arXiv subjects

Marcel Reginatto

Publications and source records attributed to Marcel Reginatto.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement of quantum systems via a classical mediator in hybrid van Hove theory

It is a matter of ongoing discussion whether quantum states can become entangled while only interacting via a classical mediator. This lively debate is deeply interwoven with the question of whether entanglement studies can prove the quantum nature of gravity. However, the answer to this fundamental question depends crucially on which hybrid quantum-classical theory is used. In this letter, we demonstrate that entanglement by a classical mediator is possible within the framework of hybrid van Hove theory, showing that existing no-go theorems on that matter do not universally apply to hybrid theories in general. After briefly recapitulating the key features of the hybrid van Hove theory, we show this using the example of two quantum spins coupled by a classical harmonic oscillator. By deriving the spin density matrix for this scenario and comparing it to its equivalent for a pure quantum system, we show that entanglement between the two spins is generated in both cases. Conclusively, this is illustrated by presenting the purity and concurrence of the spin-spin system as a decisive measure for entanglement. Our results further imply that quantum entanglement studies cannot rule out consistent quantum theories featuring classical gravity.

quant-ph↗

arXiv2025

Classical and mixed classical-quantum systems from van Hove's unitary representation of contact transformations

Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used to develop a novel formulation of classical mechanics in Hilbert space. This formulation differs from the Koopman-von Neumann theory in many ways. Classical observables are represented by van Hove operators, which satisfy a commutation algebra isomorphic to the Poisson algebra of functions in phase space. Moreover, these operators are both observables and generators of transformations, which makes it unnecessary to introduce unobservable auxiliary operators as in the Koopman-von Neumann theory. In addition, for consistency with classical mechanics, a constraint must be imposed that fixes the phase of the wavefunction. The approach can be extended to hybrid mixed classical-quantum systems in Hilbert space. The formalism is applied to the measurement of a quantum two-level system (qubit) by a classical apparatus.

quant-ph↗

arXiv2024

Three statistical descriptions of classical systems and their extensions to hybrid quantum-classical systems

We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a Hilbert space approach using van Hove operators which provides an alternative to the Koopman-von Neumann formulation. In all cases, there is a natural way to define classical observables and a corresponding Lie algebra that is isomorphic to the usual Poisson algebra in phase space. We show that in the case of classical particles, the three descriptions are equivalent and indicate how they are related. We then modify and extend these descriptions to introduce hybrid models where a classical particle interacts with a quantum particle. The approach of ensembles on phase space and the Hilbert space approach, which are novel, lead to equivalent hybrid models, while they are not equivalent to the hybrid model of the approach of ensembles on configuration space. Thus, we end up identifying two inequivalent types of hybrid systems, making different predictions, especially when it comes to entanglement. These results are of interest regarding ``no-go'' theorems about quantum systems interacting via a classical mediator which address the issue of whether gravity must be quantized. Such theorems typically require assumptions that make them model dependent. The hybrid systems that we discuss provide concrete examples of inequivalent models that can be used to compute simple examples to test the assumptions of the ``no-go'' theorems and their applicability.

quant-ph↗

arXiv2022

Comment on "Vindication of entanglement-based witnesses of non-classicality in hybrid systems"

Models of quantum-classical interactions fall into two classes: those which allow the generation of quantum entanglement via a classical mediator (such as gravity), and those which do not. Marconato and Marletto have recently sought to distinguish between these classes by claiming that known members of the first class (based on the configuration-ensemble formalism introduced by us) fail to model the mediator as a 'classical' system, and are nonlocal. We explicitly show that this claim is incorrect, and expose a large number of errors and misconceptions in their reasoning. We also point to a very simple and transparent example of the generation of entanglement between two qubits via a classical bit. It follows that there are models permitting the generation of entanglement via quantum-classical interactions that lie outside the remit of the theorem cited by Marconato and Marletto. We clarify the reasons for the limited applicability of various no-go theorems for entanglement generation.

quant-ph↗

arXiv2022

Measurement of a quantum system with a classical apparatus using ensembles on configuration space

Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle that is prepared in a superposition of two localized states. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. A subsequent observation of the pointer leads to an update of its probability density. From this we can obtain information about the position of the quantum particle, leading to an update of its wave function. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications. Furthermore, it resolves fundamental issues that appear in the case of a quantum description of the apparatus.

quant-ph↗

arXiv2018

Entanglement of quantum fields via classical gravity

We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that there are solutions for which two quantum fields are in an entangled state, even though their interaction occurs solely via a common classical gravitational field, and that such entangled solutions can evolve from initially unentangled ones. These results support the observation of a previous paper that an observed generation of entanglement would not provide a definitive test of the nonclassical nature of gravity.

gr-qc↗

arXiv2018

On two recent proposals for witnessing nonclassical gravity

Two very similar proposals have been made recently for witnessing nonclassical features of gravity, by Bose et al. and by Marletto and Vedral. However, while these proposals are asserted to be very general, they are in fact based on a very strong claim: that quantum systems cannot become entangled via a classical intermediary. We point out that the support provided for this claim is only applicable to a very limited class of quantum-classical interaction models, corresponding to Koopman-type dynamics. We show that the claim is also valid for mean-field models, but that it is contradicted by explicit counterexamples based on the configuration-ensemble model. Thus, neither proposal provides a definitive test of nonclassical gravity.

quant-ph↗

arXiv2017

Another look through Heisenberg's microscope

Heisenberg introduced his famous uncertainty relations in a seminal 1927 paper entitled "The Physical Content of Quantum Kinematics and Mechanics". He motivated his arguments with a gedanken experiment, a gamma ray microscope to measure the position of a particle. A primary result was that, due to the quantum nature of light, there is an inherent uncertainty in the determinations of the particle's position and momentum dictated by an indeterminacy relation, $δq δp \sim h$. Heisenberg offered this demonstration as "a direct physical interpretation of the [quantum mechanical] equation $\textbf{pq} - \textbf{qp} = -i\hbar$" but considered the indeterminacy relation to be much more than this. He also argued that it implies limitations on the very meanings of position and momentum and emphasized that these limitations are the source of the statistical character of quantum mechanics. In addition, Heisenberg hoped but was unable to demonstrate that the laws of quantum mechanics could be derived directly from the uncertainty relation. In this paper, we revisit Heisenberg's microscope and argue that the Schrödinger equation for a free particle does indeed follow from the indeterminacy relation together with reasonable statistical assumptions.

quant-ph↗

arXiv2014

Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics

Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schroedinger equation follows naturally from information geometry.

quant-ph↗

arXiv2013

Cosmology with quantum matter and a classical gravitational field

I consider a hybrid cosmological model with a classical gravitational field and a quantized massive scalar field in spherically symmetric gravity. The interaction between classical and quantum fields is described using the formalism of ensembles on configuration space, an approach that provides an alternative to semiclassical gravity. After giving an outline of the formulation as it applies to spherically symmetric gravity, I discuss a particular solution that is analogous to the Einstein universe of classical relativity.

gr-qc↗

arXiv2013

Information geometry, dynamics and discrete quantum mechanics

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture. We do this in three steps. Our starting point is information geometry, the natural geometry of the space of probability distributions. Dynamics requires additional structure. To evolve the probabilities $P^k$, we introduce coordinates $S^k$ canonically conjugate to the $P^k$ and a symplectic structure. We then seek to extend the metric structure of information geometry, to define a geometry over the full space of the $P^k$ and $S^k$. Consistency between the metric tensor and the symplectic form forces us to introduce a Kähler geometry. The construction has notable features. A complex structure is obtained in a natural way. The canonical coordinates of the Kähler space are precisely the wave functions of quantum mechanics. The full group of unitary transformations is obtained. Finally, one may associate a Hilbert space with the Kähler space, which leads to the standard version of quantum theory. We also show that the metric that we derive here using purely geometrical arguments is precisely the one that leads to Wootters' expression for the statistical distance for quantum systems.

math-ph↗

arXiv2013

Cosmology with quantum matter and a classical gravitational field: the approach of configuration-space ensembles

I consider the formulation of hybrid cosmological models that consists of a classical gravitational field interacting with a quantized massive scalar field in the formalism of ensembles on configuration space. This is a viable approach that provides an alternative to semiclassical gravity. I discuss a particular, highly nonclassical solution in two approximations, minisuperspace and spherically-symmetric midisuperspace. In both cases, the coupling of the quantum scalar field and classical gravitational field leads to a cosmological model which has a quantized radius of the universe.

gr-qc↗

arXiv2013

From information to quanta: A derivation of the geometric formulation of quantum theory from information geometry

It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of probabilities (information geometry), the description of dynamics using a Hamiltonian formalism (symplectic geometry), and requirements of consistency (Kähler geometry). The theory that results is standard quantum mechanics, but in a geometrical formulation that includes also a particular case of a family of nonlinear gauge transformations introduced by Doebner and Goldin. The analysis is carried out for the case of discrete quantum mechanics. The work presented here relies heavily on, and extends, previous work done in collaboration with M. J. W. Hall.

quant-ph↗

arXiv2013

A Pedestrian Approach to the Measurement Problem in Quantum Mechanics

The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that operational prescriptions, which are integral to experimental physics, have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the "measurement problem". In this paper, we fully embrace the ensemble interpretation of quantum mechanics that obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts, remains. However, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. The pedestrian approach presented here suggests that the measurement problem is, in some sense, ill-posed and might never be resolved. This state of affairs is, in part, the result of searching for a theoretical answer to what is fundamentally an experimental question. This point of view is tenable so long as one is willing to view physical theories as providing models of nature rather than complete descriptions of reality. Among other things, these considerations lead us to suggest that the Copenhagen interpretation's insistence on the classicality of the measurement apparatus should be replaced by the requirement that a measurement, which is specified operationally, should simply be of sufficient precision.

physics.hist-ph↗

arXiv2012

Nonlocal signaling in the configuration space model of quantum-classical interactions

When interactions are turned off, the theory of interacting quantum and classical ensembles due to Hall and Reginatto is shown to suffer from a nonlocal signaling effect that is effectively action at a distance. This limits the possible applicability of the theory. In its present form, it is restricted to those situations in which interactions are always on, such as classical gravity interacting with quantized matter.

quant-ph↗

arXiv2011

Quantum theory from the geometry of evolving probabilities

We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao metric. This metric induces a metric over the space of probabilities. Our next step is to set the probabilities in motion. To do this, we introduce a canonically conjugate field S and a symplectic structure; this gives us Hamiltonian equations of motion. We show that it is possible to extend the metric structure to the full space of the {P,S} and this leads in a natural way to a Kaehler structure; i.e., a geometry that includes compatible symplectic, metric and complex structures. The simplest geometry that describes these spaces of evolving probabilities has remarkable properties: the natural, canonical variables are precisely the wave functions of quantum mechanics; the Hamiltonian for the quantum free particle can be derived from a representation of the Galilean group using purely geometrical arguments; and it is straightforward to associate with this geometry a Hilbert space which turns out to be the Hilbert space of quantum mechanics. We are led in this way to a reconstruction of quantum theory based solely on the geometry of probabilities in motion.

quant-ph↗

arXiv2008

Measurement Analysis and Quantum Gravity

We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments which speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.

gr-qc↗

arXiv2005

Interacting classical and quantum ensembles

A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem, based on a universally-applicable formalism for ensembles on configuration space. This approach overcomes difficulties arising in previous attempts, and in particular allows for backreaction on the classical ensemble, conservation of probability and energy, and the correct classical equations of motion in the limit of no interaction. Applications include automatic decoherence for quantum ensembles interacting with classical measurement apparatuses; a generalisation of coherent states to hybrid harmonic oscillators; and an equation for describing the interaction of quantum matter fields with classical gravity, that implies the radius of a Robertson-Walker universe with a quantum massive scalar field can be sharply defined only for particular `quantized' values.

quant-ph↗