arXiv subjects

Alberto Riccardi

Publications and source records attributed to Alberto Riccardi.

11 recordsLinked to original sources

arXiv2026

Tight Entropic Uncertainty Relations

Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the variance-based uncertainty relations because they only depend on the Born statistics of the outcomes and not on the outcomes themselves, and because bounds $\gamma$ typically are state independent. Here we provide a state-independent lower bound $\gamma_s$ that is better than the textbook Maassen-Uffink bound and, in the limit of the parameter $s\to 2$, becomes asymptotically tight for all $A,B$. The bound can be extended to Renyi entropies. After the submission of this paper, we found out that the main results presented here were already on page 6 of https://quantum-journal.org/papers/q-2018-03-30-59/pdf/

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arXiv2023

A protocol for global multiphase estimation

Global estimation strategies allow to extract information on a phase or a set of phases without any prior knowledge, which is, instead, required for local estimation strategies. We devise a global multiphase protocol based on Holevo's estimation theory and apply it to the case of digital estimation, i.e. we estimate the phases in terms of the mutual information between them and the corresponding estimators. In the single-phase scenario, the protocol encompasses two specific known optimal strategies. We extend them to the simultaneous estimation of two phases and evaluate their performance. Then, we retrieve the ultimate digital bound on precision when a generic number of phases is simultaneously estimated. We show that in the multiphase strategy there is only a constant quantum advantage with respect to a sequence of independent single-phase estimations. This extends a recent similar result, which settled a controversy on the search for the multiphase enhancement.

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arXiv2022

Quantum metrology of noisy spreading channels

We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh's curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with $N$ average photons allow to asymptotically estimate the parameter with a $\sqrt{N}$ better precision than classical states with same energy.

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arXiv2022

Tight bounds from multiple-observable entropic uncertainty relations

We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular, we introduce state-independent and state-dependent entropic inequalities. Interestingly, the violation of these inequalities is strictly connected with the presence of quantum correlations. We show that the additivity of EUR holds only for EUR that involve two observables, while this is not the case for inequalities that consider more than two observables or the addition of the von Neumann entropy of a subsystem. We apply them to bipartite systems and to several classes of states of a three-qubit system.

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arXiv2020

Squeezing metrology: a unified framework

Quantum metrology theory has up to now focused on the resolution gains obtainable thanks to the entanglement among N probes. Typically, a quadratic gain in resolution is achievable, going from the 1/sqrt(N) of the central limit theorem to the 1/N of the Heisenberg bound. Here we focus instead on quantum squeezing and provide a unified framework for metrology with squeezing, showing that, similarly, one can generally attain a quadratic gain when comparing the resolution achievable by a squeezed probe to the best N-probe classical strategy achievable with the same energy. Namely, here we give a quantification of the Heisenberg squeezing bound for arbitrary estimation strategies that employ squeezing. Our theory recovers known results (e.g.~in quantum optics and spin squeezing), but it uses the general theory of squeezing and holds for arbitrary quantum systems.

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arXiv2020

Quantum thermodynamics of two bosonic systems

We study the energy exchange between two bosonic systems that interact via bilinear transformations in the mode operators. The first mode is considered as the thermodynamic system, while the second is regarded as the bath. This work finds its roots in a very recent formulation of quantum thermodynamics [1] which allows to consider baths that are not described by the usual Boltzmann-Gibbs canonical form. Baths can possess quantum properties, such as squeezing or coherence, and can be initially correlated with the system, even through entanglement. We focus mainly on the case of Gaussian states, by quantifying the relation between their defining parameters, namely the mean values of the quadratures and the covariance matrix, and relevant thermodynamical quantities such as the heat exchanged and the work performed during the interaction process. We fully solve the case of initially uncorrelated Gaussian states and provide the most general form of the first law of thermodynamics in this case. We also discuss the case of initially correlated states by considering a number of relevant examples, studying how correlations can assist some phenomena, e.g. work extraction or anomalous heat flows. Finally, we present an information-theoretic approach based on the Renyi entropy of order two for clarifying more generally the role of correlations on heat exchanges.

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arXiv2019

Optimal entanglement witnesses from limited local measurements

We address the problem of optimising entanglement witnesses when a limited fixed set of local measurements can be performed on a bipartite system, thus providing a procedure, feasible also for experiments, to detect entangled states using only the statistics of these local measurements. We completely characterize the class of entanglement witnesses of the form $W = P ^Γ$, where $Γ$ denotes partial transposition, that can be constructed from the measurements of the bipartite operators $σ_{x}\otimesσ_{x},$ $σ_{y}\otimesσ_{y}$ and $σ_{z}\otimesσ_{z}$ in the case of two-qubit systems. In particular, we consider all possible extremal decomposable witnesses within the considered class that can be defined from this set of measurements. Finally, we discuss possible extensions to higher dimension bipartite systems when the set of available measurements is characterized by the generalized Gell-Mann matrices. We provide several examples of entanglement witnesses, both decomposable and indecomposable, that can be constructed with these limited resources.

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arXiv2018

State independent uncertainty relations from eigenvalue minimization

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the many known techniques developed to this aim. To demonstrate the simplicity of the method we analyze multiple instances, both previously known and novel, that involve two or more observables, both bounded and unbounded.

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arXiv2018

Tripartite entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios

In the present work, we study tripartite quantum steering of quantum correlations arising from two local dichotomic measurements on each side in the two types of partially device-independent scenarios: $1$-sided device-independent scenario where one of the parties performs untrusted measurements while the other two parties perform trusted measurements and $2$-sided device-independent scenario where one of the parties performs trusted measurements while the other two parties perform untrusted measurements. We demonstrate that tripartite steering in the $2$-sided device-independent scenario is weaker than tripartite steering in the $1$-sided device-independent scenario by using two families of quantum correlations. That is these two families of quantum correlations in the $2$-sided device-independent framework detect tripartite entanglement through tripartite steering for a larger region than that in the $1$-sided device-independent framework. It is shown that tripartite steering in the $2$-sided device-independent scenario implies the presence of genuine tripartite entanglement of $2\times 2 \times 2$ quantum system, even if the correlation does not exhibit genuine nonlocality or genuine steering.

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arXiv2018

Multipartite steering inequalities based on entropic uncertainty relations

We investigate quantum steering for multipartite systems by using entropic uncertainty relations. We introduce entropic steering inequalities whose violation certifies the presence of different classes of multipartite steering. These inequalities witness both steerable states and genuine multipartite steerable states. Furthermore, we study their detection power for several classes of states of a three-qubit system.

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arXiv2017

Tight entropic uncertainty relations for systems with dimension three to five

We consider two (natural) families of observables $O_k$ for systems with dimension $d=3,4,5$: the spin observables $S_x$, $S_y$ and $S_z$, and the observables that have mutually unbiased bases as eigenstates. We derive tight entropic uncertainty relations for these families, in the form $\sum_kH(O_k)\geqslantα_d$, where $H(O_k)$ is the Shannon entropy of the measurement outcomes of $O_k$ and $α_d$ is a constant. We show that most of our bounds are stronger than previously known ones. We also give the form of the states that attain these inequalities.

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