arXiv subjects

Fabricio Toscano

Publications and source records attributed to Fabricio Toscano.

At least 19 recordsLinked to original sources

arXiv2026

Twisted Gaussian Schell States in Quantum Optics: Twist-Assisted Nonclassicality and Entanglement

We introduce the Twisted Gaussian Schell (TGS) state, a two-mode mixed Gaussian state defined as the quantum-optical analog of the Twisted Gaussian Schell-model beam of classical paraxial optics, characterized by the so-called twist phase. In the TGS state, the twist parameter arises when an asymmetric two-mode thermal state is subject to local squeezing after the action of phase shifters and a beam splitter. Its defining quantum feature is nonclassicality: although the state is separable in its natural bipartition, when the twist parameter is nonzero there are global quadratures that can be squeezed below the shot-noise limit. The nonclassicality has also a direct signature in the joint photon-number distribution, which we obtain in closed form. Moreover, coupling each mode to an ancillary vacuum at a balanced beam splitter yields a four-mode state with entanglement in select $2\times2$ bipartitions, with local description given by two TGS states, and all $1\times3$ bipartitions. For fixed input squeezing, increasing the twist parameter activates entanglement where the state is otherwise separable and deepens it where already present. The classical physicality bound on the twist parameter coincides with the quantum physicality condition. These results advance the two-way bridge between classical beam engineering and quantum information.

quant-ph↗

arXiv2025

A Fluctuation-Dissipation Structure of Quantum Dynamical Semigroups Reveals a Unique Internal Hamiltonian

We refine a fluctuation-dissipation framework for quantum dynamical semigroups to resolve a long-standing ambiguity in Markovian master equations. For finite-dimensional systems, we prove that the underlying diffusion-dissipation structure - rooted in a classical Markov process analogy - is invariant under Lindblad generator symmetries. This invariance uniquely identifies the internal Hamiltonian. Our framework provides a universal principle for objectively distinguishing coherent from incoherent parts of the dynamics, enabling an unambiguous determination of a system's inherent energy structure.

quant-ph↗

arXiv2024

Quantum thermodynamics for general bipartite interacting autonomous systems

The internal energy of individual subsystems is not well defined in interacting quantum systems, leading to ambiguities in the definition of thermodynamic quantities. Applying the Schmidt basis formalism to general bipartite autonomous quantum systems, we demonstrate that the master equation describing subsystem evolution adheres to the principle of minimal dissipation. This enables to define internal energy of each subsystem in a consistent way. Moreover, by utilizing general aspects of open quantum systems, we show that this master equation is unique. We analyze heat and work for each subsystem as derived from this formalism, providing deeper insights into the thermodynamics of interacting quantum systems.

quant-ph↗

arXiv2023

Optimal quantum teleportation protocols for fixed average fidelity

We demonstrate that among all quantum teleportation protocols giving rise to the same average fidelity, those with aligned Bloch vectors between input and output states exhibit the minimum average trace distance. This defines optimal protocols. Furthermore, we show that optimal protocols can be interpreted as the perfect quantum teleportation protocol under the action of correlated one-qubit channels. In particular, we focus on the deterministic case, for which the final Bloch vector length is equal for all measurement outcomes. Within these protocols, there exists one type that corresponds to the action of uncorrelated channels: these are depolarizing channels. Thus, we established the optimal quantum teleportation protocol under a very common experimental noise.

quant-ph↗

arXiv2023

Thermal equilibrium in Gaussian dynamical semigroups

We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamic, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices, and the identification of different Gaussian dynamical semigroups which shares the same thermal equilibrium state.

quant-ph↗

arXiv2021

Fluctuation and dissipation in memoryless open quantum evolutions

Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum dynamical semigroup, we find a decomposition of the infinitesimal generator of the dynamics, that allows to relate the von Neumann entropy rate with the divergence-based quantum Fisher information, at any time. Applied to quantum Gaussian channels that are dynamical semigroups, our decomposition leads to the quantum analog of the generalized classical de Bruijn identity, thus expressing the quantum fluctuation-dissipation relation in that kind of channels. Finally, from this perspective, we analyze how stationarity arises.

quant-ph↗

arXiv2019

Work statistics for sudden quenches in interacting quantum many-body systems

Work in isolated quantum systems is a random variable and its probability distribution function obeys the celebrated fluctuation theorems of Crooks and Jarzynski. In this study, we provide a simple way to describe the work probability distribution function for sudden quench processes in quantum systems with large Hilbert spaces. This description can be constructed from two elements: the level density of the initial Hamiltonian, and a smoothed strength function that provides information about the influence of the perturbation over the eigenvectors in the quench process, and is especially suited to describe quantum many-body interacting systems. We also show how random models can be used to find such smoothed work probability distribution and apply this approach to different one-dimensional spin-$1/2$ chain models. Our findings provide an accurate description of the work distribution of such systems in the cases of intermediate and high temperatures in both chaotic and integrable regimes.

quant-ph↗

arXiv2018

Quantum work for sudden quenches in Gaussian random Hamiltonians

In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum version of the celebrated fluctuation theorems, due to Jarzynski and Crooks, that apply when the system is driven away from an initial equilibrium thermal state. Such a particular pdf depends basically on the details of the initial and final Hamiltonians, on the temperature of the initial thermal state and on how some external parameter is changed during the coherent process. Using random matrix theory we derive a simple analytic expression that describes the general behavior of the work characteristic function $G(u)$, associated with this particular work pdf for sudden quenches, valid for all the traditional Gaussian ensembles of Hamiltonians matrices. This formula well describes the general behavior of $G(u)$ calculated from single draws of the initial and final Hamiltonians in all ranges of temperatures.

quant-ph↗

arXiv2018

Uncertainty Relations for coarse-grained measurements: an overview

Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continnuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, a number of uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90$^{th}$ anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.

quant-ph↗

arXiv2017

Unified framework to determine Gaussian states in continuous variable systems

Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the reduced states in a given bipartition of a multipartite quantum system bears information on the entanglement in such bipartition. For Gaussian states, the reduced states are also Gaussian, so there determination requires essentially the experimental determination of their covariance matrix. Here, we develop strategies to determine the covariance matrix of an arbitrary n-mode bosonic Gaussian state through measurement of the total phase acquired when appropriate metaplectic evolutions, associated with quadratic Hamiltonians, are applied. Simply one-mode metaplectic evolutions, such rotations, squeezing and shear transformations, in addition to a single two-mode rotation, allows to determine all the covariance matrix elements of a n-mode bosonic system. All the single-mode metaplectic evolutions are applied conditionally to a state in which an ancilla qubit is entangled with the n-mode system. The ancillary system provides, after measurement, the value of the total phase of each evolution. The proposed method is experimentally friendly to be implemented in the most currently used continuous variable systems.

quant-ph↗

arXiv2017

Attainability of the quantum information bound in pure state models

The attainability of the quantum Cramér-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher information associated to a given measurement on the quantum state of a system which encodes the information about the parameter coincides with the quantum Fisher information associated to that quantum state. Braunstein and Caves [PRL {\bf 72}, 3439 (1994)] have shown that the QIB can always be achieved via a projective measurement in the eigenvectors basis of an observable called symmetric logarithmic derivative. However, such projective measurement depends, in general, on the value of the parameter to be estimated. Requiring, therefore, the previous knowledge of the quantity one is trying to estimate. For this reason, it is important to investigate under which situation it is possible to saturate the QCR without previous information about the parameter to be estimated. Here, we show the complete solution to the problem of which are all the initial pure states and the projective measurements that allow the global saturation of the QIB, without the knowledge of the true value of the parameter, when the information about the parameter is encoded in the system by a unitary process.

quant-ph↗

arXiv2016

Quantum Speed Limit Bounds in an Open Quantum Evolution

Quantum mechanics dictates bounds for the minimal evolution time between predetermined initial and final states. Several of these Quantum Speed Limit (QSL) bounds were derived for non-unitary dynamics using different approaches. Here, we perform a systematic analysis of the most common QSL bounds in the damped Jaynes-Cummings model, covering the Markovian and non-Markovian regime. We show that only one of the analysed bounds cleaves to the essence of the QSL theory outlined in the pioneer works of Mandelstam \& Tamm and Margolus \& Levitin in the context of unitary evolutions. We also show that all of QSL bounds analysed reflect the fact that in our model non-Markovian effects speed up the quantum evolution. However, it is not possible to infer the Markovian or non-Markovian behaviour of the dynamics only analysing the QSL bounds.

quant-ph↗

arXiv2012

Optimal Uncertainty Relations for Extremely Coarse-grained Measurements

We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of coarse-grained measurements. We then sharpen a Heisenberg-like uncertainty relation derived previously in [Europhys. Lett. 97, 38003, (2012)] that uses variances and reduces to the usual one in the case of infinite precision measurements. Our sharpened uncertainty relation is meaningful for any amount of coarse graining. That is, there is always a non-trivial uncertainty relation for coarse-grained measurement of the non-commuting observables, even in the limit of extremely large coarse graining.

quant-ph↗

arXiv2011

How do wave packets spread? Time evolution on Ehrenfest time scales

We derive an extension of the standard time dependent WKB theory which can be applied to propagate coherent states and other strongly localised states for long times. It allows in particular to give a uniform description of the transformation from a localised coherent state to a delocalised Lagrangian state which takes place at the Ehrenfest time. The main new ingredient is a metaplectic operator which is used to modify the initial state in a way that standard time dependent WKB can then be applied for the propagation. We give a detailed analysis of the phase space geometry underlying this construction and use this to determine the range of validity of the new method. Several examples are used to illustrate and test the scheme and two applications are discussed: (i) For scattering of a wave packet on a barrier near the critical energy we can derive uniform approximations for the transition from reflection to transmission. (ii) A wave packet propagated along a hyperbolic trajectory becomes a Lagrangian state associated with the unstable manifold at the Ehrenfest time, this is illustrated with the kicked harmonic oscillator.

math-ph↗

arXiv2011

Heisenberg Uncertainty Relation for Coarse-grained Observables

We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for coarse-grained measurements that are always valid, even for detectors with low precision. These relations should be particularly relevant in experimental demonstrations of squeezing in quantum optics, quantum state reconstruction, and the development of trustworthy entanglement criteria.

quant-ph↗

arXiv2011

Decoherence, entanglement decay, and equilibration produced by chaotic environments

We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long times scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.

quant-ph↗

arXiv2010

Phase Space Structure of Generalized Gaussian Cat States

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of {\em mixed} Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.

quant-ph↗

arXiv2008

Scaling laws in the quantum to classical transition in chaotic systems

We study the quantum to classical transition in a chaotic system surrounded by a diffusive environment. The emergence of classicality is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with $\hbar^2_{\rm eff}/D$, where $\hbar_{\rm eff}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum to classical transition when it is measured comparing the corresponding phase space distributions. We discuss here the meaning of both scalings in the precise definition of a frontier between the classical and quantum behavior. We also show that there are quantum coherences that the Renyi entropy is unable to detect which questions its use in the studies of decoherence.

quant-ph↗