Quantum Mechanical Correlation Research Articles

Projective measurements can probe nonclassical work extraction and time correlations

Quantum correlation functions are a natural way to encode multitime information, as they are ubiquitous in analysis from fluctuation theorems to information scrambling. Correlation functions can be identified with quasiprobabilities associated to quantum processes. In this work we show how these can be measured via error-cancellation techniques, using projective measurements only and no ancillae. The scheme is implemented in a nitrogen-vacancy center in diamond undergoing a unitary quantum work protocol. We reconstruct quantum-mechanical time correlations encoded in the Margenau-Hills quasiprobabilities by observing work extraction peaks five times those of sequential projective energy measurement schemes and in violation of newly derived stochastic bounds. We interpret the phenomenon via anomalous energy exchanges due to the underlying negativity of the quasiprobability distribution. Published by the American Physical Society 2024

Single-photon level ultrafast time-resolved measurement using two-color dual-comb-based asynchronous linear optical sampling

We demonstrated an ultrafast time-resolved measurement method operating at the single-photon level and employing a two-color comb-based asynchronous optical sampling (ASOPS) setup. We harnessed the two-color ASOPS photon counting approach to achieve long-term averaging of the ultralow intensity signal with a synchronized optical trigger signal, which minimizes residual timing jitter between the two combs. A pulse-width limited picosecond cross-correlation signal was successfully obtained with a power level of <1 photon/pulse. This approach enables the thorough study of ultrafast time-resolved detection of entangled photon pairs, quantum mechanical correlations in the time-frequency domain and finds wide use in optical quantum technology.

First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems.

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Derivation of Highly Predictive 3D-QSAR Models for hERG Channel Blockers Based on the Quantum Artificial Neural Network Algorithm.

The hERG potassium channel serves as an annexed target for drug discovery because the associated off-target inhibitory activity may cause serious cardiotoxicity. Quantitative structure-activity relationship (QSAR) models were developed to predict inhibitory activities against the hERG potassium channel, utilizing the three-dimensional (3D) distribution of quantum mechanical electrostatic potential (ESP) as the molecular descriptor. To prepare the optimal atomic coordinates of dataset molecules, pairwise 3D structural alignments were carried out in order for the quantum mechanical cross correlation between the template and other molecules to be maximized. This alignment method stands out from the common atom-by-atom matching technique, as it can handle structurally diverse molecules as effectively as chemical derivatives that share an identical scaffold. The alignment problem prevalent in 3D-QSAR methods was ameliorated substantially by dividing the dataset molecules into seven subsets, each of which contained molecules with similar molecular weights. Using an artificial neural network algorithm to find the functional relationship between the quantum mechanical ESP descriptors and the experimental hERG inhibitory activities, highly predictive 3D-QSAR models were derived for all seven molecular subsets to the extent that the squared correlation coefficients exceeded 0.79. Given their simplicity in model development and strong predictability, the 3D-QSAR models developed in this study are expected to function as an effective virtual screening tool for assessing the potential cardiotoxicity of drug candidate molecules.

Inelastic Compton scattering: Tool to validate quantum mechanical potential energies

Inelastic γ-ray scattering (Compton scattering) is a distinguished tool to explore the electronic and magnetic response of various substances and is also an emphatic technique to validate the quantum mechanical exchange and correlation potentials used in the DFT calculations. Charge and magnetic Compton profiles are used to deduce the electron/spin momentum densities in functional materials like dichalcogenides, ferrites, ferroelectrics, chromates, Heusler alloys, oxides, etc. In this review, besides salient features of basic principles of Compton scattering, we have included representative studies on Compton profiles and relative nature of bonding in lead titanate/lead zirconate. Temperature dependency of spin moments using magnetic Compton profiles of Pr doped NiFe2O4 system has also be discussed. Recent work on charge and magnetic Compton scattering of variety of materials is reviewed.

Linear response for pseudo-Hermitian Hamiltonian systems: Application to PT -symmetric qubits

Motivated by the recent advances in modelling the pseudo-Hermitian Hamiltonian (pHH) systems using superconducting qubits we analyze their quantum dynamics subject to a small time-dependent perturbation. In particular, We develop the linear response theory formulation suitable for application to various pHH systems and compare it to the ones available in the literature. We derive analytical expressions for the generalized temporal quantum-mechanical correlation function $C(t)$ and the time-dependent dynamic susceptibility $\chi(t) \propto \text{Im} ~C(t)$. We apply our results to two \textit{PT}-symmetric non-Hermitian quantum systems: a single qubit and two unbiased/biased qubits coupled by the exchange interaction. For both systems we obtain the eigenvalues and eigenfunctions of the Hamiltonian, identify \textit{PT}-symmetry unbroken and broken quantum phases and quantum phase transitions between them. The temporal oscillations of the dynamic susceptibility of the qubits polarization ($z$-projection of the total spin), $\chi(t)$, relate to {\it ac} induced transitions between different eigenstates and we analyze the dependencies of the oscillations frequency and the amplitude on the gain/loss parameter $\gamma$ and the interaction strength $g$. Studying the time dependence of $\chi(t)$ we observe different types of oscillations, i.e. undamped, heavily damped and amplified ones, related to the transitions between eigenstates with broken (unbroken) $PT$-symmetry. These predictions can be verified in the microwave transmission experiments allowing controlled simulation of the pHH systems.

Exciton dynamics in conjugated polymer systems

Exciton dynamics in π-conjugated polymers systems encompass multiple time and length scales. Ultrafast femtosecond processes are intrachain and involve a quantum mechanical correlation of the exciton and nuclear degrees of freedom. In contrast, post-picosecond processes involve the incoherent Förster transfer of excitons between polymer chains. Exciton dynamics is also strongly determined by the spatial and temporal disorder that is ubiquitous in conjugated polymers. Since excitons are delocalized over hundreds of atoms, a theoretical understanding of these processes is only realistically possible by employing suitably parametrized coarse-grained exciton-phonon models. Moreover, to correctly account for ultrafast processes, the exciton and phonon modes must be treated on the same quantum mechanical basis and the Ehrenfest approximation must be abandoned. This further implies that sophisticated numerical techniques must be employed to solve these models. This review describes our current theoretical understanding of exciton dynamics in conjugated polymer systems. We begin by describing the energetic and spatial distribution of excitons in disordered polymer systems, and define the crucial concept of a “chromophore” in conjugated polymers. We also discuss the role of exciton-nuclear coupling, emphasizing the distinction between “fast” and “slow” nuclear degrees of freedom in determining “self-trapping” and “self-localization” of exciton-polarons. Next, we discuss ultrafast intrachain exciton decoherence caused by exciton-phonon entanglement, which leads to fluorescence depolarization on the timescale of 10-fs. Interactions of the polymer with its environment causes the stochastic relaxation and localization of high-energy delocalized excitons onto chromophores. The coupling of excitons with torsional modes also leads to various dynamical processes. On sub-ps timescales it causes exciton-polaron formation (i.e., exciton localization and local polymer planarization). Conversely, on post-ps timescales stochastic torsional fluctuations cause exciton-polaron diffusion along the polymer chain and at higher temperatures to transient exciton delocalization via extended exciton states. We next describe a first-principles, Förster-type model of interchain exciton transfer and diffusion in the condensed phase, whose starting point is a realistic description of the donor and acceptor chromophores. Finally, we discuss condensed phase transient exciton delocalization in highly-ordered nanofibers. We survey experimental results and explain how they can be understood in terms of our theoretical description of exciton dynamics coupled to information on polymer multiscale structures. The review also contains a brief critique of computational methods to simulate exciton dynamics.

Foundations of Quantum Computing: II. The Many Faces of ‎Quantum Uncertainty

In this Part II we focus on a few key elements of quantum mechanics essential for understanding of quantum technologies ‎and computing. We begin with a subtle but important similarity between classical and quantum mechanics which is typically ‎overlooked in favor of apparent differences. Further, it is reminded that classical motion can be obtained via averaging ‎over quantum distributions/wave functions and, conversely, quantum distributions can be recast as a superposition of virtual ‎classical paths. Relatedly, we emphasize the importance of the case intermediate between classical and quantum mechanics – ‎that is, quasi-classical mechanics. The above background facilitates additional insights and heuristics into the mechanisms of ‎widely acclaimed long-distance correlations in quantum mechanics and the origins of the coherency in quantum ensembles in the ‎context of wave-particle duality. ‎

Quantum Simulation of Antiferromagnetic Heisenberg Chain with Gate-Defined Quantum Dots

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

Quantum Artificial Neural Network Approach to Derive a Highly Predictive 3D-QSAR Model for Blood-Brain Barrier Passage.

A successful passage of the blood–brain barrier (BBB) is an essential prerequisite for the drug molecules designed to act on the central nervous system. The logarithm of blood–brain partitioning (LogBB) has served as an effective index of molecular BBB permeability. Using the three-dimensional (3D) distribution of the molecular electrostatic potential (ESP) as the numerical descriptor, a quantitative structure-activity relationship (QSAR) model termed AlphaQ was derived to predict the molecular LogBB values. To obtain the optimal atomic coordinates of the molecules under investigation, the pairwise 3D structural alignments were conducted in such a way to maximize the quantum mechanical cross correlation between the template and a target molecule. This alignment method has the advantage over the conventional atom-by-atom matching protocol in that the structurally diverse molecules can be analyzed as rigorously as the chemical derivatives with the same scaffold. The inaccuracy problem in the 3D structural alignment was alleviated in a large part by categorizing the molecules into the eight subsets according to the molecular weight. By applying the artificial neural network algorithm to associate the fully quantum mechanical ESP descriptors with the extensive experimental LogBB data, a highly predictive 3D-QSAR model was derived for each molecular subset with a squared correlation coefficient larger than 0.8. Due to the simplicity in model building and the high predictability, AlphaQ is anticipated to serve as an effective computational screening tool for molecular BBB permeability.

Belief-invariant and quantum equilibria in games of incomplete information

Drawing on ideas from game theory and quantum physics, we investigate nonlocal correlations from the point of view of equilibria in games of incomplete information. These equilibria can be classified in decreasing power as general communication equilibria, belief-invariant equilibria and correlated equilibria, all of which contain the familiar Nash equilibria.The notion of belief-invariant equilibrium appeared in game theory in the 90s. However, the class of non-signalling correlations associated to belief-invariance arose naturally already in the 80s in the foundations of quantum mechanics.In the present work, we explain and unify these two origins of the idea and study the above classes of equilibria, together with quantum correlated equilibria, using tools from quantum information but the language of (algorithmic) game theory. We present a general framework of belief-invariant communication equilibria, which contains correlated equilibria and quantum correlated equilibria as special cases. Our framework also contains the theory of Bell inequalities and their violations due to non-locality, which is a question of intense interest in the foundations of quantum mechanics, and it was indeed the original motivation for the aforementioned studies. Moreover, in our framework we can also model quantum games where players have conflicting interests, a recent developing topic in physics.We then use our framework to show new results related to the social welfare of equilibria. Namely, we exhibit a game where belief-invariance is socially better than any correlated equilibrium, and a game where all non-belief-invariant communication equilibria have a suboptimal social welfare. We also show that optimal social welfare can in certain cases be achieved by quantum mechanical correlations, which do not need an informed mediator to be implemented, and go beyond the classical “sunspot” or shared randomness approach.

Quantum-mechanical correlations and Tsirelson bound from geometric algebra

The Bell-Clauser-Horne-Shimony-Holt inequality can be used to show that no local hidden-variable theory can reproduce the correlations predicted by quantum mechanics (QM). It can be proved that certain QM correlations lead to a violation of the classical bound established by the inequality, while all correlations, QM and classical, respect a QM bound (the Tsirelson bound). Here, we show that these well-known results depend crucially on the assumption that the values of physical magnitudes are scalars. The result implies, first, that the origin of the Tsirelson bound is geometrical, not physical; and, second, that a local hidden-variable theory does not contradict QM if the values of physical magnitudes are vectors.

Calculation of Maximal Number of Areas of Longitudinal Periodic Localization of Drifting Electrons in Metallic Explorer with Electric Current of Conductivity

The results of approximate calculation of the maximal value of the quantum number of n = nm for the quantized standing longitudinal electronic de Broglie half-waves λezn/2 = l0/n long and, accordingly, of the maximal number of nm of the quantized areas of the longitudinal periodic localization with the length of Δznh of drifting lone electrons in the cylindrical explorers of eventual sizes (long l0 and radius of r0) with the axial-flow current of conductivity of i0(t) of the indicated kinds and peak-temporal parameters (PTP) are presented, taking into account the quantum-wave nature of the electric current of conductivity of i0(t) of different kinds (permanent, variable, and impulsive) and PTP in the metallic explorers. The results of verification of the obtained calculations of the quantum-mechanical correlation for the determination of the quantum number nm confirm its possibility to be applied in such areas of engineering as high-voltage heavy-current impulsive technique and electrophysical treatment of metals by a strong electromagnetic field and by a pressure of a large impulsive current.

Correlation Functions of Quantum Artin System

It was conjectured by Maldacena, Shenker and Stanford that the classical chaos can be diagnosed in thermal quantum systems by using an out-of-time-order correlation function. The Artin dynamical system defined on the fundamental region of the modular group SL(2,Z) represents a well defined example of a highly chaotic dynamical system in its classical regime. We investigated the influence of the classical chaotic behaviour on the quantum–mechanical properties of the Artin system calculating the corresponding out-of-time-order thermal quantum–mechanical correlation functions. We demonstrated that the two- and four-point correlation functions of the Liouiville-like operators decay exponentially with temperature dependent exponents and that the square of the commutator of the Liouiville-like operators separated in time grows exponentially.

Backaction-free measurement of quantum correlations via quantum time-domain interferometry

Time-domain interferometry (TDI) is a method to probe space-time correlations among particles in condensed matter systems. Applying TDI to quantum systems raises the general question, whether two-time correlations can be reliably measured without adverse impact of the measurement backaction onto the dynamics of the system. Here, we show that a recently developed quantum version of TDI (QTDI) indeed can access the full quantum-mechanical two-time correlations without backaction. We further generalize QTDI to weak classical continuous-mode coherent input states, alleviating the need for single-photon input fields. Finally, we interpret our results by splitting the space-time correlations into two parts. While the first one is associated to projective measurements and thus insensitive to backaction, we identify the second contribution as arising from the coherence properties of the state of the probed target system, such that it is perturbed or even destroyed by measurements on the system.

CALCULATION-EXPERIMENTAL DETERMINATION OF THE AVERAGE NUMBER OF QUANTIZED LONGITUDINAL ELECTRON DE BROGLIE HALF WAVES IN A CYLINDRICAL CONDUCTOR WITH PULSED AXIAL CURRENT

Purpose: Implementation of calculation-experimental determination of average number n0m of the quantized longitudinal electron de Broglie half waves of length λezm/2 in the metal cylindrical conductor with the pulsed axial current of high density. Methodology. Scientific bases of theoretical electrophysics and quantum physics, theoretical bases of the electrical engineering, electrophysics bases of technique of high-voltage and high pulsed currents. Results: The results of calculation-experimental estimations of average number n0m of the quantized longitudinal electron de Broglie half waves in the round continuous zincked steel wire of radius 0.8mm and of length 320 mm with aperiodic pulsed axial current i0(t) of temporal shape 9 ms/160 ms of high density (at its amplitude of δ0m=0.37 kA/mm2). It is shown that in examined case the numeral value of the average quantized number from data of calculation and experiment makes n0m=9, and test average length of quantized longitudinal electron de Broglie half waves in the indicated steel wire appears approximately equal to λezm/2≈34 mm. Electrophysical results are confirmed during the high current high temperature experiment conducted by a powerful high-voltage equipment calculation information on the choice of average value of quantized number n0m for longitudinal «hot» areas of the width Δz of the wire, different anomalous enhanceable concentration of drifting lone electrons and accordingly temperature of Joule heating. Originality: On the basis of the known conformities to the law of atomic and quantum physics new quantum-mechanical calculation correlation is obtained for determination in a metallic conductor with axial current of conductivity i0(t) of different type (direct, alternating and pulsed) of average number n0m of the quantized longitudinal electron de Broglie half waves and accordingly longitudinal «hot» areas of the width Δz of periodic localization along the conductor of drifting lone electrons. Practical Value: Obtained results allow to make an evaluation prognosis on finding of possible places of longitudinal periodic localization of drifting lone electrons on narrow areas of the width Δz of current-carrying parts of power wires and cables of objects of electrical power energy, production and dwellings apartments, showing up most strongly (expressed) in malfunctions of operation of cable-conductor products with the currents of short-circuit and high current density.

Genuine temporal correlations can certify the quantum dimension

Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped 171Yb+ ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.

Quantum Coherence Preservation in Extremely Dispersive Plasmonic Media

Quantum plasmonics experiments have on multiple occasions reported the observation of quantum coherence of discrete plasmons, which exhibit remarkable preservation of quantum interference visibility, a seemingly surprising feature for systems mixing light and matter with high ohmic losses during propagation. However, most experiments to date used essentially weakly-confined plasmons, which experience limited light-matter hybridization, thus limiting the potential for decoherence. Here, we report quantum coherence of plasmons near the surface plasmon polariton (SPP) resonance frequency, where plasmonic dispersion and confinement is much stronger than in previous experiments. We generated polarization-entangled pairs of photons using spontaneous parametric down conversion and transmitted one of the photons through a plasmonic hole array designed to convert incident single photons into highly-dispersive single SPPs. We find the quality of photon entanglement after the plasmonic channel to be unperturbed by the introduction of a highly dispersive plasmonic element. Our findings provide a lower bound of 100 femtoseconds for the pure dephasing time for dispersive plasmons in gold, and show that even in a highly dispersive regime surface plasmons preserve quantum mechanical correlations, making possible harnessing the power of extreme light confinement for integrated quantum photonics.

Capturing vacuum fluctuations and photon correlations in cavity quantum electrodynamics with multitrajectory Ehrenfest dynamics

We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems by generalizing the application of mixed quantum classical dynamics techniques. We employ the multitrajectory implementation of Ehrenfest mean-field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the cavity photon field through a detailed comparison with exact benchmark quantum mechanical observables and correlation functions. By properly accounting for the quantum statistics of the vacuum field, while using mixed quantum classical (mean-field) trajectories to describe the evolution, we identify a surprisingly accurate and promising route towards describing quantum effects in realistic correlated light-matter systems.

Probing unitary two-time correlations in a neutral atom quantum simulator

Measuring unitarily-evolved quantum mechanical two-time correlations is challenging in general. In a recent paper Uhrich et al 2017 Phys. Rev. A 96 022127, a considerable simplification of this task has been pointed out to occur in spin-1/2 lattice models, bringing such measurements into reach of state-of-the-art or near-future quantum simulators of such models. Here, we discuss the challenges of an experimental implementation of measurement schemes of two-time correlations in quantum gas microscopes or microtrap arrays. We propose a modified measurement protocol that mitigates these challenges, and we rigorously estimate the accuracy of the protocols by means of Lieb–Robinson bounds. On the basis of these bounds, we identify a parameter regime in which the proposed protocols allow for accurate measurements of the desired two-time correlations.