arXiv subjects

Raphael C. Drumond

Publications and source records attributed to Raphael C. Drumond.

17 recordsLinked to original sources

arXiv2026

Unraveling the Quantum Mpemba Effect on Markovian Open Quantum Systems

In recent years, the quantum Mpemba effect (QME), which occurs when an out-of-equilibrium system reaches equilibrium faster than another that is closer to equilibrium, has attracted significant attention from the scientific community as an intriguing and counterintuitive phenomenon. It generalizes its classical counterpart by extending the concept beyond temperature equilibration. This paper approaches the QME in Markovian open quantum systems from different perspectives. First, we propose a physical mechanism based on decoherence-free subspaces. Second, we show that an exponential enhancement of the decay rate toward equilibrium, scaling with system size, can be obtained, leading to an extreme version of the phenomenon in Markovian open quantum systems. Third, we study the strong Mpemba effect through the unravelings of Davies maps, revealing subtleties in the choice of figures of merit used to identify the QME. Finally, we propose a microscopic model to gain deeper insight into bath dynamics in this context.

quant-ph↗

arXiv2021

Quantum quench thermodynamics at high temperatures

The entropy produced when a system undergoes an infinitesimal quench is directly linked to the work parameter susceptibility, making it sensitive to the existence of a quantum critical point. Its singular behavior at $T=0$, however, disappears as the temperature is raised, hindering its use as a tool for spotting quantum phase transitions. Notwithstanding the entropy production can be split into classical and quantum components, related with changes in populations and coherences. In this paper we show that these individual contributions continue to exhibit signatures of the quantum phase transition, even at arbitrarily high temperatures. This is a consequence of their intrinsic connection to the derivatives of the energy eigenvalues and eigenbasis. We illustrate our results in two prototypical quantum critical systems, the Landau-Zener and $XY$ models.

quant-ph↗

arXiv2021

Contributions from populations and coherences in non-equilibrium entropy production

The entropy produced when a quantum system is driven away from equilibrium can be decomposed in two parts, one related with populations and the other with quantum coherences. The latter is usually based on the so-called relative entropy of coherence, a widely used quantifier in quantum resource theories. In this paper we argue that, despite satisfying fluctuation theorems and having a clear resource-theoretic interpretation, this splitting has shortcomings. First, it predicts that at low temperatures the entropy production will always be dominated by the classical term, irrespective of the quantum nature of the process. Second, for infinitesimal quenches, the radius of convergence diverges exponentially as the temperature decreases, rendering the functions non-analytic. Motivated by this, we provide here a complementary approach, where the entropy production is split in a way such that the contributions from populations and coherences are written in terms of a thermal state of a specially dephased Hamiltonian. The physical interpretation of our proposal is discussed in detail. We also contrast the two approaches by studying work protocols in a transverse field Ising chain, and a macrospin of varying dimension.

quant-ph↗

arXiv2021

Relating compatibility and divisibility of quantum channels

We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if it reproduces its action by sequential composition with a third channel. (In)compatibility is of central importance for studying the difference between classical and quantum dynamics. The relevance of divisibility stands in its close relationship with the onset of Markovianity. We emphasize the simulability character of compatibility and divisibility, and, despite their structural difference, we find a set of channels -- self-degradable channels -- for which the two notions coincide. We also show that, for degradable channels, compatibility implies divisibility, and that, for anti-degradable channels, divisibility implies compatibility. These results motivate further research on these classes of channels and shed new light on the meaning of these two largely studied notions.

quant-ph↗

arXiv2020

Heat rectification on the XX chain

In order to better understand the minimal ingredients for thermal rectification, we perform a detailed investigation of a simple spin chain, namely, the open XX model with a Lindblad dynamics involving global dissipators. We use a Jordan-Wigner transformation to derive a mathematical formalism to compute the heat currents and other properties of the steady state. We have rigorous results to prove the occurrence of thermal rectification even for slightly asymmetrical chains. Interestingly, we describe cases where the rectification does not decay to zero as we increase the system size, that is, the rectification remains finite in the thermodynamic limit. We also describe some numerical results for more asymmetrical chains. The presence of thermal rectification in this simple model indicates that the phenomenon is of general occurrence in quantum spin systems.

quant-ph↗

arXiv2020

Rectification induced by geometry in two-dimensional quantum spin lattices

We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains subject to two reservoirs at the boundaries, modeled by quantum master equations. We discuss the differences in the rectification for some one-dimensional cases, and present numerical results of the rectification coefficient R for different values of the anisotropy parameter of the XXZ model, and different configurations of boundary drives, including both local and non-local dissipators. Our results also show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model, indicating that the phenomenon of rectification due to geometry may be of general occurrence in quantum spin systems.

quant-ph↗

arXiv2020

Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations

Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyze what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want to know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained.

quant-ph↗

arXiv2020

Quantum coherence and criticality in irreversible work

The irreversible work during a driving protocol constitutes one of the most widely studied measures in non-equilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understand the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. For quenches in the transverse field, we find that for finite temperatures the contribution from coherence can, in certain cases, account for practically all of the entropy production. At low temperatures, however, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. Alternatively, if the quench is performed in the anisotropy parameter, we find that there are situations where all of the entropy produced is due to quantum coherences.

quant-ph↗

arXiv2020

Energy current manipulation and reversal of rectification in graded XXZ spin chains

This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths with fixed, different magnetization. We take graded versions of the model, i.e., asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen the inner parameters of the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of the energy and of the spin currents occur in opposite directions, i.e., if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from the right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.

cond-mat.stat-mech↗

arXiv2019

Quantum Ising model in a period-2 modulated transverse field

We study a finite spin-$\frac{1}{2}$ Ising chain with a spatially alternating transverse field of period 2. By means of a Jordan-Wigner transformation for even and odd sites, we are able to map it into a one-dimensional model of free fermions. We determine the ground-state energies in the positive- and negative-parity subspaces (subspaces with an even or odd total number of down spins, respectively) and compare them in order to establish the ground-state energy for the entire Hamiltonian. We derive closed-form expressions for this energy gap between the different parity subspaces and analyze its behavior and dependence on the system size in the various regimes of the applied field. Finally, we suggest an expression for the correlation length of such a model that is consistent with the various values found in the literature for its behavior in the vicinity of critical points.

quant-ph↗

arXiv2019

Shielding Property in Higher Dimensions

When the reduced state of a many-body quantum system is independent of its remaining parts, we say it shows what has become known by shielding property. Under some assumptions, equilibrium states of quantum transverse Ising models do manifest such phenomenon. Namely, imagine a many-body quantum system described by a lattice in the presence of an external magnetic field. Suppose there exists a separating interface on this lattice splitting the system into two subsets such that they only interact one another through that interface. In addition, suppose also that the applied external magnetic field is null on the interface. The shielding property states that the reduced state of the set in one side of the interface has no dependence on the Hamiltonian parameters of the set in the other side. This statement was proved in [N. Móller et al, PRE 97, 032101 (2018)] for the case where there is only one site in the interface. For lattices with more sites in the interface, it was conjectured that the shielding property is true when the system is in the ground state. For the case of positive temperatures, it does not hold and there are counterexamples to show that. Here we show that the conjecture does hold true for ground states, but under an additional condition. This condition is met, in particular, if the Hamiltonian terms associated to the interface are frustration-free.

quant-ph↗

arXiv2018

Small violations of Bell inequalities for multipartite pure random states

For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probability of random $N$-qu$d$it pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some conditions on the local dimension the probability to find any significant amount of violation goes to zero exponentially fast as the number of parts goes to infinity. In addition, we also prove that if the number of parts is at least 3, this probability also goes to zero as the the local Hilbert space dimension goes to infinity.

quant-ph↗

arXiv2017

A Shielding Property for Thermal Equilibrium States on the Quantum Ising Model

We show that Gibbs states of non-homogeneous transverse Ising chains satisfy a \emph{shielding} property. Namely, whatever the fields on each spin and exchange couplings between neighboring spins are, if the field in one particular site is null, the reduced states of the subchains to the right and to the left of this site are \emph{exactly} the Gibbs states of each subchain alone. Therefore, even if there is a strong exchange coupling between the extremal sites of each subchain, the Gibbs states of the each subchain behave as if there is no interaction between them. In general, if a lattice can be divided into two disconnected regions separated by an interface of sites with zero applied field, we can guarantee a similar result only if the surface contains a single site. Already for an interface with two sites we show an example where the property does not hold. When it holds, however, we show that if a perturbation of the Hamiltonian parameters is done in one side of the lattice, the other side is completely unchanged, with regard to both its equilibrium state and dynamics.

quant-ph↗

arXiv2017

Bounding entanglement spreading after a local quench

We consider the variation of von Neumann entropy of subsystem reduced states of general many- body lattice spin systems due to local quantum quenches. We obtain Lieb-Robinson-like bounds that are independent of the subsystem volume. The main assumptions are that the Hamiltonian satisfies a Lieb-Robinson bound and that the volume of spheres on the lattice grows at most exponentially with their radius. More specifically, the bound exponentially increases with time but exponentially decreases with the distance between the subsystem and the region where the quench takes place. The fact that the bound is independent of the subsystem volume leads to stronger constraints (than previously known) on the propagation of information throughout many-body systems. In particular, it shows that bipartite entanglement satisfies an effective "light cone", regardless of system size. Further implications to t density-matrix renormalization-group simulations of quantum spin chains and limitations to the propagation of information are discussed.

quant-ph↗

arXiv2015

Self-catalytic conversion of pure quantum states

Conversion of entangled states under (Stochastic) Local Operations and Classical Communication admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself to perform as a catalyst, which we call a self-catalytic process. We show explicit examples of self-catalysis. Necessary and sufficient conditions for the phenomenon to take place are discussed. We numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increases the probability of conversion, but do not make the process deterministic. By the end we conjecture that under LOCC the probability of finding a self-catalytic reaction does not increase monotonically with the dimensions whereas SLOCC does increase.

quant-ph↗

arXiv2015

Universality of finite time disentanglement

In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD happens for all dynamics but those when all maps of the family are induced by local unitary operations. We prove this conjecture valid for two important cases: i) when all maps are induced by unitaries; ii) for pairs of qubits, when all maps are unital. Moreover, we prove some general results about unitaries/CPTP maps preserving product/pure states

quant-ph↗

arXiv2008

Geometry of Entanglement Sudden Death: Explicit Examples

In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In [M. O. Terra Cunha, New J. Phys. 9, 237 (2007)] a geometrical explanation was offered and a classification of all possible scenarios was given. Some classes were exemplified, but it was still an open question whether there were examples for the other ones. This was solved in [R.C. Drumond and M.O. Terra Cunha, arXiv:0809.4445v1]. Here we briefly review the problem, state our results in a precise way, discuss the generality of the approach, and add some speculative desirable generalizations.

quant-ph↗