arXiv subjects

Donato Farina

Publications and source records attributed to Donato Farina.

At least 19 recordsLinked to original sources

arXiv2026

Spatial Leggett-Garg inequalities

We formulate a spatial extension of the Leggett-Garg inequality by considering three distant observers locally measuring a many-body system at three subsequent times. The spatial form is especially suitable to test the ability of quantum devices to generate spatio-temporal correlations in a Hamiltonian-agnostic manner. We illustrate our proposal for a Heisenberg chain in a magnetic field, showing indeed that the first inequality-violation time scales proportionally to the distance between measuring parties. We attribute this phenomenon to Lieb-Robinson physics and, confirming this connection, we find that violations are anticipated when increasing the interaction range. The inequality violation is readily observable in current quantum simulation platforms, particularly Rydberg atoms arrays and ultracold atoms in optical lattices. In outlook, spatial Leggett-Garg inequalities constitute a practical tool for benchmarking the complex non-relativistic dynamics of many-body quantum systems.

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arXiv2026

Non-Hermitian entropy production from fluctuation theorems

We develop a first-principles thermodynamic framework for non-Hermitian dynamics based on a post-selected version of the fluctuation theorem. This allows us to identify a quantity that remains positive throughout the non-Hermitian evolution and can be interpreted as the entropy production of the post-selected dynamics. We relate this quantity to previously proposed notions of non-Hermitian entropy and derive an associated second law. Furthermore, we establish a connection with information-theoretic quantities, in particular the Petz-Rényi divergences, and leverage this connection to derive upper and lower bounds. Finally, we decompose the entropy production into incoherent and coherent contributions, identifying distinctive features of the coherent term in the vicinity of exceptional points. We illustrate our results using a paradigmatic model of non-Hermitian evolution based on a two-level system.

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arXiv2026

Local and Global Master Equations through the Lens of Non-Hermitian Physics

We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.

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arXiv2026

Charging Quantum Batteries via Dissipative Quenches

We investigate work extraction in open quantum batteries composed of interacting spin chains weakly coupled to engineered environments. Focusing on two- and four-qubit XX models initially prepared in thermal Gibbs states, we analyze how dissipation and dephasing, acting either locally or collectively, can generate and shape ergotropy during both transient and steady-state dynamics. By introducing a continuous interpolation between parallel and collective noise channels, we systematically characterize the impact of environmental structure on work extractability. We show that purely dissipative dynamics can activate finite ergotropy from completely passive thermal states, giving rise to temperature-dependent transient regimes where hotter initial states temporarily outperform colder ones in an ergotropic Mpemba-like fashion. In contrast, collective dissipation leads to steady states whose passivity crucially depends on the initial temperature and system size, a behavior we trace back to the emergence of non-trivial dark subspaces. Finally, we demonstrate that dephasing channels suppress both transient advantages and steady-state work extraction, highlighting the qualitative difference between dissipative and dephasing environments.

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arXiv2026

Certifying ergotropy under partial information

Ergotropy, the maximum work extractable from a quantum system, is a central resource in quantum physics. Computing ergotropy is well established when the system state is fully known, but its estimation under partial information remains an open problem. Here we introduce a general certification framework that lower bounds ergotropy using only the expectation values of a limited set of arbitrary observables. The method naturally applies in the finite-statistics regime, yielding confidence-certified bounds that explicitly incorporate shot noise. We benchmark our approach on both synthetic data and experimental measurements from an IBM quantum processor. This establishes a robust and experimentally accessible tool for certifying extractable work in realistic quantum settings.

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arXiv2026

Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations

Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation methods can be used to generate the phase diagram for one- and two-dimensional quantum systems. To do so, we formulate a relaxed version of the ground-state problem as a semidefinite program, which we can solve efficiently. Then, by taking the resulting vector of moments for different model parameters, we identify all phase transitions based on their cosine similarity. Furthermore, we show how spontaneous symmetry breaking is naturally captured by bounding the corresponding observable. Using these methods, we reproduce the phase transitions for the one-dimensional transverse field Ising model and the two-dimensional frustrated bilayer Heisenberg model. We also illustrate how the phase diagram of the latter changes when a next-nearest-neighbor interaction is introduced. Overall, our work demonstrates how relaxation methods provide a novel framework for studying and understanding quantum phase transitions.

cond-mat.str-el↗

arXiv2026

Certification of quantum properties with imperfect measurements

The accurate characterization of quantum systems is essential for the advancement of quantum technologies. In particular, certifying convex functions of quantum states plays a central role in many applications. We present a certification method for experimentally prepared quantum states that accounts for both shot noise and measurement imperfections in the data-acquisition stage. Building upon previous work, our method extends confidence regions to accommodate imperfect control over measurements. The values of the functions can then be bounded using convex optimization techniques. We provide explicit prescriptions for quantifying the noise contribution from finite statistics and for estimating the effect of measurement imperfections. By jointly incorporating statistical and systematic errors, the method yields a robust certification framework for quantum experiments.

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arXiv2026

Bounding many-body properties under partial information and finite measurement statistics

Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite programming approaches enable probabilistic bounds from finite-shot measurements of easily accessible, yet informationally incomplete, observables. Here we render these methods scalable in the number of qubits by instead utilizing moment-matrix relaxations. After introducing the general formalism, we show how the approach can be adapted with specific knowledge of the system, such as it being the ground state of a given Hamiltonian, possessing specific symmetries or being the steady state of a given Lindbladian. Our approach defines a scalable real-world certification scheme leveraging semidefinite programming relaxations and experimental estimations which, unavoidably, contain shot noise.

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arXiv2025

Tomographic characterization of non-Hermitian Hamiltonians in reciprocal space

Non-Hermitian Hamiltonians enrich quantum physics by extending conventional phase diagrams, enabling novel topological phenomena, and realizing exceptional points with potential applications in quantum sensing. Here, we present an experimental photonic platform capable of simulating a non-unitary quantum walk generated by a peculiar type of non-Hermitian Hamiltonian, largely unexplored in the literature. The novelty of this platform lies in its direct access to the reciprocal space, which enables us to scan the quasi-momentum across the entire Brillouin zone and thus achieve a precise tomographic reconstruction of the underlying non-Hermitian Hamiltonian, indicated by the comparison between theoretical predictions and experimental measurements. From the inferred Hamiltonian, it is possible to retrieve complex-valued band structures, resolve exceptional points in momentum space, and detect the associated parity-time symmetry breaking through eigenvector coalescence. Our results, presented entirely in quasi-momentum space, represent a substantial shift in perspective in the study of non-Hermitian phenomena.

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arXiv2025

Boosting thermalization of classical and quantum many-body systems

Understanding and optimizing the relaxation dynamics of many-body systems is essential both for foundational studies in quantum thermodynamics and for applications such as quantum simulation and quantum computing. Efficient preparation of thermal states of a many-body Hamiltonian is governed by the spectral properties of the associated Lindbladian, in particular its spectral gap, which determines the slowest relaxation rate. In this work, we develop a systematic framework for constructing Lindbladians that prepare thermal states. Our approach reveals a simple relation between the relaxation dynamics at finite and infinite temperatures. The framework is scalable to larger system sizes when implemented using tensor-network methods. We find that efficient thermalization requires that the relaxation dynamics respect the symmetries of the thermal state, which reduces the number of free parameters. By applying gradient-based optimization to the Lindbladians, we enhance the spectral gap and thereby boost thermalization. When applied to both classical and quantum spin models, our method demonstrates a substantial enhancement of the spectral gap. For larger system sizes, our approach provides a variational upper bound and enables a certified lower bound on the minimum relaxation rate.

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arXiv2025

Certifying steady-state properties of open quantum systems

Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified bounds on the expectation value of an arbitrary observable in the steady state of Lindbladian dynamics. We illustrate our method on a series of many-body systems, including paradigmatic spin-1/2 chains and two-dimensional ladders, considering both equilibrium and nonequilibrium steady-states. We benchmark our method with state-of-the-art tensor-network approaches that, unlike our method, are only able to provide estimates, with no guarantee, on steady-state quantities. For the tested models, only modest computational effort is needed to obtain certified non-trivial bounds for system sizes intractable by exact methods. Our method introduces the first general numerical tool for bounding steady-state properties of open quantum dynamics, opening a new avenue in the understanding of stable configurations in many-body systems.

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arXiv2025

Local ergotropy dynamically witnesses many-body localized phases

Many-body localization is a dynamical phenomenon characteristic of strongly interacting and disordered many-body quantum systems which fail to achieve thermal equilibrium. From a quantum information perspective, the fingerprint of this phenomenon is the logarithmic growth of the entanglement entropy over time. We perform intensive numerical simulations, applied to a paradigmatic model system, showing that the local ergotropy, the maximum extractable work via local unitary operations on a small subsystem in the presence of Hamiltonian coupling, dynamically witnesses the change from ergodic to localized phases. Within the many-body localized phase, both the local ergotropy and its quantum fluctuations slowly vary over time with a characteristic logarithmic law analogous to the behaviour of entanglement entropy. This showcases how directly leveraging local control, instead of local observables or entropies analyzed in previous works, provides a thermodynamic marker of localization phenomena based on the locally extractable work.

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arXiv2025

Boosting projective methods for quantum process and detector tomography

We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of completely positive trace-preserving matrices. By integrating this method with alternate projection techniques, we achieve a three-order-of-magnitude improvement in approximating the closest quantum channel to an arbitrary Hermitian matrix compared to existing methods without compromising computational efficiency. Our second method extends this approach to quantum detector tomography, demonstrating superior efficiency compared to current techniques. Through numerical simulations, we evaluate our protocols across channels of up to four qubits in quantum process tomography and systems of up to six qubits in quantum detector tomography, showcasing superior precision and efficiency.

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arXiv2024

Parallel ergotropy: Maximum work extraction via parallel local unitary operations

Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite systems. In this framework, we consider a quantum battery made up of many interacting sub-systems and study the maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting functional parallel ergotropy. Focusing on the bipartite case, we first observe that parallel ergotropy outperforms work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum available work and the second agent B, subsequently, extracts what is left on the other part. For the agents, this showcases the need of cooperating for an overall benefit. Secondly, from the informational point of view, we observe that the parallel capacity of a state can detect entanglement and compare it with the statistical entanglement witness that exploits fluctuations of stochastic work extraction. Additionally, we face the technical problem of computing parallel ergotropy. We derive analytical upper bounds for specific classes of states and Hamiltonians and provide receipts to obtain numerical upper bounds via semi-definite programming in the generic case. Finally, extending the concept of parallel ergotropy, we demonstrate that system's free-time evolution and application of local unitaries allow one to saturate the gap with the ergotropy of the whole system.

quant-ph↗

arXiv2024

Extended local ergotropy

A fundamental problem in quantum thermodynamics is to properly quantify the work extractable from out-of-equilibrium systems. While for closed systems, maximum quantum work extraction is defined in terms of the ergotropy functional, this question is unclear in open systems interacting with an environment. The concept of local ergotropy has been proposed, but it presents several problems, such as it is not guaranteed to be non-increasing in time. Here we introduce the concept of extended local ergotropy by exploiting the free evolution of the system-environment compound. At variance with the local ergotropy, the extended local ergotropy is greater, is non-increasing in time, and activates the potential of work extraction in many cases. We then concentrate on specific schemes in which we alternate repeated local unitaries and free system-environment evolution. We provide examples based on the Jaynes-Cummings model, presenting practical protocols and analytic results that serve as proof of principle for the aforementioned advantages.

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arXiv2024

Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization

A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but much less is known beyond this regime. Here we propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map. The idea is to replace its unphysical Choi operator with its closest physical one, mimicking recent work on quantum process tomography. We also show that the regularized dynamics is more accurate in terms of reproducing the exact dynamics: this allows to heuristically push the utilization of these master equations in moderate coupling regimes, where the loss of positivity can have relevant impact.

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arXiv2024

Certification of quantum state functions under partial information

Convex functions of quantum states play a key role in quantum physics, with examples ranging from Bell inequalities to von Neumann entropy. However, in experimental scenarios, direct measurements of these functions are often impractical. We address this issue by introducing two methods for determining rigorous confidence bounds for convex functions based on informationally incomplete measurements. Our approach outperforms existing protocols by providing tighter bounds for a fixed confidence level and number of measurements. We evaluate the performance of our methods using both numerical and experimental data. Our findings demonstrate the efficacy of our approach, paving the way for improved quantum state certification in real-world applications.

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arXiv2024

Deep Neural Network-assisted improvement of quantum compressed sensing tomography

Quantum compressed sensing is the fundamental tool for low-rank density matrix tomographic reconstruction in the informationally incomplete case. We examine situations where the acquired information is not enough to allow one to obtain a precise compressed sensing reconstruction. In this scenario, we propose a Deep Neural Network-based post-processing to improve the initial reconstruction provided by compressed sensing. The idea is to treat the estimated state as a noisy input for the network and perform a deep-supervised denoising task. After the network is applied, a projection onto the space of feasible density matrices is performed to obtain an improved final state estimation. We demonstrate through numerical experiments the improvement obtained by the denoising process and exploit the possibility of looping the inference scheme to obtain further advantages. Finally, we test the resilience of the approach to out-of-distribution data.

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