arXiv subjects

Matteo G. A. Paris

Publications and source records attributed to Matteo G. A. Paris.

At least 109 records · Page 6Linked to original sources

arXiv2021

Transport efficiency of continuous-time quantum walks on graphs

Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and on the specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but in general they are uncorrelated.

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arXiv2020

Squeezing as a resource to counteract phase diffusion in optical phase estimation

We address a phase estimation scheme using Gaussian states in the presence of non-Gaussian phase noise. At variance with previous analysis, we analyze situations in which the noise occurs before encoding phase information. In particular, we study how squeezing may be profitably used before or after phase diffusion. Our results show that squeezing the probe after the noise greatly enhances the sensitivity of the estimation scheme, as witnessed by the increase of the quantum Fisher information. We then consider a realistic setup where homodyne detection is employed at the measurement stage, and address its optimality as well as its performance in the two different scenarios.

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arXiv2020

On the quantumness of multiparameter estimation problems for qubit systems

The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumness R, a measure that has been recently introduced in order to quantify how much incompatible are the parameters to be estimated. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e. the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model it is equal to the difference between the bounds and, in general, their behaviour qualitatively coincide. On the other hand, we also find evidence that for certain quantum statistical models the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters.

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arXiv2020

Scattering as a quantum metrology problem: a quantum walk approach

We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher information as a mean to quantify the maximal possible accuracy in the estimation of the height of the barrier. We introduce suitable initial states of the walker and derive the reflection and transmission probabilities of the scattered state. We show that while the quantum Fisher information is affected by the width and central momentum of the initial wave packet, this dependency is weaker for the quantum signal-to-noise ratio. We also show that a dichotomic position measurement provides a nearly optimal detection scheme.

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arXiv2020

Continuous-time quantum walks in the presence of a quadratic perturbation

We address the properties of continuous-time quantum walks with Hamiltonians of the form $\mathcal{H}= L + λL^2$, being $L$ the Laplacian matrix of the underlying graph and being the perturbation $λL^2$ motivated by its potential use to introduce next-nearest-neighbor hopping. We consider cycle, complete, and star graphs because paradigmatic models with low/high connectivity and/or symmetry. First, we investigate the dynamics of an initially localized walker. Then, we devote attention to estimating the perturbation parameter $λ$ using only a snapshot of the walker dynamics. Our analysis shows that a walker on a cycle graph is spreading ballistically independently of the perturbation, whereas on complete and star graphs one observes perturbation-dependent revivals and strong localization phenomena. Concerning the estimation of the perturbation, we determine the walker preparations and the simple graphs that maximize the Quantum Fisher Information. We also assess the performance of position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Besides fundamental interest, our study may find applications in designing enhanced algorithms on graphs.

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arXiv2020

Tight bound on finite-resolution quantum thermometry at low temperatures

Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound can be saturated by monitoring the non-equilibrium dynamics of a single-qubit probe. We support this finding by accurate numerical simulations of a spin-boson model. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.

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arXiv2020

Nonclassical steering and the Gaussian steering triangoloids

Nonclassicality according to the singularity or negativity of the Glauber P-function is a powerful resource in quantum information, with relevant implications in quantum optics. In a Gaussian setting, and for a system of two modes, we explore how P-nonclassicality may be conditionally generated or influenced on one mode by Gaussian measurements on the other mode. Starting from the class of two-mode squeezed thermal states (TMST), we introduce the notion of nonclassical steering (NS) and the graphical tool of Gaussian triangoloids. In particular, we derive a necessary and sufficient condition for a TMST to be nonclassically steerable, and show that entanglement is only necessary. We also apply our criterion to noisy propagation of a twin-beam state, and evaluate the time after which NS is no longer achievable. We then generalize the notion of NS to the full set of Gaussian states of two modes, and recognize that it may occur in a weak form, which does not imply entanglement, and in a strong form that implies EPR-steerability and, a fortiori, also entanglement. These two types of NS coincide exactly for TMSTs, and they merge with the previously known notion of EPR steering. By the same token, we recognize a new operational interpretation of P-nonclassicality: it is the distinctive property that allows one-party entanglement verification on TMSTs.

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arXiv2020

Quantum probing beyond pure dephasing

Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.

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arXiv2020

Discrimination of Ohmic thermal baths by quantum dephasing probes

We address the discrimination of structured baths at different temperatures by dephasing quantum probes. We derive the exact reduced dynamics and evaluate the minimum error probability achievable by three different kinds of quantum probes, namely a qubit, a qutrit and a quantum register made of two qubits. Our results indicate that dephasing quantum probes are useful in discriminating low values of temperature, and that lower probabilities of error are achieved for intermediate values of the interaction time. A qutrit probe outperforms a qubit one in the discrimination task, whereas a register made of two qubits does not offer any advantage compared to two single qubits used sequentially.

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arXiv2020

Mechanical oscillator thermometry in the nonlinear optomechanical regime

Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressure interaction. To measure the temperature of the mechanical oscillator, initially in a thermal state, we use light as a probe to coherently interact with it and create an entangled state. We show that the optical probe gets a nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusion process. To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinear Kerr medium before a homodyne detector. Remarkably, placing the Kerr medium enhances the precision to nearly saturate the ultimate quantum bound given by the quantum Fisher information. Furthermore, it also simplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature, which avoids the need for adaptive sensing protocols.

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arXiv2020

Quantum-classical dynamical distance and quantumness of quantum walks

We introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this quantum-classical dynamical distance, showing that at short times $\text{D}_{\text{CQ}}(t)$ is proportional to the coherence of the walker, i.e. a genuine quantum feature, whereas for long times it depends only on the size of the graph. At intermediate times, $\text{D}_{\text{CQ}}(t)$ does depend on the graph topology through its algebraic connectivity. Our results show that the difference in the dynamical behaviour of classical and quantum walks is entirely due to the emergence of quantum features at short times. In the long time limit, quantumness and the different nature of the generators of the dynamics, e.g. the open system nature of CW and the unitary nature of QW, are instead contributing equally.

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arXiv2020

Nonclassical steering with two-mode Gaussian states

Singularity or negativity of Glauber P-function is a widespread notion of nonclassicality, with important implications in quantum optics and with the character of an irreducible resource. Here we explore how P-nonclassicality may be generated by conditional Gaussian measurements on bipartite Gaussian states. This nonclassical steering may occur in a weak form, which does not imply entanglement, and in a strong form that implies EPR-steerability and thus entanglement. We show that field quadratures are the best measurements to remotely generate nonclassicality, and exploit this result to derive necessary and sufficient conditions for weak and strong nonclassical steering. For two-mode squeezed thermal states (TMST), weak and strong nonclassical steering coincide, and merge with the notion of EPR steering. This also provides a new operational interpretation for P-function nonclassicality as the distinctive feature that allows one-party entanglement verification on TMSTs.

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arXiv2020

Quantum enhanced metrology of Hamiltonian parameters beyond the Cramèr-Rao bound

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cramèr-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in classical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, non-regular statistical models may appear, for which the Cramèr-Rao theorem does not hold. In turn, the achievable precision may exceed the Cramèr-Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cramèr-Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.

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arXiv2020

Quantum thermometry by single-qubit dephasing

We address the dephasing dynamics of a qubit as an effective process to estimate the temperature of its environment. Our scheme is inherently quantum, since it exploits the sensitivity of the qubit to decoherence, and does not require thermalization with the system under investigation. We optimize the quantum Fisher information with respect to the interaction time and the temperature in the case of Ohmic-like environments. We also find explicitly the qubit measurement achieving the quantum Cramer- Rao bound to precision. Our results show that the conditions for optimal estimation originate from a non-trivial interplay between the dephasing dynamics and the Ohmic structure of the environment. In general, optimal estimation is achieved neither when the qubit approaches the stationary state, nor for full dephasing.

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arXiv2020

Experimental realization of local-to-global noise transition in a two-qubit optical simulator

We demonstrate the transition from local to global noise in a two-qubit all-optical quantum simulator subject to classical random fluctuations. Qubits are encoded in the polarization degree of freedom of two entangled photons generated by parametric down-conversion (PDC) while the environment is implemented using their spatial degrees of freedom. The ability to manipulate with high accuracy the number of correlated pixels of a spatial-light-modulator and the spectral PDC width, allows us to control the transition from a scenario where the qubits are embedded in local environments to the situation where they are subject to the same global noise. We witness the transition by monitoring the decoherence of the two-qubit state.

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arXiv2020

Quantum probes for universal gravity corrections

We address estimation of the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation performances. At first, we review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system, which is proportional to a parameter depending on the minimum length. We then systematically study the effects of this perturbation on different state preparations for several 1-dimensional systems, and we evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure. Eventually, we investigate the role of dimensionality by analysing the use of two-dimensional square well and harmonic oscillator systems to probe the minimal length. Our results show that quantum probes are convenient resources, providing potential enhancement in precision. Additionally, our results provide a set of guidelines to design possible future experiments to detect minimal length.

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arXiv2020

Photonic Realization of a Quantum Finite Automaton

We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages. The realization exploits the polarization degree of freedom of single photons and their manipulation through linear optical elements. We use techniques of confidence amplification to reduce the acceptance error probability of the automaton. It is worth remarking that the quantum finite automaton we physically realize is not only interesting per se, but it turns out to be a crucial building block in many quantum finite automaton design frameworks theoretically settled in the literature.

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arXiv2019

Two-qubit quantum probes for the temperature of an Ohmic environment

We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploits decoherence as resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super- Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath, or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the interplay between correlations among the probes and correlations within the bath, and show that entanglement improves thermometry at short times whereas, if the interaction time is not constrained, coherence rather than entanglement, is the key resource in quantum thermometry.

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