arXiv subjects

Roberto Franzosi

Publications and source records attributed to Roberto Franzosi.

At least 19 recordsLinked to original sources

arXiv2026

Geometric Aspects of Entanglement

Quantum entanglement is a fundamental resource in quantum information theory, yet its general characterization and quantification remain challenging, especially in multipartite systems. In this work we investigate entanglement from a geometric perspective, focusing on the Riemannian structure induced by the Fubini--Study metric on the projective Hilbert space of multi-qubit quantum states. By exploiting the local-unitary invariance of this metric, we derive the entanglement distance (ED), a geometric measure that quantifies entanglement as an obstruction to locally minimizing the sum of squared Fubini--Study distances generated by local operations. We analyze the properties of ED for pure multi-qubit states and discuss its behavior under local operations and classical communication. In particular, we show that ED reproduces established entanglement measures in well-defined and restricted settings. For pure states of two qubits, ED reduces to an exact monotone function of the concurrence and, independently, to an explicit monotone function of the entropy of entanglement. These results provide a clear geometric interpretation of standard bipartite entanglement measures within the present framework, while highlighting the limitations of such correspondences beyond the two-qubit case.

quant-ph↗

arXiv2026

Entanglement Dynamics in Katz-Weighted Graph States

We investigate the entanglement dynamics of quantum states defined on graphs with non-local Ising interactions governed by the Katz kernel of the underlying network. The interaction pattern is physically motivated by a gapped fermionic mediator propagating on the same graph, whose perturbative elimination yields an effective Katz-weighted Ising Hamiltonian. Using the Entanglement Distance, we derive an exact analytical expression for the entanglement generated from an initially separable state and apply it to representative deterministic graph families. We then characterize the dynamics in different propagation regimes. In the weak-Katz regime, the dynamics admits a systematic motif expansion with triangles entering at first order order and four-cycles, local degree structure, and overlappin triangles appearing at second order. In the strong-propagation regime, the interaction is instead dominated by the principal adjacency mode and by the localization properties of its eigenvector. For Erdős--Rényi graphs, the weak-propagation expansion can be averaged analytically, revealing a locally tree-like contribution in the sparse regime and saturation of the Entanglement Distance density in the dense regime. Our results connect entanglement dynamics with both the walk-based and spectral structure of complex networks.

quant-ph↗

arXiv2026

A Geometric Theory of Quantum Entanglement

Entanglement Distance (ED) was originally proposed as a geometric measure of entanglement derived from the Fubini-Study metric on the projective Hilbert space. Independently, the Meyer-Wallach and Scott measures quantify multipartite entanglement via linear entropy. In this work, we demonstrate that these two seemingly distinct frameworks are mathematically identical for pure states of arbitrary finite dimensions. We prove that ED arises naturally as the trace of the Fubini-Study metric tensor over the local subalgebra of observables. Crucially, this geometric unification yields a direct operational interpretation: the global entanglement of a pure state is exactly proportional to the total Quantum Fisher Information (QFI) available for local unitary estimation. This bridges abstract information geometry with quantum metrology, demonstrating that ED dynamically quantifies resourcefulness for distributed quantum sensing, identifying Heisenberg-limited sensitivity in regimes where standard variance-based witnesses fail.

quant-ph↗

arXiv2026

Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review

We review a theoretical and experimental programme addressing two closely related phenomena in biophysics: the classical analogue of Fröhlich phonon condensation in macromolecules driven out of thermal equilibrium, and the resulting activation of long-range resonant electrodynamic intermolecular forces.The first is obtained by applying the time-dependent variational principle (TDVP) to the quantum Wu-Austin model,yielding a fully classical Hamiltonian in action-angle variables whose nonlinear rate equations display a nonequilibrium phase transition: supplied energy is channelled into the lowest-frequency collective mode. The second is based on a classical electrodynamic Hamiltonian for two coupled oscillating dipoles, whose normal modes predict long-range (1/r^3) resonant interactions. These are absent at thermal equilibrium but emerge under out-of-equilibrium coherent oscillations.We also discuss how to link Fröhlich rate equations directly to Hamilton equations, clarifying the role of bath-mediated nonlinear couplings and the conditions for strong condensation at room temperature.In addition, TDVP is applied to a Davydov-Holstein-Fröhlich model describing electron-phonon dynamics along a specific DNA sequence and its cognate restriction enzyme EcoRI. The time-domain Fourier cross-spectrum of the resulting electron currents shows a sharp co-resonance peak for the canonical recognition sequence, which disappears under randomisation, providing a sequence-specific electrodynamic signature of DNA-protein recognition.Experimental evidence from THz near-field spectroscopy, fluorescence correlation spectroscopy, and direct protein clustering is reviewed. Together these results support the view that metabolic energy can drive macromolecules into coherent oscillatory states, activating selective long-range electrodynamic forces relevant to biochemical organisation in living matter.

physics.bio-ph↗

arXiv2026

A microcanonical approach to criticality in the mean-field $ϕ^4$ model: evidence of intrinsic microcanonical structure before the thermodynamic limit

Collective critical behavior is often identified with thermodynamic nonanalyticities and divergences emerging only in the infinite-size limit. Here we adopt a complementary viewpoint: criticality is a structural property due to the rearrangement of the interactions among system's constituents that already exists at finite size and becomes singular only asymptotically. We show that the microcanonical entropy derivatives provide a natural finite-$N$ arena where such structure is encoded in intrinsic extremal/inflection morphologies, and that microcanonical inflection-point analysis (MIPA) turns these morphologies into a unique finite-size critical marker and a well-defined critical trajectory. Using the mean-field $ϕ^4$ model as a stringent benchmark, we reconstruct $β_N(\varepsilon)$ and $γ_N(\varepsilon)$ from microcanonical simulations, validate them against analytic results, and demonstrate that the MIPA trajectory converges to the exact thermodynamic critical point while simultaneously organizing the approach of other observables to their asymptotic behavior. Our results elevate finite-size criticality from a rounded remnant of the thermodynamic limit to a measurable and predictive object in its own right, with direct relevance to modern finite-system platforms and numerical studies.

cond-mat.stat-mech↗

arXiv2025

Multipartite entanglement features of primordial non-gaussianities

We discuss some entanglement features associated with cubic non-Gaussian perturbations in single-field inflationary scenarios. We adopt standard momentum-space techniques to show how multipartite entanglement arises for inflationary perturbation modes, focusing on the dynamics of the comoving curvature perturbation. In particular, we quantify entanglement generation via the recently proposed Entanglement Distance, which introduces a geometric interpretation of quantum correlations in terms of the Fubini-Study metric. In the continuum limit, we show that the Entanglement Distance arising from displacement transformations is proportional to the total number of excitations in the quantum state for cubic perturbations, thus providing an upper bound on the von Neumann entanglement entropy of any reduced state compatible with such excitations. Within the interaction picture, we further observe that the quantum correlations arising from cubic gravitational interactions are typically much larger than the standard squeezing contribution, in agreement with previous studies focusing on von Neumann entropy generation across the Hubble horizon. We further show how the inflationary parameters affect the total amount of such correlations, highlighting in particular their dependence on the inflationary energy scales and the number of e-foldings during slow-roll.

gr-qc↗

arXiv2025

Entanglement in Quantum Systems Based on Directed Graphs

We investigate the entanglement properties of quantum states associated with directed graphs. Using a measure derived from the Fubini-Study metric, we quantitatively relate multipartite entanglement to the local connectivity of the graph. In \emph{Entanglement in Directed Graph States}, (2025), arXiv:2505.10716, it is demonstrated that the vertex degree distribution fully determines this entanglement measure and remains invariant under vertex relabeling, highlighting its topological character. As a consequence, the measure depends only on the total degree of each vertex, making it independent of the distinction between incoming and outgoing edges. We apply our framework to several specific graph structures, including hierarchical networks, neural network-inspired graphs, full binary tree and linear bridged cycle graphs, demonstrating how their combinatorial properties influence entanglement distribution. These results provide a geometric perspective on quantum correlations in complex systems, offering potential applications in the design and analysis of quantum networks.

quant-ph↗

arXiv2025

Geometric multipartite entanglement from gravitational particle production

We explore novel generation of genuine multipartite entanglement within gravitational particle production processes during inflationary stages. To this end, we focus on perturbative production mechanisms, considering a non-minimally coupled scalar inflaton field with quartic self-coupling potential and computing probability amplitudes arising from its gravitational interaction with background perturbations. The corresponding entanglement amount is quantified using the recently proposed Entanglement Distance, that provides a \emph{geometric interpretation of particle entanglement, in terms of the Fubini-Study metric}. We observe that, in the limit of negligible squeezing, the total amount of entanglement is dominated by the infrared cutoff scale, in agreement with previous studies analyzing the von Neumann entropy within bipartite scenarios. We then show that \emph{non-negligible multipartite entanglement signatures may emerge across inflation, even during the latest stages of slow-roll}, highlighting their dependence on inflationary momentum scales. Generalizations to regimes with non-negligible squeezing, cubic non-Gaussianities, additional spectator fields and possible observational signatures are also discussed.

gr-qc↗

arXiv2025

Entanglement in Directed Graph States

We investigate a family of quantum states defined by directed graphs, where the oriented edges represent interactions between ordered qubits. As a measure of entanglement, we adopt the Entanglement Distance - a quantity derived from the Fubini - Study metric on the system's projective Hilbert space. We demonstrate that this measure is entirely determined by the vertex degree distribution and remains invariant under vertex relabeling, underscoring its topological nature. Consequently, the entanglement depends solely on the total degree of each vertex, making it insensitive to the distinction between incoming and outgoing edges. These findings offer a geometric interpretation of quantum correlations and entanglement in complex systems, with promising implications for the design and analysis of quantum networks.

quant-ph↗

arXiv2024

Enhancing Quantum Entanglement Through Parametric Control of Atom-Cavity States

Dicke states form a class of entangled states that has attracted much attention for their applications in various quantum algorithms. They emerge as eigenstates of the Tavis-Cummings Hamiltonian, a simplification of the Dicke model, which describes an assembly of two-level atoms trapped in an electromagnetic cavity. In this letter, we show that in the regime where the field energy is large with respect to the atomic energy splitting, precise control of the ground state can be implemented. Specifically, pure Dicke states can be selected and produced by appropriate tuning of the parameters. This result may have important applications in quantum engineering and quantum information theory.

quant-ph↗

arXiv2024

Entanglement Signature of the Superradiant Quantum Phase Transition

Entanglement and quantum correlations between atoms are not usually considered key ingredients of the superradiant phase transition. Here we consider the Tavis-Cummings model, a solvable system of two-levels atoms, coupled with a single-mode quantized electromagnetic field. This system undergoes a superradiant phase transition, even in a finite-size framework, accompanied by a spontaneous symmetry breaking, and an infinite sequence of energy level crossings. We find approximated expressions for the ground state, its energy, and the position of the level crossings, valid in the limit of a very large number of photons with respect to that of the atoms. In that same limit, we find that the number of photons scales quadratically with the coupling strength, and linearly with the system size, providing a new insight into the superradiance phenomenon. Resorting to novel multipartite measures, we then demonstrate that this quantum phase transition is accompanied by a crossover in the quantum correlations and entanglement between the atoms (qubits). The latters therefore represent suited order parameters for this transition. Finally, we show that these properties of the quantum phase transition persist in the thermodynamic limit.

quant-ph↗

arXiv2024

Unveiling the geometric meaning of quantum entanglement: discrete and continuous variable systems

We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric structure, and investigate its deep link with the entanglement of the states of this space. As a measure, we adopt the Entanglement Distance E preliminary proposed in [1]. Our analysis shows that entanglement has a geometric interpretation: E(|psi>) is the minimum value of the sum of the squared distances between |psi> and its conjugate states, namely the states v^mu . sigma^mu |psi>, where v^mu are unit vectors and mu runs on the number of parties. We derive a general method to determine when two states are not the same state up to the action of local unitary operators. We prove that the entanglement distance, along with its convex roof expansion to mixed states, fulfills the three conditions required for an entanglement measure: that is i) E(|psi>) =0 iff |psi> is fully separable; ii) E is invariant under local unitary transformations; iii) E doesn't increase under local operation and classical communications. Two different proofs are provided for this latter property. We also show that in the case of two qubits pure states, the entanglement distance for a state |psi> coincides with two times the square of the concurrence of this state. We propose a generalization of the entanglement distance to continuous variable systems. Finally, we apply the proposed geometric approach to the study of the entanglement magnitude and the equivalence classes properties, of three families of states linked to the Greenberger-Horne-Zeilinger states, the Briegel Raussendorf states and the W states. As an example of an application for the case of a system with continuous variables, we have considered a system of two coupled Glauber coherent states.

quant-ph↗

arXiv2023

Entanglement, quantum correlators and connectivity in graph states

In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure of entanglement. Additionally, we propose a novel approach to probe the underlying graph connectivity of genuine graph states, using quantum correlators of Pauli matrices. Our findings also reveal interesting implications for measurement processes, demonstrating the equivalence of certain projective measurements. Finally, we emphasize the simplicity of data analysis within this framework. This work contributes to a deeper understanding of the entanglement and connectivity properties of graph states, offering valuable insights for quantum information processing and quantum computing applications. In this work, we do not resort to the celebrated stabilizer formalism, which is the framework typically preferred for the study of this type of state; on the contrary, our approach is solely based on the concepts of expectation values, quantum correlations and projective measurement, which have the advantage of being very intuitive and fundamental tools of quantum theory.

quant-ph↗

arXiv2023

Routing a quantum state in a bio-inspired network

We consider a spin network resembling an $α$-helix structure and study quantum information transfer over this bio-inspired network. The model we use is the Davydov model in its elementary version without a phononic environment. We investigate analytically and numerically the perfect state transfer (PST) in such a network which provides an upper bound on the probability of quantum states transfer from one node to another. We study PST for different boundary conditions on the network and show it is reachable between certain nodes and with suitable spin-spin couplings.

quant-ph↗

arXiv2022

Entanglement and Quantum Correlation Measures from a Minimum Distance Principle

Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as, for instance, quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly computable measure for the entanglement of multipartite mixed-states is still lacking. In this work, {\it i)} we derive from a minimum distance principle, an explicit measure able to quantify the degree of quantum correlation for pure or mixed multipartite states; {\it ii)} through a regularization process of the density matrix, we derive an entanglement measure from such quantum correlation measure; {\it iii)} we prove that our entanglement measure is \textit{faithful} in the sense that it vanishes only on the set of separable states. Then, a comparison of the proposed measures, of quantum correlation and entanglement, allows one to distinguish between quantum correlation detached from entanglement and the one induced by entanglement, hence to define the set of separable but non-classical states. Since all the relevant quantities in our approach, descend from the geometry structure of the projective Hilbert space, the proposed method is of general application. Finally, we apply the derived measures as an example to a general Bell diagonal state and to the Werner states, for which our regularization procedure is easily tractable.

quant-ph↗

arXiv2022

Topological Theory of Phase Transitions

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase transitions. In fact, in correspondence of a phase transition there are peculiar geometrical changes of the mechanical manifolds that are found to stem from changes of their topology. These findings, together with two theorems, have suggested that a topological theory of phase transitions can be formulated to go beyond the limits of the existing theories. Among other advantages, the new theory applies to phase transitions in small $N$ systems (that is, at nanoscopic and mesoscopic scales), and in the absence of symmetry-breaking. However, the preliminary version of the theory was incomplete and still falsifiable by counterexamples. The present work provides a relevant leap forward leading to an accomplished development of the topological theory of phase transitions paving the way to further developments and applications of the theory that can be no longer hampered.

cond-mat.stat-mech↗

arXiv2021

Transition between random and periodic electron currents on a DNA chain

By resorting to a model inspired to the standard Davydov and Holstein-Fröhlich models, in the present paper we study the motion of an electron along a chain of heavy particles modelling a sequence of nucleotides proper to a DNA fragment. Starting with a model Hamiltonian written in second quantization, we use the Time Dependent Variational Principle to work out the dynamical equations of the system. It is found that under the action of an external source of energy transferred to the electron, and according to the excitation site, the electron current can display either a broad frequency spectrum or a sharply peaked frequency spectrum. This sequence-dependent charge transfer phenomenology is suggestive of a potentially rich variety of electrodynamic interactions of DNA molecules under the action of electron excitation. This could imply the activation of interactions between DNA and transcription factors, or between DNA and external electromagnetic fields.

physics.bio-ph↗

arXiv2021

Entanglement Protection of Classically Driven Qubits in a Lossy Cavity

Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we investigate the effect of the classical driving field on the generation entanglement between two qubits interacting with a bosonic environment. We discuss the effect of the classical field on the generation of entanglement between two (different) qubits and the conditions under which it has a constructive role in protecting the initial-state entanglement from decay induced by its environment. In particular, in the case of similar qubits, we locate a stationary sub-space of the system Hilbert space, characterized by states non depending on the environment properties as well as on the classical driving-field. Thus, we are able to determine the conditions to achieve maximally entangled stationary states after a transient interaction with the environment. We show that, overall, the classical driving field has a constructive role for the entanglement protection in the strong coupling regime. Also, we illustrate that a factorable initial-state can be driven in an entangled state and, even, in an entangled steady-state after the interaction with the environment.

quant-ph↗