arXiv subjects

Jan Mandrysch

Publications and source records attributed to Jan Mandrysch.

5 recordsLinked to original sources

arXiv2026

Causality and realizability of local operations in quantum field theory

As noted by Sorkin, regarding quantum instruments whose Kraus operators are localizable within some spacetime region as operations accessible therein leads to superluminal communication. This so-called Sorkin paradox can be resolved by further constraining the set of allowed local operations in quantum field theory (QFT). In this spirit, Fewster and Verch proposed a framework for local QFT operations that generalizes non-relativistic quantum measurement theory and does not lead to Sorkin-like paradoxes. Shortly afterwards, Jubb (and later Oeckl) identified the minimal conditions that QFT instruments must satisfy to be compatible with Einstein's causality. In this work, we study both approaches in the quantum field theory of the free scalar field. First, we prove that a very wide class of causal instruments is FV-realizable: namely, those whose measurement channels are random displacements of the field operators. As we show, this class allows implementing arbitrary instruments in a heralded, probabilistic way, as well as non-demolition measurements deterministically. Second, we construct examples of causal channels that do not admit an approximate FV realization. Some of such causal, not FV-realizable channels violate basic physical principles, so they should not be part of any measurement theory for QFT. Third, we investigate the difficulty of characterizing the set of QFT channels that can be generated through the composition of several FV schemes. In this regard, we find a countable family of simple QFT channels for which no Turing machine can discriminate between channels within or far away from the implementable set.

hep-th↗

arXiv2025

Relative entropy for locally squeezed states

Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy remain notoriously difficult. Thus far, results in closed form have only been obtained for ground states, coherent states, and, more recently, single-mode squeezed states. In this work, we extend the analysis to multi-mode squeezed states, imposing that the squeezing generators be local either in space or in spacetime, which results in a continuum of squeezed modes. We provide a detailed and self-contained analysis of such states for a free scalar quantum field on Minkowski spacetime, connecting also with older results on the essential self-adjointness of the Wick square, and showing that they lie in the folium of the Minkowski vacuum representation. Although the local squeezing is natural from a foundational standpoint, we uncover a severe incompatibility between locality and squeezing: the relative entropy between a locally squeezed state and the vacuum generally diverges, however small the squeezing is. This shows that while locally squeezed states are well-defined elements of the state space of a free quantum field, they are infinitely different from the vacuum, in contrast to coherent states whose relative entropy with respect to the vacuum is finite.

quant-ph↗

arXiv2024

Quantum Field Measurements in the Fewster-Verch Framework

The Fewster-Verch (FV) framework provides a local and covariant approach for defining measurements in quantum field theory (QFT). Within this framework, a probe QFT represents the measurement device, which, after interacting with the target QFT, undergoes an arbitrary local measurement. Remarkably, the FV framework is free from Sorkin-like causal paradoxes and robust enough to enable quantum state tomography. However, two open issues remain. First, it is unclear if the FV framework allows conducting arbitrary local measurements. Second, if the probe field is interpreted as physical and the FV framework as fundamental, then one must demand the probe measurement to be itself implementable within the framework. That would involve a new probe, which should also be subject to an FV measurement, and so on. It is unknown if there exist non-trivial FV measurements for which such an ``FV-Heisenberg cut" can be moved arbitrarily far away. In this work, we advance the first problem by proving that Gaussian-modulated measurements of locally smeared fields fit within the FV framework. We solve the second problem by showing that any such measurement admits a movable FV-Heisenberg cut. As a technical byproduct, we establish that state transformations induced by finite-rank perturbations of the classical phase space underlying a linear scalar field preserve the Hadamard property.

hep-th↗

arXiv2023

Numerical results on Quantum Energy Inequalities in Integrable Models at the Two-Particle level

In this article, we study the impact of self-interaction and multiparticle states on sustaining negative energies in relativistic quantum systems. For physically reasonable models, one usually requires bounds on both magnitude and duration of the accumulation of negative energy, typically given in form of a quantum energy inequality (QEI). Such bounds have applications in semiclassical gravity where they exclude exotic spacetime geometries and imply the formation of singularities. The essence of this article is a novel numerical method for determining optimal QEI bounds at the one- or two-particle level, extending previous work focused on the one-particle case and overcoming a new type of technical challenge associated with the two-particle scenario. Our method is tailored for integrable models in quantum field theory constructed via the S-matrix boostrap. Applying the method to a representative model, the sinh-Gordon model, we confirm self-interaction as the source of negative energy, with stronger interactions leading to more pronounced negativities. Moreover, we establish the validity of QEIs and the averaged weak energy condition (AWEC) at the one- and two-particle level. Lastly, we identify a constrained one-parameter class of nonminimal stress tensor expressions satisfying QEIs at both levels, with more stringent constraints emerging from the QEI bounds at the two-particle level.

hep-th↗

arXiv2023

Quantum energy inequalities in integrable models with several particle species and bound states

We investigate lower bounds to the time-smeared energy density, so-called quantum energy inequalities (QEI), in the class of integrable models of quantum field theory. Our main results are a state-independent QEI for models with constant scattering function and a QEI at one-particle level for generic models. In the latter case, we classify the possible form of the stress-energy tensor from first principles and establish a link between the existence of QEIs and the large-rapidity asymptotics of the two-particle form factor of the energy density. Concrete examples include the Bullough-Dodd, the Federbush, and the $O(n)$-nonlinear sigma models.

math-ph↗