arXiv subjects

Yves Caudano

Publications and source records attributed to Yves Caudano.

12 recordsLinked to original sources

arXiv2026

Computational quantum field theory for fermion pair creation in 2-dimensional curved spacetimes

Similarly to the well-known phenomenon of particle / anti-particle pair production in strong electromagnetic fields (the Schwinger effect), the na\"ive matter field vacuum state can be excited by time-dependent, curved spacetime geometries. This gravitational pair creation corresponds to tunnelling out of a false vacuum. In this work, we study this non-perturbative process using a spacetime resolved numerical approach in the interaction picture. To achieve this, we extend the framework of Computational Quantum Field Theory (CQFT), which allows for efficient numerical time evolution of quantum fields, to spin-$1/2$ fermions in curved spacetime. Using this extended framework, we investigate vacuum excitation of a Dirac field induced by a spacetime-curvature quench. In particular, we evolve the fermionic Minkowski vacuum in a $1\!+\!1$-dimensional idealized curved spacetime characterized by a localized ``curvature bump'' generated by a smooth, localized Gaussian deformation of flat spacetime. Vacuum excitation is quantified by computing the fermion--antifermion pair numbers defined with respect to the basis corresponding to flat-spacetime (Minkowski) which is the asymptotic metric corresponding to an observor at infinity. We analyze how the excitation depends on the strength and spatial extent of the curvature deformation and discuss the numerical implementation of CQFT in curved backgrounds. While the post-quench geometry considered here is static and no electromagnetic field is included, the present work establishes a foundation for future investigations of particle creation in genuinely time-dependent curved spacetimes and in the presence of electromagnetic backgrounds.

hep-th↗

arXiv2025

A paradox in the quantum-mechanical treatment of destructive measurements on photons

Measurements on photons are frequently cited as confirmations of predictions of quantum mechanics (QM), in particular in the context of Bell's theorem. In this paper we show, however, that we cannot ever claim to have measured a property of a photon if we treat a destructive measurement {of the value of a property of a photon prepared in a superposition of eigenstates} in the framework of orthodox QM.

quant-ph↗

arXiv2025

Wick rotation derivation for weak values of the density and time-dependent density functional theory

The equations of time-dependent density functional theory are derived, via the expression for a quantum weak value, from ring polymer self-consistent field theory using a mathematical correspondence between time and imaginary time. The imaginary time path integral formalism of Feynman, in which inverse temperature is seen to be a Wick rotation of time, allows one to write the equilibrium partition function of a quantum system in a form mathematically isomorphic with the path integral expression for the dynamics. Therefore the self-consistent field theory equations which are solutions to the equilibrium partition function are Wick rotated back into a set of dynamic equations, which are shown to give an expression for a quantum weak value of the one-particle density. Remarkably, weak values emerge naturally here without being postulated, as an intermediate step before recovering the standard expression for the density. The weak value expression in turn leads to the equations of time-dependent density functional theory. This first-principles derivation does not use the theorems of density functional theory, which are instead applied to guarantee equivalence with standard quantum mechanics. An expression for finite-temperature dynamics is also given, which shows that a ring polymer model for quantum particles holds for time-dependent systems as well as equilibrium situations. Issues arising in time-dependent density functional theory, such as causality, initial state dependence, and $v$-representability, are discussed in the context of the ring polymer derivation.

quant-ph↗

arXiv2024

Leveraging modular values in quantum algorithms: the Deutsch-Jozsa

We present a novel approach to quantum algorithms, by taking advantage of modular values, i.e., complex and unbounded quantities resulting from specific post-selected measurement scenarios. Our focus is on the problem of ascertaining whether a given function acting on a set of binary values is constant (uniformly yielding outputs of either all 0 or all 1), or balanced (a situation wherein half of the outputs are 0 and the other half are 1). Such problem can be solved by relying on the Deutsch-Jozsa algorithm. The proposed method, relying on the use of modular values, provides a high number of degrees of freedom for optimizing the new algorithm inspired from the Deutsch-Jozsa one. In particular, we explore meticulously the choices of the pre- and post-selected states. We eventually test the novel theoretical algorithm on a quantum computing platform. While the outcomes are currently not on par with the conventional approach, they nevertheless shed light on potential for future improvements, especially with less-optimized algorithms. We are thus confidend that the proposed proof of concept could prove its validity in bridging quantum algorithms and modular values research fields.

quant-ph↗

arXiv2023

On the relevance of weak measurements in dissipative quantum systems

We investigate the impact of dissipation on weak measurements. While weak measurements have been successful in signal amplification, dissipation can compromise their usefulness. More precisely, we show that in systems with non-degenerate eigenstates, weak values always converge to the expectation value of the measured observable as dissipation time tends to infinity, in contrast to systems with degenerate eigenstates, where the weak values can remain anomalous, i.e., outside the range of eigenvalues of the observable, even in the limit of an infinite dissipation time. In addition, we propose a method for extracting information about the dissipative dynamics of a system using weak values at short dissipation times. Specifically, we explore the amplification of the dissipation rate in a two-level system and the use of weak values to differentiate between Markovian and non-Markovian dissipative dynamics. We also find that weak measurements operating around a weak atom-cavity coupling can probe the atom dissipation through the weak value of non-Hermitian operators within the rotating-wave approximation of the weak interaction.

quant-ph↗

arXiv2023

Revisiting weak values through non-normality

Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify measured signals by exploiting a quantity called a weak value, but also to overcome philosophical difficulties related to the system perturbation induced by the measurement process. The method finds many applications and raises many philosophical questions as well, especially about the proper interpretation of the observations. In this paper, we show that any weak value can be expressed as the expectation value of a suitable non-normal operator. We propose a preliminary explanation of their anomalous and amplification behavior based on the theory of non-normal matrices and their link with non-normality: the weak value is different from an eigenvalue when the operator involved in the expectation value is non-normal. Our study paves the way for a deeper understanding of the measurement phenomenon, helps the design of experiments, and it is a call for collaboration to researchers in both fields to unravel new quantum phenomena induced by non-normality.

quant-ph↗

arXiv2022

Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation

This work examines the argument of weak values for general observables and develops a geometric description on the Bloch sphere. We apply the Majorana symmetric representation to reach this goal. The weak value of a general observable is proportional to the weak value of an effective projector: it is constructed from the application of the observable over the initial state, after normalization by a constant of proportionality that is real. The argument of the weak value of a projector on a pure state of an $N$-level system corresponds to a symplectic area in the complex projective space $(\text{CP}^{N-1})$. This symplectic area cannot be visualized directly but it can be represented geometrically with a sum of $N-1$ solid angles on the Bloch sphere using the Majorana stellar representation. By combining these two ideas, we show that the argument of the weak value of any observable (i.e., not just projectors) can be described with the Majorana representation, as the sum of $N-1$ solid angles on the Bloch sphere. These two approaches provide two geometrical descriptions, a first one in the complex projective space $\text{CP}^{N-1}$ and a second one on the Bloch sphere, after mapping the problem from the original $N$-dimensional quantum state space $(\text{CP}^{N-1})$ to a multi-qubit description in three-dimensional space by making use of the Majorana representation. These results can also be applied to the argument of the third-order Bargmann invariant, the most fundamental order as the argument of any higher order invariant can be expressed as a sum of the argument of third-order Bargmann invariants, as well as to the argument of the Kirkwood-Dirac quasi-probability distribution. Finally, we focus on the argument of the weak value of a general spin-1 operator when its modulus diverges towards infinity.

quant-ph↗

arXiv2022

Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems

Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in $N$-dimensional quantum systems in terms of geometric phases. We formulate an arbitrary weak value in function of three real vectors on the unit sphere in $N^2-1$ dimensions, $S^{N^2-2}$. These vectors are linked to the initial and final states, and to the weakly measured observable, respectively. We express pure states in the complex projective space of $N-1$ dimensions, $\mathbb{C}\textrm{P}^{N-1}$, which has a non-trivial representation as a $2N-2$ dimensional submanifold of $S^{N^2-2}$ (a generalization of the Bloch sphere for qudits). The argument of the weak value of a projector on a pure state of an $N$-level quantum system describes a geometric phase associated to the symplectic area of the geodesic triangle spanned by the vectors representing the pre-selected state, the projector and the post-selected state in $\mathbb{C}\textrm{P}^{N-1}$. We then proceed to show that the argument of the weak value of a general observable is equivalent to the argument of an effective Bargmann invariant. Hence, we extend the geometrical interpretation of projector weak values to weak values of general observables. In particular, we consider the generators of SU($N$) given by the generalized Gell-Mann matrices. Finally, we study in detail the case of the argument of weak values of general observables in two-level systems and we illustrate weak measurements in larger dimensional systems by considering projectors on degenerate subspaces, as well as Hermitian quantum gates.

quant-ph↗

arXiv2022

Spontaneous Symmetry Breaking: The Case of Crazy Clock and Beyond

In this account, we describe the crazy-clock phenomenon involving the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration with new iodine phase) transition after a Briggs-Rauscher (BR) oscillatory process. While the BR crazy-clock phenomenon is known, it is the first time that crazy-clock behavior is linked and explained with the symmetry-breaking phenomenon, highlighting the entire process in a novel way. The presented phenomenon has been thoroughly investigated by running more than 60 experiments, and evaluated by using statistical cluster K-means analysis. The mixing rate, as well as the magnetic bar shape and dimensions, have a strong influence on the transition appearance. Although the transition for both mixing and no-mixing conditions are taking place completely randomly, by using statistical cluster analysis we obtain different numbers of clusters (showing the time-domains where the transition is more likely to occur). In the case of stirring, clusters are more compact and separated, revealed new hidden details regarding the chemical dynamics of nonlinear processes. The significance of the presented results is beyond oscillatory reaction kinetics since the described example belongs to the small class of chemical systems that shows intrinsic randomness in their response and it might be considered as a real example of a classical liquid random number generator.

cond-mat.mtrl-sci↗

arXiv2018

Molding Molecular and Material Properties by Strong Light-Matter Coupling

When atoms come together and bond, we call these new states molecules, and their properties determine many aspects of our daily life. Strangely enough, it is conceivable for light and molecules to bond, creating new hybrid light-matter states with far-reaching consequences for these strongly coupled materials. Even stranger, there is no `real' light needed to obtain the effects, it simply appears from the vacuum, creating `something from nothing'. Surprisingly, the setup required to create these materials has become moderately straightforward. In its simplest form, one only needs to put a strongly absorbing material at the appropriate place between two mirrors, and quantum magic can appear. Only recently has it been discovered that strong coupling can affect a host of significant effects at a material and molecular level, which were thought to be independent of the `light' environment: phase transitions, conductivity, chemical reactions, etc. This review addresses the fundamentals of this opportunity: the quantum mechanical foundations, the relevant plasmonic and photonic structures, and a description of the various applications, connecting materials chemistry with quantum information, nonlinear optics and chemical reactivity. Ultimately, revealing the interplay between light and matter in this new regime opens attractive avenues for many applications in the material, chemical, quantum mechanical and biological realms.

cond-mat.mtrl-sci↗

arXiv2017

Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N-1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N-1 contributions. Their modulus is determined by the product of N-1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N-1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox [1] from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.

quant-ph↗

arXiv2016

Interferences in quantum eraser reveal geometric phases in modular and weak values

In this letter, we present a new procedure to determine completely the complex modular values of arbitrary observables of pre- and post-selected ensembles, which works experimentally for all measurement strengths and all post-selected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by controlling simultaneously the visibility and the phase in a quantum eraser interference experiment. Modular and weak values are closely related. Using entangled qubits for the probed and meter systems, we show that the phase of the modular and weak values has a topological origin. This phase is completely defined by the intrinsic physical properties of the probed system and its time evolution. The physical significance of this phase can thus be used to evaluate the quantumness of weak values.

quant-ph↗