike systems coupled to quantum fields are often employed as toy models for measurements in quantum field theory. In this paper, we identify the field observables recorded by such models. In the case of detector models that work in the strong coupling regime, we show that the detector's pointer variable is correlated with time-extended smeared field amplitudes, and it is insensitive to the particle content of the field's state. Then, we show that detector models that work in the weak coupling regime can account for particle phenomenology, such as the existence of a particlelike time-of-arrival and resonant behavior. Finally, we develop an improved field-detector interaction model, adapting the formalism of quantum Brownian motion, that is exactly solvable. This model confirms the association of field and particle properties in the strong and weak coupling regimes, respectively. Further, it can also describe the intermediate regime, in which the field-particle characteristics ``merge.'' In contrast to standard perturbation techniques, this model also recovers the relativistic Breit-Wigner resonant behavior in the weak coupling regime. The modulation of particle-field duality by a single tunable parameter is a novel feature that is, in principle, experimentally accessible.
Based on our results for the detector-field system in Gaussian states, I am addressing the following issues about the quantum dynamics of atoms or detectors moving in a relativistic quantum field: First, the dynamics of the detectors as an open quantum quantum system, hence the entanglement creation and sudden death processes between the detectors, are non-Markovian in general. Second, the excitations of the accelerated detectors in the Unruh effect depend only on the kinematics of the detectors. The event horizon for the detector is not essential in this effect, and the particle notion of the quantum field is not needed here. Third, entanglement dynamics of the detectors are independent of time-slicing scheme. Local projective measurements on point-like detectors are also consistent in different time-slicing schemes even in the presence of relativistic quantum fields.
We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the initial state. We also show that an experimental distinction of different probability assignments is possible especially in near-field measurements. We also analyze causality in relativistic measurements. We consider a quantum state obtained by a spacetime-localized operation on the vacuum, and we show that detection probabilities are typically characterized by small transient non-causal terms. We explain that these terms originate from Feynman propagation of the initial operation, because the Feynman propagator does not vanish outside the light cone. We discuss possible ways to restore causality, and we argue that this may not be possible in measurement models that involve switching the field–apparatus coupling on and off.