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Lagrangians can differ by a total derivative without altering the equations of motion, thus encoding the same physics. This is true both classically and quantum mechanically. We show, however, that in the context of open quantum systems, two Lagrangians that differ by a total derivative can lead to inequivalent reduced dynamics. While these Lagrangians are connected via unitary transformations at the level of the global system-plus-environment description, the equivalence breaks down after tracing out the environment. We argue that only those Lagrangians for which the canonical and mechanical momenta of the system coincide lead to operationally meaningful dynamics. Applying this insight to quantum electrodynamics (QED), we derive the master equation for bremsstrahlung due to an accelerated nonrelativistic electron upto second order in the interaction. The resulting reduced dynamics predicts decoherence in the position basis and closely matches the Caldeira-Leggett form, thus resolving previous discrepancies in the literature. Our findings have implications for both QED and gravitational decoherence, where similar ambiguities arise.

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024 (Second Terrestrial Very-Long-Baseline Atom Interferometry Workshop, Imperial College, April 2024), building on the initial discussions during the inaugural workshop held at CERN in March 2023 (First Terrestrial Very-Long-Baseline Atom Interferometry Workshop, CERN, March 2023). Like the summary of the first workshop (Abend et al. in AVS Quantum Sci. 6:024701, 2024), this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions (Memorandum of Understanding for the Terrestrial Very Long Baseline Atom Interferometer Study).

We investigate the gravitational Poissonian spontaneous localization (GPSL) model, a hybrid classical-quantum model in which classical Newtonian gravity emerges from stochastic collapses of the mass density operator, and consistently couples to quantum matter. Unlike models based on continuous weak measurement schemes, we show that GPSL ensures vacuum stability; this, together with its applicability to identical particles and fields, makes it a promising candidate for a relativistic generalization. We analyze the model’s general properties, and compare its predictions with those based on continuous weak measurement schemes. Notably, here the gravitational feedback enters entirely through the non-Hermitian jump operators, without modifying the unitary part of the dynamics. We show that this leads to a short-range gravitational back-reaction and permits decoherence rates below those of any model based on continuous weak measurement schemes. We provide explicit examples, including the dynamics of a single particle and a rigid sphere, to illustrate the distinctive phenomenology of the model. Finally, we discuss the experimental testability of GPSL, highlighting both interferometric and non-interferometric strategies to constrain its parameters and distinguish it from competing models.

Stochastic unravelings of Lindblad-type master equations, such as stochastic Schrödinger equations, provide powerful tools to model open quantum systems and continuous measurement processes. The same master equation can be unraveled in different ways; while these unravelings differ at the level of quantum trajectories, by construction they all yield the same averaged dynamics for the density operator. A recent question of both foundational and practical relevance is whether such unravelings can be operationally distinguished, given that certain nonlinear quantities—such as covariances and higher-order moments of conditional expectation values—are unraveling dependent. We show that these quantities cannot be accessed unless the measurement scheme (i.e., the unraveling) is known in advance. This renders any operational protocol to distinguish unravelings fundamentally unfeasible. We further establish that assuming access to such nonlinear quantities without prior knowledge of the unraveling would enable superluminal signaling, violating relativistic causality.

Quantum secure direct communication (QSDC) is an evolving quantum communication framework based on transmitting secure information directly through a quantum channel, without relying on key-based encryption such as in quantum key distribution (QKD). Optical QSDC protocols, utilizing discrete and continuous variable encodings, show great promise for future technological applications. We present the first table-top continuous-variable QSDC proof of principle, analyzing its implementation and comparing the use of coherent against squeezed light sources. A simple beam-splitter attack is analyzed by using Wyner wiretap channel theory. Our study illustrates the advantage of squeezed states over coherent ones for enhanced security and reliable communication in lossy and noisy channels. Our practical implementation, utilizing mature telecom components, could foster secure quantum metropolitan networks compatible with advanced multiplexing systems.

Spontaneous collapse models aim to solve the long-standing measurement problem in quantum mechanics by modifying the theory's dynamics to include objective wave-function collapses. These collapses occur randomly in space, bridging the gap between quantum and classical behavior. A central feature of these models is their dependence on mass density, which directly influences how and when collapse events occur. In this work, we explore a generalized framework in which the collapse dynamics depend on arbitrary functions of the mass density, extending previous models. We analyze the theoretical consistency of these generalizations, investigate their predictions, and compare them with experimental data. Our findings show that only a limited range of mass-dependence functions are viable, with significant implications for the future development and empirical testability of collapse-based models. Importantly, they also indicate that a well-justified model denoted here as PSL shows much more resilience to experimental falsification than standard collapse models.

The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory, but also because it would give a new and unexpected twist to the search for a unified theory of quantum and gravitational phenomena, possibly overcoming the current impasse. The Diósi-Penrose model is the most popular incarnation of this idea. It predicts a progressive breakdown of quantum superpositions when the mass of the system increases; as such, it is susceptible to experimental verification. Current experiments set a lower bound R 0 ≳ 4 Å for the free parameter of the model, excluding some versions of it. In this work we search for an upper bound, coming from the request that the collapse is effective enough to guarantee classicality at the macroscopic scale: we find out that not all macroscopic systems collapse effectively. If one relaxes this request, a reasonable (although to some degree arbitrary) bound is found to be: R 0 ≲ 10 6 Å. This will serve to better direct future experiments to further test the model.

We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves two significant advancements. First, we employ a repetition of unitary gates on a set of n system qubits and, remarkably, only a single ancillary bath qubit representing the environment. It follows that, for the typical case of m locality of the Lindblad operators, we reach an exponential improvement of the number of ancilla in terms of m and up to a polynomial improvement in ancilla overhead for large n with respect to other approaches. Although stochasticity is introduced, requiring multiple circuit realizations, the sampling overhead is independent of the system size. Second, we show that, under fixed accuracy conditions, our algorithm enables a reduction in the number of Trotter steps compared to other approaches, substantially decreasing circuit depth. These advancements hold particular significance for near-term quantum computers, where minimizing both width and depth is critical due to inherent noise in their dynamics.

Quantum computers are inherently affected by noise. While in the long term, error correction codes will account for noise at the cost of increasing physical qubits, in the near term, the performance of any quantum algorithm should be tested and simulated in the presence of noise. As noise acts on the hardware, the classical simulation of a quantum algorithm should not be agnostic on the platform used for the computation. In this paper, we apply the recently proposed noisy gates approach to efficiently simulate noisy optical circuits described in the dual rail framework. The evolution of the state vector is simulated directly, without requiring the mapping to the density matrix framework. Notably, we test the method on both the gate-based and measurement-based quantum computing models, showing that the approach is very versatile. We also evaluate the performance of a photonic variational quantum algorithm to solve the MAX-2-CUT problem. In particular we design and simulate an ansatz, which is resilient to photon losses up to p∼10-3 making it relevant for near-term applications.

In this work the spontaneous electromagnetic radiation from atomic systems, induced by dynamical wave-function collapse, is investigated in the x-ray domain. Strong departures are evidenced with respect to the simple cases considered until now in the literature, in which the emission is either perfectly coherent (protons in the same nuclei) or incoherent (electrons). In this low-energy regime the spontaneous radiation rate strongly depends on the atomic species under investigation and, for the first time, is found to depend on the specific collapse model.

The continuous spontaneous localization (CSL) model is the most studied among collapse models, which describes the breakdown of the superposition principle for macroscopic systems. Here, we derive an upper bound on the parameters of the model by applying it to the rotational noise measured in a recent short-distance gravity experiment [Lee, Phys. Rev. Lett. 124, 101101 (2020)0031-900710.1103/PhysRevLett.124.101101]. Specifically, considering the noise affecting the rotational motion, we found that despite being a tabletop experiment the bound is only one order of magnitude weaker than that from LIGO for the relevant values of the collapse parameter. Further, we analyze possible ways to optimize the shape of the test mass to enhance the collapse noise by several orders of magnitude and eventually derive stronger bounds that can address the unexplored region of the CSL parameters space.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more kilometer–scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

Károlyházy’s original proposal, suggesting that space-time fluctuations could be a source of decoherence in space, faced a significant challenge due to an unexpectedly high emission of radiation (13 orders of magnitude more than what was observed in the latest experiment). To address this issue, we reevaluated Károlyházy’s assumption that the stochastic metric fluctuation must adhere to a wave equation. By considering more general correlation functions of space-time fluctuations, we resolve the problem and consequently revive the aforementioned proposal.

We present a novel method for simulating the noisy behavior of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behavior of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at the link, https://pypi.org/project/quantum-gates.

Noninterferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on the fact that, according to these models, the dynamics is driven by noise that, besides collapsing the wave function in space, generates a diffusive motion with characteristic signatures, which, though small, can be tested. The noninterferometric approach might seem applicable only to those models that implement the collapse through noisy dynamics, not to any model, that collapses the wave function in space. Here, we show that this is not the case: under reasonable assumptions, any collapse dynamics (in space) is diffusive. Specifically, we prove that any space-translation covariant dynamics that complies with the no-signaling constraint, if collapsing the wave function in space, must change the average momentum of the system and/or its spread.

We study the effects of the electromagnetic vacuum on the motion of a nonrelativistic electron. First we derive the equation of motion for the expectation value of the electron's position operator. We show how this equation has the same form as the classical Abraham-Lorentz equation but, at the same time, is free of the well-known runaway solution. Second, we study decoherence induced by vacuum fluctuations. We show that decoherence due to vacuum fluctuations that appears at the level of the reduced density matrix of the electron, obtained after tracing over the radiation field, does not correspond to actual irreversible loss of coherence.

In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question ’what are collapse models (and in general any physical theory) about?’; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role.

Around 40 years have passed since the first pioneering works introduced the possibility of using quantum physics to enhance communications safety. Nowadays, quantum key distribution (QKD) exited the physics laboratories to become a mature technology, triggering the attention of States, military forces, banks, and private corporations. This work takes on the challenge of bringing QKD closer to a consumer technology: deployed optical fibers by telecommunication companies of different States have been used to realize a quantum network, the first-ever connecting three different countries. This work also emphasizes the necessity of networks where QKD can come up besides classical communications, whose coexistence currently represents the main limitation of this technology. This network connects Trieste to Rijeka and Ljubljana via a trusted node in Postojna. A key rate of over 3 kbps in the shortest link and a 7-hour-long measurement demonstrate the system's stability and reliability. The network has been used to present the QKD at the G20 Digital Ministers' Meeting in Trieste. The experimental results, together with the interest that one of the most important events of international politics has attracted, showcase the maturity of the QKD technology bundle, placing it in the spotlight for consumer applications in the near term.

Models of dynamical wave function collapse consistently describe the breakdown of the quantum superposition with the growing mass of the system by introducing non-linear and stochastic modifications to the standard Schrödinger dynamics. Among them, Continuous Spontaneous Localization (CSL) was extensively investigated both theoretically and experimentally. Measurable consequences of the collapse phenomenon depend on different combinations of the phenomenological parameters of the model—the strength (Formula presented.) and the correlation length (Formula presented.) —and have led, so far, to the exclusion of regions of the admissible ((Formula presented.)) parameters space. We developed a novel approach to disentangle the (Formula presented.) and (Formula presented.) probability density functions, which discloses a more profound statistical insight.

Modern physics lays its foundations on the pillars of Quantum Mechanics (QM), which has been proven successful to describe the microscopic world of atoms and particles, leading to the construction of the Standard Model. Despite the big success, the old open questions at its very heart, such as the measurement problem and the wave function collapse, are still open. Various theories consider scenarios which could encompass a departure from the predictions of the standard QM, such as extra-dimensions or deformations of the Lorentz/Poincaré symmetries. At the Italian National Gran Sasso underground Laboratory LNGS, we search for evidence of new physics proceeding from models beyond standard QM, using radiation detectors. Collapse models addressing the foundations of QM, such as the gravity-related Diósi–Penrose (DP) and Continuous Spontaneous Localization (CSL) models, predict the emission of spontaneous radiation, which allows experimental tests. Using a high-purity Germanium detector, we could exclude the natural parameterless version of the DP model and put strict bounds on the CSL one. In addition, forbidden atomic transitions could prove a possible violation of the Pauli Exclusion Principle (PEP) in open and closed systems. The VIP-2 experiment is currently in operation, aiming at detecting PEP-violating signals in Copper with electrons; the VIP-3 experiment upgrade is foreseen to become operative in the next few years. We discuss the VIP-Lead experiment on closed systems, and the strong bounds it sets on classes of non-commutative quantum gravity theories, such as the (Formula presented.) –Poincaré theory.