01817nas a2200181 4500008004100000245006100041210006100102260001400163520125300177100003201430700001901462700002201481700002201503700002001525700002801545700002501573856003701598 2024 eng d00aEstimation of Hamiltonian parameters from thermal states0 aEstimation of Hamiltonian parameters from thermal states c1/18/20243 a

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n−−√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

1 aGarcía-Pintos, Luis, Pedro1 aBharti, Kishor1 aBringewatt, Jacob1 aDehghani, Hossein1 aEhrenberg, Adam1 aHalpern, Nicole, Yunger1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2401.1034301255nas a2200169 4500008004100000245007000041210006900111260001400180300000800194490000600202520075000208100002500958700001300983700003200996700002001028856003701048 2021 eng d00aEnergy storage and coherence in closed and open quantum batteries0 aEnergy storage and coherence in closed and open quantum batterie c7/15/2021 a5050 v53 a

We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case. 

1 aCaravelli, Francesco1 aYan, Bin1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia uhttps://arxiv.org/abs/2012.1502600815nas a2200157 4500008004100000245004700041210004400088260001300132300001100145490000800156520033100164100003200495700002000527700002200547856008800569 2021 eng d00aGarcía-Pintos, Hamma, and del Campo Reply0 aGarcíaPintos Hamma and del Campo Reply c7/9/2021 a0289020 v1273 a

We acknowledge that a derivation reported in Phys. Rev. Lett. 125, 040601 (2020) is incorrect as pointed out by Cusumano and Rudnicki. We respond by giving a correct proof of the claim “fluctuations in the free energy operator upper bound the charging power of a quantum battery” that we made in the Letter.

1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia1 adel Campo, Adolfo uhttps://www.quics.umd.edu/publications/garc%C3%ADa-pintos-hamma-and-del-campo-reply01577nas a2200157 4500008004100000245006300041210006300104260001300167520107800180100003201258700002401290700002101314700002201335700002501357856003701382 2021 eng d00aUnifying Quantum and Classical Speed Limits on Observables0 aUnifying Quantum and Classical Speed Limits on Observables c8/9/20213 a

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit divides into Mandalestam and Tamm's original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, generalizing both to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds to the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits, and that a preferred basis of \emph{speed operators} serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

1 aGarcía-Pintos, Luis, Pedro1 aNicholson, Schuyler1 aGreen, Jason, R.1 adel Campo, Adolfo1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2108.0426101546nas a2200145 4500008004100000245006600041210006600107260001400173520107500187100001801262700002601280700003201306700002501338856003701363 2020 eng d00aClassical Models of Entanglement in Monitored Random Circuits0 aClassical Models of Entanglement in Monitored Random Circuits c4/14/20203 a

The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

1 aShtanko, Oles1 aKharkov, Yaroslav, A.1 aGarcía-Pintos, Luis, Pedro1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2004.0673601237nas a2200145 4500008004100000245008300041210006900124260001400193490000800207520076500215100003200980700002001012700002201032856003701054 2020 eng d00aFluctuations in Extractable Work Bound the Charging Power of Quantum Batteries0 aFluctuations in Extractable Work Bound the Charging Power of Qua c7/22/20200 v1253 a

We study the connection between the charging power of quantum batteries and the fluctuations of the stored work. We prove that in order to have a non-zero rate of change of the extractable work, the state ρW of the battery cannot be an eigenstate of a `\emph{work operator}', defined by F ≡ HW + β−1log(ρW), where HW is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the stored work upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine. 

1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia1 adel Campo, Adolfo uhttps://arxiv.org/abs/1909.0355801387nas a2200157 4500008004100000245002900041210002900070260001300099490000600112520096500118100002501083700003201108700003201140700002001172856003701192 2020 eng d00aRandom Quantum Batteries0 aRandom Quantum Batteries c5/5/20200 v23 a

Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.

1 aCaravelli, Francesco1 aDe Wit, Ghislaine, Coulter-1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia uhttps://arxiv.org/abs/1908.0806401779nas a2200145 4500008004100000245007300041210006900114260001400183490000800197520131100205100002601516700002201542700003201564856003701596 2020 eng d00aTime evolution of correlation functions in quantum many-body systems0 aTime evolution of correlation functions in quantum manybody syst c3/19/20200 v1243 a

We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green's functions-- in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times ⟨A(t)B⟩β→⟨A⟩β⟨B⟩β, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

1 aAlhambra, Álvaro, M.1 aRiddell, Jonathon1 aGarcía-Pintos, Luis, Pedro uhttps://arxiv.org/abs/1906.1128001726nas a2200145 4500008004100000245006100041210006000102260001500162520126300177100002801440700003201468700002201500700002101522856003701543 2020 eng d00aTime-information uncertainty relations in thermodynamics0 aTimeinformation uncertainty relations in thermodynamics c09/21/20203 a

Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit -- a time-information uncertainty relation -- imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its initial standard deviation. From this general bound, we establish a family of speed limits for heat, work, entropy production, and entropy flow depending on the experimental constraints on the system. In all of these inequalities, the time scale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam-Tamm version of the time-energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical assumptions about the stochastic dynamics or their function. 

1 aNicholson, Schuyler, B.1 aGarcía-Pintos, Luis, Pedro1 adel Campo, Adolfo1 aGreen, Jason, R. uhttps://arxiv.org/abs/2001.05418