arXiv subjects

Lucas C. Céleri

Publications and source records attributed to Lucas C. Céleri.

At least 37 records · Page 2Linked to original sources

arXiv2022

Quantum Markov monogamy inequalities

Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary conditions for all Markov processes. We address here the problem of the information-theoretic analysis of constraints on Markov processes in the quantum regime. We show the existence of a novel class of quantum data processing inequalities called here quantum Markov monogamy inequalities. This new class of necessary conditions on quantum Markov processes is inspired by its counterpart for classical Markov processes, and thus providing a strong link between classical and quantum constraints on Markovianity. We go on to construct a family of multitime quantum Markov monogamy inequalities, based on the process tensor formalism and that exploits multitime correlations. We then show, by means of an explicit example, that the Markov monogamy inequalities can be stronger than the usual quantum data processing inequalities.

quant-ph↗

arXiv2021

Two-point measurement of entropy production from the outcomes of a single experiment with correlated photon pairs

Fluctuation theorems are one of the pillars of non-equilibrium thermodynamics. Broadly speaking, they concern the statistical distribution of quantities such as heat, work or entropy production. Quantum experiments, however, usually can only assess these distributions indirectly. In this letter we provide an experimental demonstration of a quantum fluctuation theorem where the distribution of entropy production is obtained directly from the outcomes (clicks) of an optical experiment. The setup consists of entangled photon pairs, one of which is sent an interferometer emulating a finite temperature amplitude damping device. Blocking specific paths of the interferometer is tantamount to restricting the possible configurations of the reservoir. And by measuring its entangled pair, we can directly implement the two-point measurement scheme, thus avoiding the destructive nature of photo-detection.

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arXiv2021

Digital-Analog Quantum Simulations Using The Cross-Resonance Effect

Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated by the systems' underlying Hamiltonian. Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on 1D chains and 2D square lattices which, in an appropriate reference frame, results in a purely two-local Hamiltonian. By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians. We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, $XY$, and Heisenberg spin models. Our dynamics simulations are Trotter error-free for the Ising and $XY$ models in 1D. We also show that the Trotter errors for 2D $XY$ and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor. In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations. We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.

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arXiv2020

Precision in estimating Unruh temperature

The goal of quantum metrology is the exploitation of quantum resources, like entanglement or quantum coherence, in the fundamental task of parameter estimation. Here we consider the question of the estimation of the Unruh temperature in the scenario of relativistic quantum metrology. Specifically, we study two distinct cases. First, a single Unruh-DeWitt detector interacting with a scalar quantum field undergoes an uniform acceleration for a finite amount of proper time, and the role of coherence in the estimation process is analyzed. After this, we consider two initially entangled detectors, one of which is inertial while the other one undergoes acceleration. Our results show that the maximum of the Fisher information, thus characterizing the maximum possible precision according to Crammér-Rao bound, occurs only for small accelerations, while it decreases fast when acceleration increases. Moreover, the role of initial coherence ---in the single detector case---, or entanglement ---in the two detectors case---, is to decrease Fisher information. Therefore, under the considered protocol, internal coherence (or entanglement) is not a resource for estimating Unruh temperature. These unexpected results show that a detection of the Unruh effect can be even more challenge than previously thought. Finally, by considering the connection between Unruh effect and Hawking radiation, we discuss how our results can be understood in the context of the estimation of Hawking temperature.

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arXiv2019

Quantum Memristors in Frequency-Entangled Optical Fields

A quantum memristor is a resistive passive circuit element with memory engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally-attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work provides the first steps of a novel route towards constructing quantum neural networks in quantum photonics.

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arXiv2019

Monogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing

The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data processing, respected by Markov chains. Second, to show a novel connection between the quantification of causality and the violation of both data processing and monogamy inequalities. Apart from its foundational relevance in the study of stochastic processes we also consider the applicability of our results in a typical quantum information setup, showing it can be useful to witness the non-Markovianity arising in a sequence of quantum non-projective measurements.

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arXiv2019

The role of quantum coherence in non-equilibrium entropy production

Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. The population unbalances are found to contribute to both an entropy flux and an entropy production rate. The decoherence, on the other hand, contributes only to the entropy production rate. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We make use of such a division to address the open-system dynamics of a spin $J$ particle, which we describe in phase space through a spin-coherent representation.

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arXiv2018

Kolmogorov-Sinai entropy and dissipation in driven classical Hamiltonian systems

A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle of maximum entropy allows to establish the connection between entropy in statistical mechanics and information entropy. In this sense, the dissipated energy in a classical Hamiltonian process, known as the thermodynamic entropy production, is connected to the relative entropy between the forward and backward probability densities. Recently, it was revealed that energetic inefficiency and model inefficiency, defined as the difference in mutual information that the system state shares with the future and past environmental variables, are equivalent concepts in Markovian processes. As a consequence, the question about a possible connection between model unpredictability and energetic inefficiency in the framework of classical physics emerges. Here, we address this question by connecting the concepts of random behavior of a classical Hamiltonian system, the Kolmogorov-Sinai entropy, with its energetic inefficiency, the dissipated work. This approach allows us to provide meaningful interpretations of information concepts in terms of thermodynamic quantities.

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arXiv2018

Canonical field quantization in momentum space and quantum space-time

We propose a way to encode acceleration directly into quantum fields, establishing a new class of fields. Accelerated quantum fields, as we have named them, have some very interesting properties. The most important is that they provide a mathematically consistent way to quantize space-time in the same way that energy and momentum are quantized in standard quantum field theories.

hep-th↗

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.

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arXiv2018

Spin-phase-space-entropy production

Quantifying the degree of irreversibility of an open system dynamics represents a problem of both fundamental and applied relevance. Even though a well-known framework exists for thermal baths, the results give diverging results in the limit of zero temperature and are also not readily extended to nonequilibrium reservoirs, such as dephasing baths. Aimed at filling this gap, in this paper we introduce a phase-space-entropy production framework for quantifying the irreversibility of spin systems undergoing Lindblad dynamics. The theory is based on the spin Husimi-Q function and its corresponding phase-space entropy, known as Wehrl entropy. Unlike the von Neumann entropy production rate, we show that in our framework, the Wehrl entropy roduction rate remains valid at any temperature and is also readily extended to arbitrary nonequilibrium baths. As an application, we discuss the irreversibility associated with the interaction of a two-level system with a single-photon pulse, a problem which cannot be treated using the conventional approach.

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arXiv2017

The sudden change phenomenon of quantum discord

Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.

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arXiv2017

Enhancing the charging power of quantum batteries

Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when $N$ batteries are charged collectively. We first derive analytic upper bounds for the collective \emph{quantum advantage} in charging power for two choices of constraints on the charging Hamiltonian. We then highlight the importance of entanglement by proving that the quantum advantage vanishes when the collective state of the batteries is restricted to be in the separable ball. Finally, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted, i.e., at most $k$ batteries are interacting. Our result is a fundamental limit on the advantage offered by quantum technologies over their classical counterparts as far as energy deposition is concerned.

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arXiv2016

Spin and localization of relativistic fermions and uncertainty relations

We discuss relations between several relativistic spin observables and derive a Lorentz-invariant characteristic of a reduced spin density matrix.A relativistic position operator that satisfies all the properties of its nonrelativistic analog does not exist. Instead we propose two causality-preserving positive operator-valued measures (POVMs) that are based on projections onto one-particle and antiparticle spaces, and on the normalized energy density. They predict identical expectation values for position. The variances differ by less than a quarter of the squared de Broglie wavelength and coincide in the nonrelativistic limit. Since the resulting statistical moment operators are not canonical conjugates of momentum, the Heisenberg uncertainty relations need not hold. Indeed, the energy density POVM leads to a lower uncertainty. We reformulate the standard equations of the spin dynamics by explicitly considering the charge-independent acceleration, allowing a consistent treatment of backreaction and inclusion of a weak gravitational field.

hep-th↗

arXiv2016

Fragile states are better for quantum metrology

In quantum metrology, quantum probe states are capable of estimating unknown physical parameters to precisions beyond classical limits. What qualities do such states possess? Here we relate the performance of a probe state at estimating a parameter $ϕ$ -- as quantified by the quantum Fisher information -- to the amount of purity it loses when $ϕ$ undergoes statistical fluctuation. This indicates that the better a state is for estimating $ϕ$, the more it decoheres when $ϕ$ is subject to noise.

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arXiv2016

Generalized Geometric Quantum Speed Limits

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the non uniqueness of a bona fide measure of distinguishability defined on the quantum state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits, and provides instances of novel bounds which are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

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arXiv2016

Experimental demonstration of information to energy conversion in a quantum system at the Landauer Limit

Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance setup to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins $S=1/2$ (qubits) molecule ---the system, the reservoir and the ancilla--- to measure the heat dissipated during the implementation of a global system-reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way we were able to verify that an operation that changes the information content of the system must necessary generate heat in the reservoir, exactly as predicted by Landauer's principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors.

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arXiv2015

Geometric lower bound for a quantum coherence measure

Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain less trivial and more robust physical constraints on quantum systems. In this sense, here we establish a geometric lower bound for the Wigner-Yanase skew information (WYSI), a well-known information theoretic quantity recently recognized as a proper quantum coherence measure. Starting from a mixed state evolving under unitary dynamics, while WYSI is a constant of motion, the lower bound indicates the rate of change of quantum statistical distinguishability between initial and final states. Our result shows that, since WYSI fits in the class of Petz metrics, this lower bound is the change rate of its respective geodesic distance on quantum state space. The geometric approach is advantageous because raises several physical interpretations of this inequality under the same theoretical umbrella.

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