arXiv subjects

Anna Sanpera

Publications and source records attributed to Anna Sanpera.

At least 37 records · Page 2Linked to original sources

arXiv2022

Open quantum systems coupled to finite baths: A hierarchy of master equations

An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium, but it induces a dynamical evolution of the bath state. In this work, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which, not only is more realistic, but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular non-interacting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model.

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arXiv2021

Entangled symmetric states and copositive matrices

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.

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arXiv2020

Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics

Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when the memory effects cannot be disregarded. Here, we derive a master equation that explicitly accounts for system-bath correlations and includes, at a coarse-grained level, a dynamically evolving bath. Such a master equation applies to a wide variety of physical systems including those described by Random Matrix Theory or the Eigenstate Thermalization Hypothesis. We obtain a local detailed balance condition which, interestingly, does not forbid the emergence of stable negative temperature states in unison with the definition of temperature through the Boltzmann entropy. We benchmark the master equation against the exact evolution and observe a very good agreement in a situation where the conventional Born-Markov-secular master equation breaks down. Interestingly, the present description of the dynamics is robust and it remains accurate even if some of the assumptions are relaxed. Even though our master equation describes a dynamically evolving bath not described by a Gibbs state, we provide a consistent nonequilibrium thermodynamic framework and derive the first and second law as well as the Clausius inequality. Our work paves the way for studying a variety of nanoscale quantum technologies including engines, refrigerators, or heat pumps beyond the conventionally employed assumption of a static thermal bath.

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arXiv2020

Storage capacity and learning capability of quantum neural networks

We study the storage capacity of quantum neural networks (QNNs) described as completely positive trace preserving (CPTP) maps, which act on an $N$-dimensional Hilbert space. We demonstrate that QNNs can store up to $N$ linearly independent pure states and provide the structure of the corresponding maps. While the storage capacity of a classical Hopfield network scales linearly with the number of neurons, we show that QNNs can store an exponential number of linearly independent states. We estimate, employing the Gardner program, the relative volume of CPTP maps with $M$ stationary states. The volume decreases exponentially with $M$ and shrinks to zero for $M\geq N+1$. We generalize our results to QNNs storing mixed states as well as input-output relations for feed-forward QNNs. Our approach opens the path to relate storage properties of QNNs to the quantum properties of the input-output states. This paper is dedicated to the memory of Peter Wittek.

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arXiv2020

Time crystallinity in open quantum systems

Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.

quant-ph↗

arXiv2019

Thermometry in the quantum regime: Recent theoretical progress

Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out-of-thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.

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arXiv2018

Dynamically induced heat rectification in quantum systems

Heat rectifiers are systems that conduct heat asymmetrically for forward and reversed temperature gradients. Here, we present an analytical study of heat rectification in linear quantum systems. We demonstrate that asymmetric heat currents can be induced in a linear system only if it is dynamically driven. The rectification can be further enhanced, even achieving maximal performance, by detuning the oscillators of the driven network. Finally, we demonstrate the feasibility of such driven harmonic network to work as a thermal transistor, quantifying its efficiency through the dynamical amplification factor.

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arXiv2018

Genuine quantum correlations in quantum many-body systems: a review of recent progress

Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.

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arXiv2018

Fluctuation-dissipation theorem for non-equilibrium quantum systems

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolutions, as given by quantum maps. Third, it brings out the full connection between the FDT and the Quantum Fisher information, the figure of merit in quantum metrology.

quant-ph↗

arXiv2017

Separability of diagonal symmetric states: a quadratic conic optimization problem

We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in $C^d\otimes C^d$ (symmetric qudits) can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT) is sufficient and necessary for separability of DS states for $d \leq 4$. Furthermore, for $d \geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

quant-ph↗

arXiv2017

Low-temperature thermometry can be enhanced by strong coupling

We consider the problem of estimating the temperature $ T $ of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their non-perturbative interaction. We argue that this is advantageous for low temperature thermometry, as we show in our model that: (i) The thermometric precision at low $ T $ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.

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arXiv2017

Magnetic phases of spin-1 lattice gases with random interactions

A spin-1 atomic gas in an optical lattice, in the unit-filling Mott Insulator (MI) phase and in the presence of disordered spin-dependent interaction, is considered. In this regime, at zero temperature, the system is well described by a disordered rotationally-invariant spin-1 bilinear-biquadratic model. We study, via the density matrix renormalization group algorithm, a bounded disorder model such that the spin interactions can be locally either ferromagnetic or antiferromagnetic. Random interactions induce the appearance of a disordered ferromagnetic phase characterized by a non-vanishing value of spin-glass order parameter across the boundary between a ferromagnetic phase and a dimer phase exhibiting random singlet order. The study of the distribution of the block entanglement entropy reveals that in this region there is no random singlet order.

cond-mat.quant-gas↗

arXiv2017

Entanglement and Nonlocality in Diagonal Symmetric States of $N$-qubits

We analyze entanglement and nonlocal properties of the convex set of symmetric $N$-qubits states which are diagonal in the Dicke basis. First, we demonstrate that within this set, positivity of partial transposition (PPT) is necessary and sufficient for separability --- which has also been reported recently in https://doi.org/10.1103/PhysRevA.94.060101 {Phys. Rev. A \textbf{94}, 060101(R) (2016)}. Further, we show which states among the entangled DS are nonlocal under two-body Bell inequalities. The diagonal symmetric convex set contains a simple and extended family of states that violate the weak Peres conjecture, being PPT with respect to one partition but violating a Bell inequality in such partition. Our method opens new directions to address entanglement and non-locality on higher dimensional symmetric states, where presently very few results are available.

quant-ph↗

arXiv2017

The separability versus entanglement problem

We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and introduce some entanglement measures. We also provide a classification of entangled states with respect to their usefulness in quantum dense coding, and present some aspects of multipartite entanglement.

quant-ph↗

arXiv2016

Quantum optics and frontiers of physics: The third quantum revolution

The year 2015 was the International Year of Light. It marked, however, also the 20th anniversary of the first observation of Bose-Einstein condensation in atomic vapors by Eric Cornell, Carl Wieman and Wolfgang Ketterle. This discovery can be considered as one of the greatest achievements of quantum optics that has triggered an avalanche of further seminal discoveries and achievements. For this reason we devote this essay for focus issue on "Quantum Optics in the International Year of Light" to the recent revolutionary developments in quantum optics at the frontiers of all physics: atomic physics, molecular physics, condensed matter physics, high energy physics and quantum information science. We follow here the lines of the introduction to our book "Ultracold atoms in optical lattices: Simulating quantum many-body systems" [1]. The book, however, was published in 2012, and many things has happened since then -- the present essay is therefore upgraded to include the latest developments.

cond-mat.quant-gas↗

arXiv2016

Achieving sub-shot-noise sensing at finite temperatures

We investigate sensing of magnetic fields using quantum spin chains at finite temperature and exploit quantum phase crossovers to improve metrological bounds on the estimation of the chain parameters. In particular, we analyze the $ XX $ spin chain and show that the magnetic sensitivity of this system is dictated by its adiabatic magnetic susceptibility, which scales extensively (linearly) in the number of spins $ N $. Next, we introduce an iterative feedforward protocol that actively exploits features of quantum phase crossovers to enable super-extensive scaling of the magnetic sensitivity. Moreover, we provide experimentally realistic observables to saturate the quantum metrological bounds. Finally, we also address magnetic sensing in the Heisenberg $ XY $ spin chain.

quant-ph↗

arXiv2015

Thermometry Precision in Strongly Correlated Ultracold Lattice Gases

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated system is a question of both, fundamental and technological importance. Here, we address such question by combining tools from quantum metrology together with the study of the quantum correlations embedded in the system at finite temperatures. Within this frame we examine the spin-$1/2$ XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable bound on the temperature precision. We then address the estimation of the temperature of the sample from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method. Finally, we demonstrate that for sufficiently low temperatures the proposed measurements are optimal to estimate accurately the temperature of the sample.

quant-ph↗

arXiv2015

Individual quantum probes for optimal thermometry

The unknown temperature of a sample may be estimated with minimal disturbance by putting it in thermal contact with an individual quantum probe. If the interaction time is sufficiently long so that the probe thermalizes, the temperature can be read out directly from its steady state. Here we prove that the optimal quantum probe, acting as a thermometer with maximal thermal sensitivity, is an effective two-level atom with a maximally degenerate excited state. When the total interaction time is insufficient to produce full thermalization, we optimize the estimation protocol by breaking it down into sequential stages of probe preparation, thermal contact and measurement. We observe that frequently interrogated probes initialized in the ground state achieve the best performance. For both fully and partly thermalized thermometers, the sensitivity grows significantly with the number of levels, though optimization over their energy spectrum remains always crucial.

quant-ph↗