arXiv subjects

Giuseppe Vitagliano

Publications and source records attributed to Giuseppe Vitagliano.

At least 19 recordsLinked to original sources

arXiv2026

Least Variable Quantum Counting Processes

Counting processes provide a fundamental description of stochastic events ranging from photon detection to clock ticks. A central question is how accurately such events can be timed when only finite memory resources are available. Here, we investigate this problem within a general framework of finite-dimensional classical and quantum counting processes. We derive a rigorous finite-memory variance bound obeyed by every classical $d$-state counting process, which is tight and saturated by a discrete Erlang-type ladder process. Through numerical optimization, we identify quantum counting processes that violate this classical bound, achieving smaller first-tick fluctuations than any classical process with the same memory size and mean tick time. For the qubit case, we further derive an analytical large-mean bound within a single-Kraus no-tick family, showing that the quantum advantage persists asymptotically within this class. The optimized quantum processes exhibit coherent conditioned dynamics and approach a continuous-time quantum-jump description as the mean increases. Our results establish a finite-memory quantum advantage in temporal precision and connect discrete-time counting processes with continuous-time quantum timekeeping.

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arXiv2026

Qutrit entanglement and joint multi-parameter estimation in an optical clock platform

Quantum metrology harnesses entanglement to improve measurement precision beyond classical limits. While standard protocols rely on two-level qubits to estimate a single parameter, extending them to entangled multi-level qudits enables the optimal simultaneous estimation of multiple parameters within a single probe. However, generating such multi-level entanglement and harnessing it for joint multi-parameter estimation in atomic clocks has remained an outstanding challenge. Here, we experimentally demonstrate genuine qutrit entanglement and joint multi-parameter estimation in an optical clock platform. Leveraging control over the ground state and two fine-structure clock states of $^{88}\text{Sr}$ atoms trapped in triple-magic optical tweezers, we generate a maximally entangled two-qutrit state with a loss-postselected fidelity of F = 0.85(1), certifying genuine multi-level entanglement. Taking advantage of this high-dimensional entanglement, we theoretically construct and experimentally realize an optimal two-qutrit metrological probe state and noise-robust readout circuit to simultaneously estimate injected phases on two optical clock transitions. We observe a joint estimation variance below the ideal individual two-level sensing threshold, and show theoretically that this advantage persists at state-of-the-art atom numbers under circuit-level noise. These results demonstrate the key building blocks towards quantum information science with high-dimensional states encoded in the internal energy levels of neutral atoms.

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arXiv2026

Characterizing resources for multiparameter estimation of SU(2) and SU(1,1) unitaries

We analyze the task of estimating a multi-parameter unitary belonging to the $SU(2)$ or $SU(1,1)$ groups, in a two-bosonic-mode scenario and investigate the scaling of the precision in terms of the total particle number. For the $SU(2)$ case, the total particle number is conserved by the evolution and we discuss optimal states in fixed-$n$ subspaces, identifying eigenstates of $J_z^2$ as useful resources, even allowing simultaneous Heisenberg precision scaling for all three parameters. In the $SU(1,1)$ case instead, the conserved quantity is the particle number difference between the two modes, and we identify useful probe states in the sector with an equal number of particles in the two modes. These states are analogous to the $SU(2)$ case and would also allow simultaneous Heisenberg precision scaling for all three parameters. We then consider the more pragmatic scenario of an estimation via expectation values of time-evolved observables, which we restrict to be the first two moments of the generators. We analyze the maximal precision achievable in this setting and we find that the twin-Fock state emerges in both the $SU(2)$ and the $SU(1,1)$ cases as the only one potentially allowing Heisenberg scaling for the estimation of two out of the three parameters. As a complement, we also consider other probe states with fluctuating number of particles, with measurements restricted to quadratic expressions in the mode operators. In this scenario, simultaneous Heisenberg scaling in multiple parameters seems mostly forbidden, with the only exception being an input two-mode squeezed state for the estimation of a two-parameter $SU(2)$. This extends to the multiparameter scenario the well-established intuition that the performance of a $SU(2)$ interferometer can be enhanced by a prior $SU(1,1)$ operation.

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arXiv2026

The uncertainty geometry of finite-dimensional position and momentum

Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational capabilities of quantum systems. Here we characterize the covariance matrices attainable by a finite-dimensional canonical pair of observables related by the discrete Fourier transform, the natural analogue of position and momentum in a finite Hilbert space. We combine analytic arguments with convex-geometric and semidefinite-programming methods based on joint numerical ranges to describe the admissible region through unitary invariants, in particular the trace and determinant of the covariance matrix. This provides a systematic way to identify extremal states, generalizing the notion of minimum-uncertainty states, and to quantify how the discrete uncertainty geometry approaches its continuous counterpart with increasing dimension. We further show that the resulting covariance-matrix characterization has direct consequences for applications: it yields accuracy bounds for multi parameter estimation protocols and separability criteria for finite-dimensional bipartite systems, including discrete analogues of continuous-variable EPR-type witnesses. Our results establish a systematic and versatile platform for connecting uncertainty relations, convex quantum geometry, metrology, and entanglement detection in finite-dimensional systems.

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arXiv2026

Estimating the best separable approximation of non-pure spin-squeezed states

We discuss the estimation of the distance of a given mixed many-body quantum state to the set of fully separable states, applied to the concrete scenario of collective spin states. Concretely, we discuss lower bounds to distances from the set of fully separable states based on entanglement criteria and upper bounds to those distances using an iterative algorithm to find the optimal separable state closest to the target. Focusing on collective states of $N$ spin-$1/2$ particles, we consider spin-squeezing inequalities (SSIs), which provide a complete set of nonlinear entanglement criteria based on collective spin variances. First, we find a lower bound to distance-based entanglement monotones, specifically the so-called best separable approximation (BSA) from the complete set of SSIs, thereby bypassing entirely a numerical optimization over a (potentially very large) set of linear entanglement witnesses. Then, we improve current algorithms to iteratively find the closest separable state to a given target state, exploiting the symmetry of the system. These results allow us to study entanglement quantitatively on thermal states of spin systems on fully-connected graphs at nonzero temperature, as well as potentially similar states arising in out-of-equilibrium situations. We thus apply our methods to investigate entanglement across different phases of a fully-connected XXZ model. We observe that our lower bound becomes often tight for zero temperature as well as for the temperature at which entanglement disappears, both of which are thus precisely captured by the SSIs. We further observe, among other things, that entanglement can arise at nonzero temperature even in the ordered phase, where the ground state is separable, revealing the potential usefulness of entanglement quantification also beyond the ground state paradigm.

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arXiv2026

Thermal Entanglement and Out-of-Equilibrium Thermodynamics in 1D Bose gases

We investigate entanglement in and out of equilibrium in a one-dimensional Bose gas in its low-energy Bogoliubov regime. In this Gaussian setting, the state is fully characterized by its covariance matrix, which allows us to detect and quantify entanglement using a covariance-based framework and associated entanglement monotones. For thermal states, we determine the optimal entanglement witness arising from the covariance matrix criterion and show that it has a remarkably simple mode-resolved structure: it is diagonal in the normal-mode basis and admits a simple analytic form that can be expressed as a product of only two normal-mode uncertainties. We then study out-of-equilibrium dynamics induced by unitary compression and show that entanglement can be generated even from initially separable thermal states. When the evolution is fully adiabatic, the optimal witness retains the same two-mode structure as in the thermal case. Departing from this regime, i.e., performing increasingly rapid compression, the optimal witness becomes genuinely more intricate. Our methods and results provide a unified and physically intuitive picture of how entanglement emerges and evolves in 1D quantum Bose gases, and identify an optimal witness structure relevant more broadly to the analysis of entanglement in quadratic bosonic models and its role in thermodynamic cycles.

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arXiv2026

Uncertainty relations between quantum Fisher information and entanglement monotones

Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum Fisher information (QFI), providing a bound to the precision, and multipartite entanglement quantifiers such as the entanglement depth. However, a connection between the QFI and entanglement monotones, i.e., functions that do not increase under Local Operations and Classical Communications, has so far remained elusive. In this work, we fill this gap by introducing a family of uncertainty relations that bound bipartite entanglement monotones from below via elements of a quantum Fisher information matrix. To further emphasize the significance of our results, we connect these relations to the achievable precision in multiparameter estimation. Considering a system split into two parts with arbitrary dimension, we also show that, while two-dimensional entanglement is sufficient to estimate a single parameter with maximal precision, genuine high-dimensional entanglement is required for multiparameter estimation. We conclude by illustrating how our method extends naturally to a multipartite splitting.

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arXiv2026

Characterizing high-dimensional multipartite entanglement beyond Greenberger-Horne-Zeilinger fidelities

Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the particles have many accessible levels, i.e., they are of high dimension, which leads to a potentially high-dimensional multipartite entangled state. These are important resources for an ever-increasing number of tasks, especially when a network of parties needs to share highly entangled states, e.g., for communicating more efficiently and securely. For these applications, as well as for purely theoretical arguments, it is important to be able to certify both the high-dimensional and the genuine multipartite nature of entangled states, possibly based on simple measurements. Here we derive a novel method that achieves this and improves over typical entanglement witnesses like the fidelity with respect to states of a Greenberger-Horne-Zeilinger (GHZ) form, without needing more complex measurements. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect GHZ states with random noise, as well as on purely randomly chosen ones and find that, in comparison with other available criteria our method provides a significant advantage and is often also simpler to evaluate.

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arXiv2025

Entanglement Dimensionality of Continuous Variable States From Phase-Space Quasi-Probabilities

The dimensionality of entanglement is a core tenet of quantum information processing, especially quantum communication and computation. While it is natural to think of this dimensionality in finite dimensional systems, many of the implementations harnessing high Schmidt numbers are actually based on discretising the observables of continuous variable systems. For those instances, a core question is whether directly utilizing the toolbox of continuous variable quantum information processing leads to better and more robust characterisations of entanglement dimensionality in infinite dimensional systems. We affirmatively answer this question by introducing Schmidt number witnesses for CV systems, based directly on covariances of infinite dimensional Bloch operators that are readily accessible in experiments. We show that the direct estimation leads to increased robustness and versatility compared to first discretising the system and using canonical discrete variable techniques, which provides strong motivation for further developments of genuine CV methods for the characterization of entanglement dimensionality, as well as for their implementation in experiments.

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arXiv2025

$su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems

Generalizing the well-known spin-squeezing inequalities, we study the relation between squeezing of collective $N$-particle $su(d)$ operators and many-body entanglement geometry in multi-particle systems. For that aim, we define the set of pseudo-separable states, which are mixtures of products of single-particle states that lie in the $(d^2-1)$-dimensional Bloch sphere but are not necessarily positive semidefinite. We obtain a set of necessary conditions for states of $N$ qudits to be of the above form. Any state that violates these conditions is entangled. We also define a corresponding $su(d)$-squeezing parameter that can be used to detect entanglement in large particle ensembles. Geometrically, this set of conditions defines a convex set of points in the space of first and second moments of the collective $N$-particle $su(d)$ operators. We prove that, in the limit $N\gg 1$, such set is filled by pseudo-separable states, while any state corresponding to a point outside of this set is necessarily entangled. We also study states that are detected by these inequalities: We show that states with a bosonic symmetry are detected if and only if the two-body reduced state violates the positive partial transpose (PPT) criterion. On the other hand, highly mixed states states close to the $su(d)$ singlet are detected which have a separable two-body reduced state and are also PPT with respect to all possible bipartitions. We also provide numerical examples of thermal equilibrium states that are detected by our set of inequalities, comparing the spin-squeezing inequalities with the $su(3)$-squeezing inequalities.

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arXiv2024

Experimental certification of high-dimensional entanglement with randomized measurements

High-dimensional entangled states offer higher information capacity and stronger resilience to noise compared with two-dimensional systems. However, the large number of modes and sensitivity to random rotations complicate experimental entanglement certification. Here, we experimentally certify three-dimensional entanglement in a five-dimensional two-photon state using 800 Haar-random measurements implemented via a 10-plane programmable light converter. We further demonstrate the robustness of this approach against random rotations, certifying high-dimensional entanglement despite arbitrary phase randomization of the optical modes. This method, which requires no common reference frame between parties, opens the door for high-dimensional entanglement distribution through long-range random links.

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arXiv2024

Leggett-Garg Macrorealism and temporal correlations

Leggett and Garg formulated macrorealist models encoding our intuition on classical systems, i.e., physical quantities have a definite value that can be measured with minimal disturbance, and with the goal of testing macroscopic quantum coherence effects. The associated inequalities, involving the statistics of sequential measurements on the system, are violated by quantum mechanical predictions and experimental observations. Such tests, however, are subject to loopholes: a classical explanation can be recovered assuming specific models of measurement disturbance. We review recent theoretical and experimental progress in characterizing macrorealist and quantum temporal correlations, and in closing loopholes associated with Leggett-Garg tests. Finally, we review recent definitions of nonclassical temporal correlations, which go beyond macrorealist models by relaxing the assumption on the measurement disturbance, and their applications in sequential quantum information processing.

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arXiv2024

Bounding entanglement dimensionality from the covariance matrix

High-dimensional entanglement has been identified as an important resource in quantum information processing, and also as a main obstacle for simulating quantum systems. Its certification is often difficult, and most widely used methods for experiments are based on fidelity measurements with respect to highly entangled states. Here, instead, we consider covariances of collective observables, as in the well-known Covariance Matrix Criterion (CMC)[1] and present a generalization of the CMC for determining the Schmidt number of a bipartite system. This is potentially particularly advantageous in many-body systems, such as cold atoms, where the set of practical measurements is very limited and only variances of collective operators can typically be estimated. To show the practical relevance of our results, we derive simpler Schmidt-number criteria that require similar information as the fidelity-based witnesses, yet can detect a wider set of states. We also consider paradigmatic criteria based on spin covariances, which would be very helpful for experimental detection of high-dimensional entanglement in cold atom systems. We conclude by discussing the applicability of our results to a multiparticle ensemble and some open questions for future work.

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arXiv2024

Witnessing environment dimension through temporal correlations

We introduce a framework to compute upper bounds for temporal correlations achievable in open quantum system dynamics, obtained by repeated measurements on the system. As these correlations arise by virtue of the environment acting as a memory resource, such bounds are witnesses for the minimal dimension of an effective environment compatible with the observed statistics. These witnesses are derived from a hierarchy of semidefinite programs with guaranteed asymptotic convergence. We compute non-trivial bounds for various sequences involving a qubit system and a qubit environment, and compare the results to the best known quantum strategies producing the same outcome sequences. Our results provide a numerically tractable method to determine bounds on multi-time probability distributions in open quantum system dynamics and allow for the witnessing of effective environment dimensions through probing of the system alone.

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arXiv2023

Characterizing entanglement dimensionality from randomized measurements

We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement dimensionality [S. Liu et al., arXiv:2208.04909], we derive an inequality that resembles well-known entanglement criteria, but contains different bounds for the different dimensionalities of entanglement. This criterion is invariant under local changes of $su(d)$ bases and can be used to find regions in the space of moments of randomized correlations, generalizing the results of [S. Imai et al., Phys. Rev. Lett. 126, 150501 (2021)] to the case of entanglement-dimensionality detection. In particular, we find analytical boundary curves for the different entanglement dimensionalities in the space of second- and fourth-order moments of randomized correlations for all dimensions $d_a = d_b = d$ of a bipartite system. We then show how our method works in practice, also considering a finite statistical sample of correlations, and we also show that it can detect more states than other entanglement-dimensionality criteria available in the literature, thus providing a method that is both very powerful and potentially simpler in practical scenarios. We conclude by discussing the partly open problem of the implementation of our method in the multipartite scenario.

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arXiv2023

Landauer vs. Nernst: What is the True Cost of Cooling a Quantum System?

Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, which states that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilized? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure quantum states. We show that perfect cooling is possible with Landauer energy cost given infinite time or control complexity. However, such optimal protocols require complex unitaries generated by an external work source. Restricting to unitaries that can be run solely via a heat engine, we derive a novel Carnot-Landauer limit, along with protocols for its saturation. This generalizes Landauer's principle to a fully thermodynamic setting, leading to a unification with the third law and emphasizes the importance of control in quantum thermodynamics.

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arXiv2023

Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles

We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. First, we derive an uncertainty relation that plays the role of a number-phase uncertainty for spin systems. It is important that the relation is given with well-defined and easily measurable quantities, and that it does not need assuming infinite dimensional systems. Based on this uncertainty relation, we show how to detect bipartite entanglement in an unpolarized Dicke state of many spin-1/2 particles. The particles are split into two subensembles, then collective angular momentum measurements are carried out locally on the two parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering criterion. Then, we present an entanglement condition that can detect bipartite entanglement in such systems. We demonstrate the utility of the criteria by applying them to a recent experiment given in K. Lange et al. [Science 360, 416 (2018)] realizing a Dicke state in a Bose-Einstein condensate of cold atoms, in which the two subensembles were spatially separated from each other. Our methods also work well if split spin-squeezed states are considered. We show in a comprehensive way how to handle experimental imperfections, such as the nonzero particle number variance including the partition noise, and the fact that, while ideally BECs occupy a single spatial mode, in practice the population of other spatial modes cannot be fully suppressed.

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arXiv2022

Finite-Function-Encoding Quantum States

We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions, i.e., multivariate functions over the ring of integers modulo $d$, and investigate some of their structural properties. We also point out some differences between polynomial and non-polynomial function encoding states: The former can be associated to graphical objects, that we dub tensor-edge hypergraphs (TEH), which are a generalization of hypergraphs with a tensor attached to each hyperedge encoding the coefficients of the different monomials. To complete the framework, we also introduce a notion of finite-function-encoding Pauli (FP) operators, which correspond to elements of what is known as the generalized symmetric group in mathematics. First, using this machinery, we study the stabilizer group associated to FFE states and observe how qudit hypergraph states introduced in arXiv:1612.06418v2 admit stabilizers of a particularly simpler form. Afterwards, we investigate the classification of FFE states under local unitaries (LU), and, after showing the complexity of this problem, we focus on the case of bipartite states and especially on the classification under local FP operations (LFP). We find all LU and LFP classes for two qutrits and two ququarts and study several other special classes, pointing out the relation between maximally entangled FFE states and complex Butson-type Hadamard matrices. Our investigation showcases also the relation between the properties of FFE states, especially their LU classification, and the theory of finite rings over the integers.

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