arXiv subjects

Tommaso Tufarelli

Publications and source records attributed to Tommaso Tufarelli.

At least 19 recordsLinked to original sources

arXiv2026

Looking down the rabbit hole: Towards quantum optimal estimation of surface roughness

Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optics. By adopting quantum parameter estimation methods, we determine the ultimate precision limits for estimating spatial moments of a general three-dimensional distribution of incoherent point sources in the sub-diffraction regime. Specializing this result to the axial profile, we show that the information on the first moment (mean height) and standard deviation (roughness) is bounded by a constant. While classical imaging techniques fail to achieve this bound, a quantum inspired imaging technique based on spatial mode demultiplexing is proven to be optimal for estimating the axial standard deviation. This provides a powerful and experimentally accessible route to measuring roughness of nearly smooth surface patches beyond the diffraction limit.

quant-ph↗

arXiv2026

Quantum Limits of Passive Optical Surface Metrology and Defect Detection

We develop a quantum statistical framework for passive optical surface metrology. Modelling a surface as an incoherent ensemble of point emitters imaged through a diffraction-limited system, we employ techniques from quantum parameter estimation and hypothesis testing to derive ultimate bounds for jointly estimating geometrical features and for deciding the presence or absence of surface defects, and we identify optimal measurements from the geometry of the point-spread-function manifold. As a representative application, we analyse a minimal surface crack model based on three point sources and show that spatial mode sorting can simultaneously enable near-quantum-limited estimation of crack width and depth and markedly enhanced detectability of the crack, compared with direct imaging. Our results pave the way towards enhanced optical inspection and characterisation of sub-diffraction surface features by probing a limited number of spatial modes without any illumination control.

quant-ph↗

arXiv2025

Hidden assumptions of integer ratio analyses in bioacoustics and music

Rhythm is ubiquitous in human culture and in nature, but hard to capture in all its complexity. A key dimension of rhythm, integer ratio categories occur when the relationship between temporal intervals can be expressed as small-integer ratios. Recent work has found integer ratio categories in most human musical cultures and some animal species' vocalizations or behavioral displays. But biological systems are noisy, and empirically measured intervals rarely form an exact small-integer ratio. Here, we mathematically assess whether the leading integer ratio analysis method makes valid statistical and biological assumptions. In particular, we (1) make the temporal properties of empirical ratios explicit, both in general and for the typical use in the literature; (2) show how the choice of ratio formula affects the probability distribution of rhythm ratios and ensuing statistical results; (3) guide the reader to carefully consider the assumptions and null hypotheses of the statistical analysis; (4) present a comprehensive methodology to statistically test integer ratios for any null hypothesis of choice. Our observations have implications for both past and future research in music cognition and animal behavior: They suggest how to interpret past findings and provide tools to choose the correct null hypotheses in future empirical work.

stat.AP↗

arXiv2025

Ergodiscord: An Operational and Distinct Notion of Quantumness of Correlations

Nonclassicality in composite quantum systems depicts several puzzling manifestations, with Einstein-Podolsky-Rosen entanglement, Schrödinger steering, and Bell nonlocality being the most celebrated ones. In addition to those, an unentangled quantum state can also exhibit nonclassicality, as evidenced from notions such as quantum discord and work deficit. In this work, we present a general framework for exploring quantumness of correlations in multipartite quantum states. By exploiting the different signatures reflected on observable quantities depending on whether subsystems of a composite systems are probed jointly or independently, we introduce an operational quantifier of nonclassicality, termed {\em ergodiscord}. As we show, this newly proposed quantifier faithfully captures nonclassicality in any bipartite quantum state, while being fundamentally distinct from the original quantum discord. Moreover, ergodiscord uncovers an intriguing phenomenon called `nonlocal energy locking', where a useful form of energy (i.e. work) gets locked in correlations of nonclassical states. We also show that a mixed nonclassical state can lock more work than the maximally entangled state of the corresponding system, establishing an interesting super-additivity phenomenon of nonlocal energy locking. The present work may inspire novel designs of quantum energy storage devices by utilizing nonclassical correlations in composite quantum systems.

quant-ph↗

arXiv2025

Multilevel Quantum Rabi Models

The quantum Rabi model, which describes the interaction between a simplified atom and a mode of the electromagnetic field, is a cornerstone of modern quantum optics. One of the key assumptions of the model is that the `atom' is a perfect two-level system. We explore what happens when one generalizes the atom to a multilevel system, with $m$ ground and $n$ excited states coupled to the same field. We focus on the case where the excited and ground states form distinct, well-separated, manifolds of near-degenerate levels (so that the spacing between the excited states on a given manifold is much less than the average spacing between the manifolds) and consider either uniform or random couplings between the individual ground and excited levels. We find that the system reduces approximately to a direct sum of Rabi models with a range of different couplings. Importantly, the strongest coupling is enhanced in a way that depends on the number of levels, for the simple case where $n=m$, the coupling scales with $n$ for uniform couplings and $2\sqrt{n}$ for random couplings (in the limit of large $n$). Our work thus suggests that multilevel Rabi systems could provide an attractive alternative route to accessing regimes of very strong coupling in light-matter systems.

quant-ph↗

arXiv2023

Anticrossing of a plasmonic nanoresonator mode and a single quantum dot at room temperature

Room-temperature strong coupling of a single quantum emitter and a single resonant plasmonic mode is a key resource for quantum information processing and quantum sensing at ambient conditions. To beat dephasing, ultrafast energy transfer is achieved by coupling single emitters to a plasmonic nanoresonator with an extremely small mode volume and optimal spectral overlap. Typically, normal mode splittings in luminescence spectra of single-emitter strongly-coupled systems are provided as evidence for strong coupling and to obtain rough estimates of the light-matter coupling strength g. However, a complete anticrossing of a single emitter and a cavity mode as well as the characterization of the uncoupled constituents is usually hard to achieve. Here, we exploit the light-induced oxygen-dependent blue-shift of individual CdSe/ZnS semiconductor quantum dots to tune their transition energy across the resonance of a scanning plasmonic slit resonator after characterizing both single emitter and nano resonator in their uncoupled states. Our results provide clear proof of single-emitter strong light-matter coupling at ambient condition as well as a value for the Rabi splitting at zero detuning 100 meV, consistent with modeling, thereby opening the path towards plexitonic devices that exploit single-photon nonlinearities at ambient conditions.

physics.optics↗

arXiv2021

General expressions for the quantum Fisher information matrix with applications to discrete quantum imaging

The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the density matrix. In this paper, we derive general expressions for the quantum Fisher information matrix which bypass matrix diagonalization and do not require the expansion of operators on an orthonormal set of states. Additionally, we can tackle density matrices of arbitrary rank. The methods presented here simplify analytical calculations considerably when, for example, the density matrix is more naturally expressed in terms of non-orthogonal states, such as coherent states. Our derivation relies on two matrix inverses which, in principle, can be evaluated analytically even when the density matrix is not diagonalizable in closed form. We demonstrate the power of our approach by deriving novel results in the timely field of discrete quantum imaging: the estimation of positions and intensities of incoherent point sources. We find analytical expressions for the full estimation problem of two point sources with different intensities, and for specific examples with three point sources. We expect that our method will become standard in quantum metrology.

quant-ph↗

arXiv2021

Single Quantum Emitter Dicke Enhancement

Coupling $N$ identical emitters to the same field mode is well-established method to enhance light matter interaction. However, the resulting $\sqrt{N}$ boost of the coupling strength comes at the cost of a "linearized" (effectively semi-classical) dynamics. Here, we instead demonstrate a new approach for enhancing the coupling constant of a \textit{single} quantum emitter, while retaining the nonlinear character of the light-matter interaction. We consider a single quantum emitter with $N$ nearly degenerate transitions that are collectively coupled to the same field mode. We show that in such conditions an effective Jaynes-Cummings model emerges, with a boosted coupling constant of order $\sqrt{N}$. The validity and consequences of our general conclusions are analytically demonstrated for the instructive case $N=2$. We further observe that our system can closely match the spectral line shapes and photon autocorrelation functions typical of Jaynes-Cummings physics, hence proving that quantum optical nonlinearities are retained. Our findings match up very well with recent broadband plasmonic nanoresonator strong-coupling experiments and will therefore facilitate the control and detection of single-photon nonlinearities at ambient conditions.

quant-ph↗

arXiv2020

Quantum estimation of coupling strengths in driven-dissipative optomechanics

We exploit local quantum estimation theory to investigate the measurement of linear and quadratic coupling strengths in a driven-dissipative optomechanical system. For experimentally realistic values of the model parameters, we find that the linear coupling strength is considerably easier to estimate than the quadratic one. Our analysis also reveals that the majority of information about these parameters is encoded in the reduced state of the mechanical element, and that the best estimation strategy for both coupling parameters is well approximated by a direct measurement of the mechanical position quadrature. Interestingly, we also show that temperature does not always have a detrimental effect on the estimation precision, and that the effects of temperature are more pronounced in the case of the quadratic coupling parameter.

quant-ph↗

arXiv2020

Refined diamond norm bounds on the emergence of objectivity of observables

The theory of Quantum Darwinism aims to explain how our objective classical reality arises from the quantum world, by analysing the distribution of information about a quantum system that is accessible to multiple observers, who probe the system by intercepting fragments of its environment. Previous work showed that, when the number of environmental fragments grows, the quantum channels modelling the information flow from system to observers become arbitrarily close - in terms of diamond norm distance - to "measure-and-prepare" channels, ensuring objectivity of observables; the convergence is formalised by an upper bound on the diamond norm distance, which decreases with increasing number of fragments. Here, we derive tighter diamond norm bounds on the emergence of objectivity of observables for quantum systems of infinite dimension, providing an approach which can bridge between the finite- and the infinite-dimensional cases. Furthermore, we probe the tightness of our bounds by considering a specific model of a system-environment dynamics given by a pure loss channel. Finally, we generalise to infinite dimensions a result obtained by Brandão et al. [Nat. Commun. 6, 7908 (2015)], which provides an operational characterisation of quantum discord in terms of one-sided redistribution of correlations to many parties. Our results provide a unifying framework to benchmark quantitatively the rise of objectivity in the quantum-to-classical transition.

quant-ph↗

arXiv2019

Non-Orthogonal Bases for Quantum Metrology

Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the analytical evaluation of the quantum Fisher information may be greatly simplified by bypassing both the diagonalization of the density matrix and the orthogonalization of the basis. The key ingredient in our method is the Gramian matrix (i.e. the matrix of scalar products between basis elements), which may be interpreted as a metric tensor for index contraction. As an application, we derive novel analytical results for several estimation problems involving noisy Schroedinger cat states.

quant-ph↗

arXiv2019

Quantum estimation of a two-phase spin rotation

We study the estimation of an infinitesimal rotation of a spin-j system, characterized by two unknown phases, and compare the estimation precision achievable with two different strategies. The first is a standard `joint estimation' strategy, in which a single probe state is used to estimate both parameters, while the second is a `sequential' strategy in which the two phases are estimated separately, each on half of the total number of system copies. In the limit of small angles we show that, although the joint estimation approach yields in general a better performance, the two strategies possess the same scaling of the total phase sensitivity with respect to the spin number j, namely $ΔΦ\simeq 1/j$. Finally, we discuss a simple estimation strategy based on spin squeezed states and spin measurements, and compare its performance with the ultimate limits to the estimation precision that we have derived above.

quant-ph↗

arXiv2019

Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations

We introduce an infinite family of quantifiers of quantum correlations beyond entanglement which vanish on both classical-quantum and quantum-classical states and are in one-to-one correspondence with the metric-adjusted skew informations. The `quantum $f-$correlations' are defined as the maximum metric-adjusted $f-$correlations between pairs of local observables with the same fixed equispaced spectrum. We show that these quantifiers are entanglement monotones when restricted to pure states of qubit-qudit systems. We also evaluate the quantum $f-$correlations in closed form for two-qubit systems and discuss their behaviour under local commutativity preserving channels. We finally provide a physical interpretation for the quantifier corresponding to the average of the Wigner-Yanase-Dyson skew informations.

quant-ph↗

arXiv2019

Towards superresolution surface metrology: Quantum estimation of angular and axial separations

We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound. Such a precision is not degraded in the sub-wavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh's criterion. Our results are qualitatively independent of the point spread function of the imaging system, and quantitatively illustrated in detail for the Gaussian instance. This analysis may have relevant applications in three-dimensional surface measurements.

quant-ph↗

arXiv2018

Generic emergence of objectivity of observables in infinite dimensions

Quantum Darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment. It was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics, whenever the system of interest has finite dimensions and the number of environment fragments is large [F. G. S. L. Brandão, M. Piani, and P. Horodecki, Nature Commun. 6, 7908 (2015)]. Despite the importance of this result, it necessarily excludes many practical systems of interest that are infinite-dimensional, including harmonic oscillators. Extending the study of Quantum Darwinism to infinite dimensions is a nontrivial task: we tackle it here by using a modified diamond norm, suitable to quantify the distinguishability of channels in infinite dimensions. We prove two theorems that bound the emergence of objectivity, first for finite energy systems, and then for systems that can only be prepared in states with an exponential energy cut-off. We show that the latter class of states includes any bounded-energy subset of single-mode Gaussian states.

quant-ph↗

arXiv2017

Exploring corrections to the Optomechanical Hamiltonian

We compare two approaches to refine the "linear model" of cavity optomechanics, in order to describe radiation pressure effects that are beyond first order in the coupling constant. We compare corrections derived from (I) a widely used phenomenological Hamiltonian that conserves the photon number and (II) a two-mode truncation of C. K. Law's microscopic model, which we take as the "true" Hamiltonian of the system. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations from second order onwards. Our numerics suggest that the phenomenological Hamiltonian significantly improves the linear model, yet it does not fully capture all second-order corrections arising from the C. K. Law model. We conclude that, even when the mechanical frequency is much lower than the cavity one, photon number conservation must be eventually given up to model cavity optomechanics with high accuracy.

quant-ph↗

arXiv2017

Quantifying genuine multipartite correlations and their pattern complexity

We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as: what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e. statistical dependencies which cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states which display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.

quant-ph↗

arXiv2017

Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements

EPR steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited for quantum communication with one untrusted party. In particular, steering of continuous variable Gaussian states has been extensively studied as a manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density matrix elements of two-mode squeezed thermal states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a nonlinear criterion, based on second moments of the pseudospin correlation matrix. This analysis reveals previously unexplored regimes where non-Gaussian measurements are more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than Gaussian observables for steering detection. Finally, we investigate continuous variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian measurements in characterizing quantum correlations of Gaussian and non-Gaussian states.

quant-ph↗