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Gianluca Francica

Publications and source records attributed to Gianluca Francica.

At least 19 recordsLinked to original sources
arXiv2026

Quantum advantage unlocked: Charging quantum batteries with K-regular graph stabilizers

Regular graphs find broad applications ranging from quantum communication to quantum computation. Motivated by this, we investigate the design of a quantum battery based on a K-regular graph, where K denotes the number of edges incident on each vertex. We show that a 0-regular graph battery exhibits extractable work that scales linearly with the system-size when charged using a K-regular graph. This linear scaling is shown to persist even when the charging is implemented via a collective K-regular charger with power-law decaying interactions. Interestingly, we prove that both the maximum average power and instantaneous power scale super-linearly in the thermodynamic limit when the connectivity of the charging graph is of the order of the system size, thereby exhibiting it quantum advantage. Furthermore, by introducing the notion of the fraction of extractable work when only subsystems are accessible, we identify this fraction to be independent of system-size if the battery is prepared in the down-polarized product state. This independence breaks down when the battery is oriented along the x- and y-directions of the Bloch sphere.

quant-ph↗
arXiv2026

Quantum advantage from negativity of a work quasiprobability distribution

Quantum batteries can be charged by performing a work ``instantaneously'' in the limit of a large number of cells, achieving a so-called quantum advantage. In general, the work exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence in the energy basis. Here we show that these two concepts of quantum thermodynamics, which apparently appear disconnected, can show a simple relation. Specifically, if a certain work distribution shows negativity asymptotically in the limit of a large number of cells and in a certain time interval, then we surely get a quantum advantage in the charging process. In particular, we prove this for a direct charging protocol performed with a class of charging Hamiltonian operators.

quant-ph↗
arXiv2024

Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions

A quantum advantage can be achieved in the unitary charging of quantum batteries if their cells are interacting. Here, we try to clarify with some analytical calculations whether and how this quantum advantage is achieved for sparse Sachdev-Ye-Kitaev (SYK) interactions and in general for fermionic interactions with disorder. To do this we perform a simple modelization of the interactions. In particular, we find that for $q$-point rescaled sparse SYK interactions the quantum advantage goes as $Γ\sim N^{\frac{α-q}{2}+1}$ for $q\geqα\geq q/2$ and $Γ\sim N^{1-\fracα{2}}$ for $q/2>α\geq 0$, where $α$ is related to the connectivity and $N$ is the number of cells. This shows how we can get $Γ\sim N$, i.e., an average power that scales as $N^2$ thanks to the disorder.

quant-ph↗
arXiv2024

Resource theories with completely passive states and passive states as free states

Work extractable from quantum system can be viewed as a resource to perform some tasks. Here, we try to related the work extractable to some resource theory. To do this, we consider completely passive states and passive states as free states and we formulate resource theories where the maximum work extractable is a monotone, by identifying the free operations. In particular, we study how the free operations act on the free states, showing how a sort of temperature plays a pivotal role in these resource theories.

quant-ph↗
arXiv2024

Work fluctuation theorems with initial quantum coherence

Fluctuation theorems are fundamental results in nonequilibrium thermodynamics beyond the linear response regime. Among these, the paradigmatic Tasaki-Crooks fluctuation theorem relates the statistics of the works done in a forward out-of-equilibrium quantum process and in a corresponding backward one. In particular, the initial states of the two processes are thermal states and thus incoherent in the energy basis. Here, we aim to investigate the role of initial quantum coherence in work fluctuation theorems, by considering a quasiprobability distribution of work. To do this, we formulate and examine the implications of a detailed fluctuation theorem, which reproduces the Tasaki-Crooks fluctuation theorem in the absence of initial quantum coherence.

cond-mat.stat-mech↗
arXiv2024

Role of quantum correlations in daemonic expected utility

Fluctuations can challenge the possibility of improving work extraction from quantum correlations. This uncertainty in the work extraction process can be addressed resorting to the expected utility hypothesis which can provide an optimal method for work extraction. We study a bipartite quantum system and examine the role of quantum correlations in a daemonic work extraction performed by certain local operations and classical communication. Specifically, we demonstrate and explain how, depending on the so-called absolute risk aversion, a non-neutral risk agent, influenced by fluctuations, views quantum correlations differently from a neutral risk agent who is affected solely by the average work.

quant-ph↗
arXiv2024

Optimal work extraction from quantum batteries based on the expected utility hypothesis

Work extraction in quantum finite systems is an important issue in quantum thermodynamics. The optimal work extracted is called ergotropy, and it is achieved by maximizing the average work extracted over all the unitary cycles. However, an agent that is non-neutral to risk is affected by fluctuations and should extract work by following the expected utility hypothesis. Thus, we investigate the optimal work extraction performed by a risk non-neutral agent by maximizing the average utility function over all the unitary cycles. We mainly focus on initial states that are incoherent with respect to the energy basis, achieving a probability distribution of work. In this case we show how the optimal work extraction will be performed with an incoherent unitary transformation, namely a permutation of the energy basis, which depends on the risk aversion of the agent. We give several examples, in particular also the work extraction from an ensemble of quantum batteries is examined. Furthermore, we also investigate how work extraction is affected by the presence of initial quantum coherence in the energy basis by considering a quasiprobability distribution of work.

quant-ph↗
arXiv2023

Fluctuation theorems and expected utility hypothesis

The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility. In particular, we wonder whether entropy could serve as a guideline for gambling. We prove the existence of a bound involving the certainty equivalent which depends on the entropy produced. Then, we examine the dependence of the certainty equivalent on the entropy by looking at specific situations, in particular the work extraction from a nonequilibrium initial state.

cond-mat.stat-mech↗
arXiv2023

Normal and superconducting currents through the Sachdev-Ye-Kitaev model

We study the current driven by an applied voltage as a function of time through the Sachdev-Ye-Kitaev model when coupled to two normal or superconducting reservoirs. For normal leads, in the strong coupling limit and for small bias, the current through the Sachdev-Ye-Kitaev model, described by a quartic interaction term, reaches monotonically the stationarity, in contrast to the case of a disordered quadratic interaction where the current has a peak before reaching the stationary phase. For superconducting leads the currents have oscillations whose frequencies are determined by the gap and the voltage, and are suppressed in the strong coupling limit. Moreover, due to different short time scales between the normal and the oscillating part of the superconducting current, a peak appears before reaching the stationarity.

cond-mat.str-el↗
arXiv2023

Hilbert space fragmentation in a long-range system

We study the role of the interaction range on the Hilbert space fragmentation and many-body scar states considering a spin-1/2 many-body Hamiltonian describing a generalized Fredkin spin chain. We show that both scar states and weak fragmentation of the Hilbert space survive for almost any range of the coupling. Finally we investigate the effects of such structures of the Hilbert space on the out-of-equilibrium dynamics, triggered by certain initial states, characterized by either local persistent oscillations or non-uniform stationary profile of the magnetization.

cond-mat.str-el↗
arXiv2023

Quasiprobability distribution of work in the quantum Ising model

A complete understanding of the statistics of the work done by quenching a parameter of a quantum many-body system is still lacking in the presence of an initial quantum coherence in the energy basis. In this case, the work can be represented by a class of quasiprobability distributions. Here, we try to clarify the genuinely quantum features of the process by studying the work quasiprobability for an Ising model in a transverse field. We consider both a global and a local quench, by focusing mainly on the thermodynamic limit. We find that, while for a global quench there is a symmetric non-contextual representation with a Gaussian probability distribution of work, for a local quench we can get quantum contextuality as signaled by a negative fourth moment of the work. Furthermore, we examine the critical features related to a quantum phase transition and the role of the initial quantum coherence as useful resource.

quant-ph↗
arXiv2023

Topological phases in the presence of disorder and longer-range couplings

We study the combined effects of disorder and range of the couplings on the phase diagram of one-dimensional topological superconductors. We consider an extended version of the Kitaev chain where hopping and pairing terms couple many sites. Deriving the conditions for the existence of Majorana zero modes, we show that either the range and the on-site disorder can greatly enhance the topological phases characterized by the appearance of one or many Majorana modes localized at the edges. We consider both a discrete and a continuous disorder distribution. Moreover we discuss the role of correlated disorder which might further widen the topological regions. Finally we show that in the purely long-range regime and in the presence of disorder, the spatial decay of the edge modes remains either algebraic or exponential, with eventually a modified localization length, as in the absence of disorder.

cond-mat.str-el↗
arXiv2023

Anomalous universal adiabatic dynamics: The case of the Fredkin model

When a system is driven across a second-order quantum phase transition, the number of defects which are produced scales with the speed of the variation of the tuning parameter according to a universal law described by the Kibble-Zurek mechanism. We study a possible breakdown of this prediction proving that the number of defects can exhibit another universal scaling law which is still related only to the critical exponents $z$ and $ν$, but differs from the Kibble-Zurek result. Finally we provide an example, the deformed Fredkin spin chain, where this violation of the standard adiabatic dynamics can occur.

cond-mat.stat-mech↗
arXiv2022

What is the most general class of quasiprobabilities of work?

How to give a statistical description of thermodynamics in quantum systems is an open fundamental question. Concerning the work, the presence of initial quantum coherence in the energy basis can give rise to a quasiprobability of work, which can take negative values. Our aim is to identify the most general quasiprobability of work satisfying some fundamental conditions. By doing so, we introduce a general notion of quasiprobability in analogy to the Gleason's theorem. Then, we use these quasiprobabilities to define the quasiprobability of work, and finally we discuss the contextuality of the protocol.

quant-ph↗
arXiv2022

Causal games of work extraction with indefinite causal order

An indefinite causal order, where the causes of events are not necessarily in past events, is predicted by the process matrix framework. A fundamental question is how these non-separable causal structures can be related to the thermodynamic phenomena. Here, we approach this problem by considering the existence of two cooperating local Maxwell's demons which try to exploit the presence of global correlations and indefinite causal order to optimize the extraction of work. Thus, we prove that it is possible to have a larger probability to lower the local energy to zero if causal inequalities are violated, and that can be extracted more average work with respect to a definite causal order. However, for non-interacting parties, for the system considered the work extractable cannot be larger than the definite causal order bound.

quant-ph↗
arXiv2022

Correlations, long-range entanglement and dynamics in long-range Kitaev chains

Long-range interactions exhibit surprising features which have been less explored so far. Here, studying a one-dimensional fermionic chain with long-range hopping and pairing, we discuss some general features associated to the presence of long-range entanglement. In particular, after determining the algebraic decays of the correlation functions, we prove that a long-range quantum mutual information exists if the exponent of the decay is not larger than one. Moreover, we show that the time evolution triggered by a quantum quench between short-range and long-range regions, can be characterized by dynamical quantum phase transitions without crossing any phase boundary. We show, also, that the adiabatic dynamics is dictated by the divergence of a topological length scale at the quantum critical point, clarifying the violation of the Kibble-Zurek mechanism for long-range systems.

cond-mat.str-el↗
arXiv2022

Quantum correlations and ergotropy

Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work extractable is equal to the ergotropy. Thus, we aim to identify and investigate the contributions to the ergotropy coming from different kinds of initial correlations (total, classical, discord and entanglement correlations). By doing so, we have introduced and studied quantifiers of correlations which are based on ergotropy. In particular, our results suggest that only discord correlations always give a positive contribution to work extraction, while total, classical and entanglement correlations can reduce the work extraction.

quant-ph↗