Quantum Subsystem Research Articles

Logarithmic corrections to the entropy of scalar field in BTZ black hole spacetime

The entanglement entropy correlates two quantum subsystems which are part of a larger system. A logarithmic divergence term present in the entanglement entropy is universal in nature and directly proportional to the conformal anomaly. We study this logarithmic divergence term of entropy for massive scalar field in [Formula: see text] dimensions by applying numerical techniques to entanglement entropy approach. This (2+1)-dimensional massive theory can be obtained from the (3+1)-dimensional massless scalar field via dimensional reduction. We also calculated mass corrections to entanglement entropy for scalar field. Finally, we observe that the area law contribution to the entanglement entropy is not affected by this mass term and the universal quantities depend upon the basic properties of the system.

Observables, gravitational dressing, and obstructions to locality and subsystems

Quantum field theory - our basic framework for describing all non-gravitational physics - conflicts with general relativity: the latter precludes the standard definition of the former's essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincare charges, and in particular any compactly-supported operator, in flat-spacetime quantum field theory must be gravitationally dressed once coupled to gravity, i.e. it must depend on the metric at arbitrarily long distances, and we put lower bounds on this nonlocal dependence. This departure from standard locality occurs in the most severe way possible: in perturbation theory about flat spacetime, at leading order in Newton's constant. The physical observables in a gravitational theory therefore do not organize themselves into local commuting subalgebras: the principle of locality must apparently be reformulated or abandoned, and in fact we lack a clear definition of the coarser and more basic notion of a quantum subsystem of the Universe. We discuss relational approaches to locality based on diffeomorphism-invariant nonlocal operators, and reinforce arguments that any such locality is state-dependent and approximate. We also find limitations to the utility of bilocal diffeomorphism-invariant operators that are considered in cosmological contexts. An appendix provides a concise review of the canonical covariant formalism for gravity, instrumental in the discussion of Poincare charges and their associated long-range fields.

Accurate Long-Time Mixed Quantum-Classical Liouville Dynamics via the Transfer Tensor Method.

In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.

Quantum-classical model of retinal photoisomerization reaction in visual pigment rhodopsin.

A quantum-classical model of photoisomerization of the visual pigment rhodopsin chromophore is proposed. At certain (and more realistic) parameter value combinations, the model is shown to accurately reproduce a number of independent experimental data on the photoreaction dynamics: the quantum yield, the time to reach the point of conical intersection of potential energy surfaces, the termination time of the evolution of quantum subsystem, as well as the characteristic low frequencies of retinal molecular lattice fluctuations during photoisomerization. In addition, the model behavior is in good accordance with experimental data about coherence and local character of quantum transition.

TINKTEP: A fully self-consistent, mutually polarizable QM/MM approach based on the AMOEBA force field.

We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the onetep linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in tinker. Distributed multipole analysis is used to obtain, on the fly, a classical representation of the QM subsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA. We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations.

Synthesis and optical properties of anion deficient nano MgO

Nanocrystalline MgO powder was synthesized via modified organic gel combustion route using Urea-Formaldehyde for the first time as fuel. The formation reaction is explained through DTA-TGA. The phase formation (Rietveld refined XRD, FTIR) and the inherent powder characteristics were analyzed in terms of particle characteristics (FESEM, HRTEM, NIR-absorption), light absorption behaviour (UV–Vis spectroscopy) and photoluminescence properties (PL-spectroscopy). The general occurrence in the form of large porous nano spheres constituted by very fine crystallites of the order of 4–25 nm with enlarged cell parameters of pure MgO were obtained. Enhanced reactivity of the produced powder is expected to originate out of the exposed polarised surfaces of these fine grains with capability to provide high energy binding sites. The non equilibrium condition prevalent under extreme speedy kinetics of the formation reaction introduced quantum subsystems in the lattice. Photoconversion between different optical centres greatly influenced the luminescence properties yielding a broad emission spectrum. The spectrum is intense because of high concentration of anion deficiency with an obvious blue shift due to lower concentration of H− traps in it. Promotion of electron in the introduced quantum subsystems under excitation provided intraband energy transfer between optical centres below the conduction band that lowered down the band gap value to 4.45 eV. Spark plasma sintering was employed for powder densification. The ultimate product constituted by nano grains of size corresponding to 200–500 nm exhibits ∼80% transmittance in IR region.

Noise in Quantum Devices: A Unified Computational Approach for Different Scattering Mechanisms

When talking about noise in quantum devices two issues must be faced: how to model the evolution of an electronic system with scattering and how this noise is practically computed in a quantum device simulator. In the present paper, we address both problems from a practical and computational point of view. In particular, as the electronic quantum subsystem is an open (normally far from equilibrium) system, we use the notion of conditional wave function, the wave function of a subsystem in Bohmian mechanics, an alternative version of quantum mechanics which along with the wave function posited definite positions for the particles. This allows us to define an effective equation in several physical situations, ranging from the simple tunneling barrier to the interaction with a bath of phonons. Finally, we present how this development can be used to compute quantum noise in a quantum device simulator.

Communication: Proper treatment of classically forbidden electronic transitions significantly improves detailed balance in surface hopping.

Surface hopping is the most popular method for nonadiabatic molecular dynamics. Many have reported that it does not rigorously attain detailed balance at thermal equilibrium, but does so approximately. We show that convergence to the Boltzmann populations is significantly improved when the nuclear velocity is reversed after a classically forbidden hop. The proposed prescription significantly reduces the total number of classically forbidden hops encountered along a trajectory, suggesting that some randomization in nuclear velocity is needed when classically forbidden hops constitute a large fraction of attempted hops. Our results are verified computationally using two- and three-level quantum subsystems, coupled to a classical bath undergoing Langevin dynamics.

Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions

Quantum transition probabilities and quantum entanglement for two-qubit states of a four-level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ group structure. Using the correspondence of the method of simulating a $3+1$ dimensional Dirac-like Hamiltonian for bispinor particles into a single trapped ion, one preliminarily obtains the analytical tools for describing ionic state transition probabilities as a typical quantum oscillation feature. For Dirac-like structures driven by generalized Poincar\'e classes of coupling potentials, one also identifies the $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ internal degrees of freedom corresponding to intrinsic parity and spin polarization as an adaptive platform for computing the quantum entanglement between the internal quantum subsystems which define two-qubit ionic states. The obtained quantum correlational content is then translated into the quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the trapping magnetic field. Experimentally, the controllable parameters simulated by ion traps can be mapped into a Dirac-like system in the presence of an electrostatic field which, in this case, is associated to ionic carrier interactions. Besides exhibiting a complete analytical profile for ionic quantum transitions and quantum entanglement, our results indicate that carrier interactions actively drive an overall suppression of the quantum entanglement.

The Schrödinger–Langevin equation with and without thermal fluctuations

The Schrödinger–Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.

Private quantum subsystems and quasiorthogonal operator algebras

We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the n-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory.

Mixed Quantum-Classical Simulations of Transient Absorption Pump-Probe Signals for a Photo-Induced Electron Transfer Reaction Coupled to an Inner-Sphere Vibrational Mode.

In a previous study (Martinez, F.; Hanna, G. Chem. Phys. Lett. 2013, 573, 77-83), we demonstrated the ability of two approximate solutions of the quantum-classical Liouville equation (QCLE) for qualitatively capturing the electronic dynamics in the pump-probe transient absorption (TA) signal of a model of a condensed phase photoinduced electron transfer reaction whose ground and excited donor states have the same equilibrium geometry. However, the question remained as to the ability of these solutions to treat the more complex situation in which the electronic states are coupled to a low-frequency inner-sphere harmonic vibrational mode (representing an intramolecular mode of the donor-acceptor complex) that shifts their equilibrium geometries with respect to each other and thereby gives rise to signatures of vibrational dynamics in the TA signal. Thus, in this study, we investigated this situation by treating the vibrational mode both quantum mechanically and classically within the context of the approximate Poisson bracket mapping equation (PBME) and forward-backward trajectory solutions (FBTS) of the QCLE. Depending on the definition of the quantum subsystem, both PBME and FBTS are capable of qualitatively capturing several of the main features in the exact TA signal and quantitatively capturing the characteristic time scale of the vibrational dynamics, despite the moderately strong subsystem-bath coupling in this model. Particularly, we found that treating the vibrational mode quantum mechanically using either PBME or FBTS better captures the signatures of the vibrational dynamics, while treating it classically using FBTS better captures the decay in the signal. These findings underscore the utility of the PBME and FBTS approaches for efficiently modeling and interpreting TA signals.

Quasi-autonomous quantum thermal machines and quantum to classical energy flow

There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific thermodynamic primitive, such as work extraction in the presence of a thermal environment, while having minimal or no control from the macroscopic regime. Beyond experimental implementations, this provides an arena in which to address certain foundational aspects such as the role of coherence in thermodynamics, the use of clock degrees of freedom and the simulation of local time-dependent Hamiltonians in a particular quantum subsystem. For small-scale systems additional issues arise. Firstly, it is not clear to what degree genuine ordered thermodynamic work has been extracted, and secondly non-trivial back-actions on the thermal machine must be accounted for. We find that both these aspects can be resolved through a judicious choice of quantum measurements that magnify thermodynamic properties up the ladder of length-scales, while simultaneously stabilising the quantum thermal machine. Within this framework we show that thermodynamic reversibility is obtained in a particular Zeno limit, and finally illustrate these concepts with a concrete example involving spin systems.

Beyond complete positivity

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any $${\mathbb {C}}$$C-linear, Hermiticity-preserving, trace-preserving map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application, we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality.

Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies

Greenberger–Horne–Zeilinger (GHZ) states are intuitively known to be the most nonclassical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. In the case of two-dimensional systems, it has been shown that GHZ states lead to an exponentially higher robustness of Bell nonclassicality against the white noise for geometrical inequalities than in the case of Weinfurter–Werner–Wolf–Żukowski–Brukner ones. We introduce geometrical Bell inequalities for collections of arbitrarily many systems of any dimensionality. We show that the violation factor of these inequalities grows exponentially with the number of parties and study their behavior in terms of dimensionality of subsystems and number of local measurements. We also investigate various strategies of assigning mathematical objects to events in the experiment, each leading to different violation ratios.

Coherence Versus Decoherence - A few Illustrative Examples

The interplay of coherence and decoherence is a vexing issue in contemporary condensed matter physics, quantum optics and quantum information theory. We present an overview of this important topical subject, in terms of three different paradigms, in which the 'noisy' effect of the environment on small quantum subsystems is analysed.

Observation of quantum recoherence of photons by spatial propagation.

Entanglement is at the heart of many unusual and counterintuitive features of quantum mechanics. Once two quantum subsystems have become entangled, it is no longer possible to ascribe an independent state to either; instead, the subsystems are completely described only as part of a greater, composite system. As a consequence of this, each entangled subsystem experiences a loss of coherence following entanglement. We refer to this decrease in coherence as decoherence. Decoherence leads inevitably to the leaking of information from each subsystem to the composite entangled system. Here, we demonstrate a process of decoherence reversal, whereby we recover information lost from the entanglement of the optical orbital angular momentum and radial profile degrees of freedom possessed by a photon pair. These results carry great potential significance, since quantum memories and quantum communication schemes depend on an experimenter’s ability to retain the coherent properties of a particular quantum system.

Resource Theory of Steering

We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. To begin with, we characterize the set of steering non-increasing operations (SNIOs) --i.e., those that do not create steering-- on arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box device. Next, we introduce the notion of convex steering monotones as the fundamental axiomatic quantifiers of steering. As a convenient example thereof, we present the relative entropy of steering. In addition, we prove that two previously proposed quantifiers, the steerable weight and the robustness of steering, are also convex steering monotones. To end up with, for minimal-dimensional systems, we establish, on the one hand, necessary and sufficient conditions for pure-state steering conversions under stochastic SNIOs and prove, on the other hand, the non-existence of steering bits, i.e., measure-independent maximally steerable states from which all states can be obtained by means of the free operations. Our findings reveal unexpected aspects of steering and lay foundations for further resource-theory approaches, with potential implications in Bell non-locality.

An introduction to the problem of bridging quantum and classical dynamics

Simulating the exact quantum dynamics of realistic interacting systems is presently a task beyond reach but for the smallest of them, as the numerical cost for solving the time-dependent Schrodinger equation scales exponentially with the number of degrees of freedom. Mixed quantum-classical methods attempt to solve this problem by starting from a full quantum description of the system and subsequently partitioning the degrees of freedom in two subsets: the quantum subsystem and the bath. A classical limit is then taken for the bath while preserving, at least approximately, the quantum evolution of the subsystem. A key, as yet not fully resolved, theoretical question is how to do so by constructing a consistent description of the overall dynamics. An exhaustive review of this class of methods is beyond the scope of this paper and we shall limit ourselves to present, as an example, a specific approach, known as the LANDM-Map method. The method stems from an attempt at taking a rigorous limit for the classical degrees of freedom starting from a path integral formulation of the full quantum problem. The results that we discuss are not new, but our intent here is to present them as an introduction to the problem of mixed quantum classical dynamics. We shall also indicate a broad classification of the available approaches, their limitations, and some open questions in this field.

Bounds on expectation values of quantum subsystems and perturbation theory

The numerical investigation of many-body quantum systems usually requires different kinds of physical approximations. The error which is made by these approximations is difficult to estimate and remains unknown in most cases. We examine an upper bound on expectation values of quantum subsystems, which enables the estimation of the maximum error that is made by physical approximations outside the subsystem. This is of special interest for perturbation theory, where the bath is commonly approximated with simplified interactions. A recently realized all-spin-based atomic-scale logic device, consisting of iron atoms and cobalt islands placed on a copper substrate, serves as a specific example for an application of the bound. Strength and weakness of these methods are critically discussed and we provide a quantitative answer to the old question in which cases a small quantum system can be used instead of a large one.