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Davide Girolami

Publications and source records attributed to Davide Girolami.

At least 19 recordsLinked to original sources
arXiv2026

Observable measures of multipartite entanglement

Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.

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arXiv2026

An Information-Theoretic Bound on Thermodynamic Efficiency and the Generalized Carnot's Theorem

We derive a bound on the efficiency of thermal engines that can be sharper than Carnot's limit. It is a function of statistical correlations between the engine internal state and Hamiltonian, can be saturated even in finite-time cycles, and applies to both classical and quantum engines. Specifically, the bound establishes the exact maximal efficiency of engines operating with multiple baths, tightening the upper limit set by Carnot's theorem. Then, we show that an engine made of a quantum dot coupled with fermionic baths can achieve the bound, even when operating beyond the quasistatic regime. The result provides a design principle for realistic energy harvesting machines.

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arXiv2026

Quantifying the Operational Cost of Multipartite Entanglement

Multipartite entanglement determines the strength and range of interactions in many-body quantum systems. Yet, it is hard to evaluate it, due to the complex structures of quantum states. Here, we introduce a generic method to quantify the k <= N-partite entanglement of an N-particle system, by maximizing an arbitrary bipartite entanglement measure within subsystems of size up to k. The resulting classification of multipartite states captures their experimental cost: creating a k-partite entangled state requires at least k-1 two-particle entangling gates. Further, we analytically calculate the newly defined k-partite entanglement of formation, which generalizes an important bipartite entanglement measure, in several classes of states, including the W states of any dimension.

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arXiv2024

Evaluating Pauli errors on cluster states by weighted distances

We address the problem of evaluating the difference between quantum states before and after being affected by errors encoded in unitary transformations. Standard distance functions, e.g., the Bures length, are not fully adequate for such a task. Weighted distances are instead appropriate information measures to quantify distinguishability of multipartite states. Here, we employ the previously introduced weighted Bures length and the newly defined weighted Hilbert-Schmidt distance to quantify how much single-qubit Pauli errors alter cluster states. We find that different errors of the same dimension change cluster states in a different way, i.e., their detectability is in general different. Indeed, they transform an ideal cluster state into a state whose weighted distance from the input depends on the specific chosen Pauli rotation, as well as the position of the affected qubit in the graph related to the state. As these features are undetected by using standard distances, the study proves the usefulness of weighted distances to monitor key but elusive properties of many-body quantum systems.

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arXiv2024

Quantification of Entanglement and Coherence with Purity Detection

Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing.

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arXiv2024

Quantitative bounds to propagation of quantum correlations in many-body systems

We investigate how much information about a quantum system can be simultaneously communicated to independent observers, by establishing quantitative limits to bipartite quantum correlations in many-body systems. As recently reported in Phys. Rev. Lett. 129, 010401 (2022), bounds on quantum discord and entanglement of formation between a single quantum system and its environment, e.g., a large number of photons, dictate that independent observers which monitor environment fragments inevitably acquire only classical information about the system. Here, we corroborate and generalize those findings. First, we calculate continuity bounds of quantum discord, which establish how much states with a small amount of quantum correlations deviate from being embeddings of classical probability distributions. Also, we demonstrate a universally valid upper bound to the bipartite entanglement of formation between an arbitrary pair of components of a many-body quantum system. The results confirm that proliferation of classical information in the Universe suppresses quantum correlations.

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arXiv2022

Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality

"How much information about a system $\mathcal{S}$ can one extract from a fragment $\mathcal{F}$ of the environment $\mathcal{E}$ that decohered it?" is the central question of Quantum Darwinism. To date, most answers relied on the quantum mutual information of $\mathcal{SF}$, or on the Holevo bound on the channel capacity of $\mathcal{F}$ to communicate the classical information encoded in $\mathcal{S}$. These are reasonable upper bounds on what is really needed but much harder to calculate -- the accessible information in the fragment $\mathcal{F}$ about $\mathcal{S}$. We consider a model based on imperfect c-not gates where all the above can be computed, and discuss its implications for the emergence of objective classical reality. We find that all relevant quantities, such as the quantum mutual information as well as various bounds on the accessible information exhibit similar behavior. In the regime relevant for the emergence of objective classical reality this includes scaling independent of the quality of the imperfect c-not gates or the size of $\mathcal{E}$, and even nearly independent of the initial state of $\mathcal{S}$.

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arXiv2021

Quantifying the difference between many-body quantum states

The quantum state overlap is the textbook measure of the difference between two quantum states. Yet, it is inadequate to compare the complex configurations of many-body systems. The problem is inherited by the widely employed quantum state fidelity and related distances. We introduce the weighted distances, a new class of information-theoretic measures that overcome these limitations. They quantify how hard it is to discriminate between two quantum states of many particles, factoring in the structure of the required measurement apparatus. Therefore, they can be used to evaluate both the theoretical and the experimental performances of complex quantum devices. We also show that the newly defined "weighted Bures length" between the input and output states of a quantum process is a lower bound to the experimental cost of the transformation. The result uncovers an exact quantum limit to our ability to convert physical resources into computational ones.

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arXiv2020

An axiomatic measure of one-way quantum information

I introduce an algorithm to detect one-way quantum information between two interacting quantum systems, i.e. the direction and orientation of the information transfer in arbitrary quantum dynamics. I then build an information-theoretic quantifier of one-way information which satisfies a set of desirable axioms. In particular, it correctly evaluates whether correlation implies one-way quantum information, and when the latter is transferred between uncorrelated systems. In the classical scenario, the quantity measures information transfer between random variables. I also generalize the method to identify and rank concurrent sources of quantum information flow in many-body dynamics, enabling to reconstruct causal patterns in complex networks.

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arXiv2019

Quantum Coherence and Intrinsic Randomness

The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as the resource for the intrinsic randomness in the measurement outcomes of a state in the computational basis. We observed in our previous work that the coherence of formation, which measures the asymptotic coherence dilution rate, indeed quantifies the uncertainty of a (classical) correlated party about the system measurement outcome. In this work, we re-derive the result from a quantum point of view and then connect the intrinsic randomness to the relative entropy of coherence, another important coherence measure that quantifies the asymptotic distillable coherence. Even though there does not exist bound coherent states, these two intrinsic randomness quantified by coherence of formation and the relative entropy of coherence are different. Interestingly, we show that this gap is equal to the quantum discord, a general form of quantum correlations, in the state of the system of interest and the correlated party, after a local measurement on the former system.

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arXiv2019

How difficult is it to prepare a quantum state?

Consider a quantum system prepared in an input state. One wants to drive it into a target state. Assuming classical states and operations as free resources, I identify a geometric cost function which quantifies the difficulty of the protocol in terms of how different it is from a classical process. The quantity determines a lower bound to the number of commuting unitary transformations required to complete the task. I then discuss the link between the quantum character of a state preparation and the amount of coherence and quantum correlations that are created in the target state.

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arXiv2018

Coherence and quantum correlations measure sensitivity to dephasing channels

We introduce measures of quantum coherence as the speed of evolution of a system under decoherence. That is, coherence is the ability to estimate a dephasing channel, quantified by the quantum Fisher information. We extend the analysis to interferometric noise estimation, proving that quantum discord is the minimum sensitivity to local dephasing. A physically motivated set of free operations for discord is proposed. The amount of discord created by strictly incoherent operations is upper-bounded by the initial coherence.

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arXiv2018

Information Geometry of Quantum Resources

I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum coherence and quantum correlations. Once confined to thought experiments, they are nowadays created and manipulated by exerting an exquisite experimental control of atoms, molecules and photons. It is important to identify and quantify such quantum features, as they are deemed to be key resources to achieve supraclassical performances in computation and communication protocols. The information geometry viewpoint elucidates the advantage provided by quantum superpositions in phase estimation. Also, it enables to link measures of coherence and entanglement to observables, which can be evaluated in a laboratory by a limited number of measurements.

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arXiv2017

Weaving and neural complexity in symmetric quantum states

We study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any order, where the weights are proportional to the correlation order. The neural complexity, originally introduced to characterize correlation patterns in classical neural networks, is here extended to the quantum scenario. We derive closed formulas of the two quantities for GHZ states mixed with white noise.

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arXiv2017

Detecting metrologically useful asymmetry and entanglement by a few local measurements

Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. Here we show how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. We show that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. We implement the detection scheme in an all-optical experiment.

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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.

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arXiv2017

Quantifying Coherence and Entanglement via Simple Measurements

Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction of the system state. We show that one can extract quantitative bounds to the relative entropy of coherence and the coherent information, coherence and entanglement quantifiers respectively, by a limited number of purity measurements. The scheme is readily implementable with current technology to verify quantum computations in large scale registers, without carrying out expensive state tomography.

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