Pure State Research Articles

How is photon-blockade breakdown different from optical bistability? A neoclassical story

The photon-blockade breakdown bistability can be intuitively explained invoking the energy spectrum of the interacting qubit-mode system. Yet, the neoclassical solution of the driven-dissipative Jaynes-Cummings model has been shown to capture several key aspects of the phenomenon. In this paper, we set out to compare a fully quantum solution with the neo- and semiclassical solutions. Although the neoclassical theory is founded on the assumption of a pure partial state for the qubit, it is not simply the γ→0 limit of the semiclassical theory, the semi- versus neoclassical duality being a case of non-commutativity of limits. Furthermore, we show that the neoclassical predictions still hold in the case of a small qubit decay. Tracing the bistable behavior for different detunings, we show that it is robust over a significant range of Δ values. We demonstrate that the aptitude of the neoclassical description is founded on the high quantum purity of the bright state of the photon-blockade breakdown bistability, which sharply differentiates this phenomenology from conventional optical bistability. It is thereby demonstrated that driven-dissipative dynamics can produce closely separable pure steady states in an interacting bipartite.

Resource-efficient quantum principal component analysis

Abstract Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum principal component analysis. 
Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue $\lambda$ with error $\epsilon$ and success probability larger than $\lambda(1-\eta)$ requests a query complexity {$\mathcal{\widetilde{O}}(\epsilon^{-1})$} and a sample complexity {$\mathcal{\widetilde{O}}(\epsilon^{-2}\eta^{-1})$}, respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in $1/\epsilon$ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum principal component analysis method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

Quantum Mixtures and Information Loss in Many-Body Systems

In our study, we investigate the phenomenon of information loss, as measured by the Kullback–Leibler divergence, in a many-fermion system, such as the Lipkin model. Information loss is introduced as the number N of particles increases, particularly when the system is in a mixed state. We find that there is a significant loss of information under these conditions. However, we observe that this loss nearly disappears when the system is in a pure state. Our analysis employs tools from information theory to quantify and understand these effects.

Solvent Acidity and Basicity Scales: Analysis of Catalan’s SB and SA Scales and Gutmann’s Acceptor Number and Comparison with Kamlet and Taft’s β and α Solvent Scales, Gutmann’s Donor Number and Abraham’s B and A Solute Scales

AbstractThe use of experimental parameters to quantify solvent properties, for example in linear free energy relationships, is well established and several scales of solvent acidity, basicity and polarity/polarizability have been developed. The success of this approach raises questions of which molecular properties contribute to particular solvent parameters and whether these contributions are found in all parameters representing a particular solvent property. In the present study, Catalan’s hydrogen bond basicity and acidity parameters, SB and SA, and Gutmann’s acceptor number, AN, a measure of a solvent’s Lewis acidity, are correlated with molecular properties derived from computational chemistry. The results are compared with the results of similar correlations with Kamlet and Taft’s β and α Solvent Scales, Gutmann’s donor number DN) and Abraham’s B and A solute scales. The results show that measures of solvent basicity, SB, β and DN all correlate strongly with the partial charge on the most negative atom in the solvent molecule and the energy of the donor orbital and, in all cases, the parameter values for hydrogen-bonded solvents are anomalous. Abraham’s B, a measure of solute hydrogen basicity, depends only on the partial charge on the most negative atom and there is no anomaly in the values for solutes that, in the pure state, form hydrogen-bonded liquids. Similarly, all measures of solvent acidity, SA, α and AN, and Abraham’s A, a measure of solute hydrogen bond acidity, depend on the partial charge on the most positive hydrogen on the molecule.

XPS Study on the determination of binding energies in high-purity TiO2 nanoparticles

This study focuses on the precise determination of the binding energies of high-purity TiO2 nano-particles, using X-ray photoelectron spectroscopy (XPS). TiO2, an essential ceramic in high-tech sectors such as electronics, aerospace and photocatalysis, was analyzed in its pure state (99.5%) directly as received from the supplier, without previous alterations. XPS spectra revealed typical bond energy peaks for Ti at 458.42 eV and 464.13 eV, corresponding to Ti2p3/2 and Ti2p1/2 levels respectively, with a difference of 5.71 eV, validating the expected electron structure for Ti in TiO2. Additionally, peaks were identified at 457.36 eV and 463.36 eV, attributable to Ti3+, present in a Ti3O5 phase, as confirmed by X-ray diffraction (XRD) analysis. The mid-height width (FWHM) of the main Ti4+ peaks, ranging from 1.08 to 1.87 eV, and 0.96 eV for the Ti3+ peaks, highlights the homogeneity and exceptional purity of the sample. These findings not only corroborate the high quality of TiO2, but also provide a crucial benchmark for the scientific community, facilitating de-tailed comparisons with other samples and encouraging the development of innovative processes and materials. This study underscores the value of the XPS technique in the characterization of advanced ceramic materials and sets a standard for future research.

Determination of binding energies in high purity 2H graphite using XPS

This study focuses on the detailed characterization of graphite, employing techniques such as X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS). Graphite, a crucial material for engineering applications and advanced technologies, was analyzed in its pure state as provided by the manufacturer, without any pretreatment. XPS analysis revealed a spectrum dominated by carbon, with binding energies confirming the expected electronic structure and the presence of surface functional groups, including oxygen, silicon, and phosphorus. Although these impurities were identified, they do not appear to have affected the binding energies of the primary carbon, suggesting that their influence is confined to the surface properties and does not extend to the internal electronic structure of the graphite. XRD corroborated the high structural purity and detected a secondary SiP2O7 phase in minimal quantities. These findings validate the high quality of the graphite and provide critical information for the scientific community, establishing a benchmark for comparisons in future studies and developments of materials. This work underscores the value of combining XPS, XRD, and SEM-EDS for the thorough characterization of carbon-based materials.

General translation of cellular to shellular polyhedral structures using reciprocity

Shell-based cellular (shellular) funicular structures (SFSs) are single-layer 2-manifold efficient structures with anticlastic curvature, designed in the context of graphic statics. This research proposes a comprehensive methodology for designing these efficient structures in the context of graphic statics. Due to the significant challenges in the process of designing these structures, and the ease of using 3D graphic statics in designing cellular funicular structures, this article proposes a general technique to translate any cellular funicular structure (CFS) to a shellular version (SFS). To address this transition, this study presents an integrated methodology coupled with a computational algorithm. This technique proposes a new tetrahedralization method using the reciprocal relationship between the force and the form diagrams, generalizing the translation technique. As a result, the research explores a spectrum of shellular funicular structures, under pure compression or tension states. Diverse design techniques are introduced, enabling the creation and manipulation of these structures through their three-dimensional spatial connectivity graphs, termed “labyrinths”. A comparison between the structural performance of cellular and shellular funicular structures with similar volume density is performed displaying that for the same boundary condition, a shellular specimen can tolerate forces three times more than a cellular structure. To emphasize the practical utility of this design methodology, the study delves into its application at micro and meso scales. Specifically, it showcases the utilization of the shellular technique in the design of the midsole structure of a sneaker. This innovative approach draws inspiration from the pressure patterns exerted by the soles of the feet, emphasizing the adaptability and versatility of the proposed design technique. The results display that shellular funicular structures, with their lightweight and efficient nature, demonstrate superior structural capacity compared to their cellular counterparts and are applicable across micro, meso, and macro scales.

A comprehensive perspective for single-mode Gaussian coherence

In this work, we theoretically investigate single-mode Gaussian quantum coherence from a comprehensive perspective. Based on analytical expressions of the first and second moments of single-mode Gaussian states undergoing various Gaussian noisy channels, we use quantum mater equation and the method of the relative entropy to quantify the quantum coherence of any single-mode Gaussian state. We demonstrate that the displaced thermal state achieves maximum quantum coherence when using only the displaced vacuum state, which is a pure coherent state. However, for various lossy noise channels, quantum coherence shows a significant decrease. In the context of a squeezed thermal state, when controlling the squeezing parameter for a given environmental temperature, quantum coherence has been witnessed to increase. The ultimate upper bound of quantum coherence is then attained with the squeezed vacuum state. In particular, we determined the most generalized scenario of the displaced squeezed thermal state. The maximum value of quantum coherence is obtained when displacement and squeeze parameters both attain maximum value. Our study might be important in the future for the characterisation as well as the estimation of various nonclassical quantum correlations in single-mode Gaussian states.

Measuring the Density Matrix of Quantum-Modeled Cognitive States

Inspired by the principles of quantum mechanics, we constructed a model of students’ misconceptions about heat and temperature, conceptualized as a quantum system represented by a density matrix. Within this framework, the presence or absence of misconceptions is delineated as pure states, while the probability of mixed states is also considered, providing valuable insights into students’ cognition based on the mental models they employ when holding misconceptions. Using the analysis model previously employed by Lei Bao and Edward Redish, we represented these results in a density matrix. In our research, we utilized the Zeo and Zadnik Thermal Concept Evaluation among 282 students from a private university in Northeast Mexico. Our objective was to extract information from the analysis of multiple-choice questions designed to explore preconceptions, offering valuable educational insights beyond the typical Correct–Incorrect binary analysis of classical systems. Our findings reveal a probability of 0.72 for the appearance of misconceptions, 0.28 for their absence, and 0.43 for mixed states, while no significant disparities were observed based on gender or scholarship status, a notable difference was observed among programs (p < 0.05). These results are consistent with the previous literature, confirming a prevalence of misconceptions within the student population.

Separability Transitions in Topological States Induced by Local Decoherence.

We study states with intrinsic topological order subjected to local decoherence from the perspective of separability, i.e., whether a decohered mixed state can be expressed as an ensemble of short-range entangled pure states. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions that precisely coincide with the threshold for the feasibility of active error correction. A key insight is that local decoherence acting on the "parent" cluster states of these models results in a Gibbs state. As an example, for the 2D (3D) toric code subjected to bit-flip errors, we show that the decohered density matrix can be written as a convex sum of short-range entangled states for p>p_{c}, where p_{c} is related to the paramagnetic-ferromagnetic transition in the 2D (3D) random bond Ising model along the Nishimori line.

Quantum G-coherence factorization law under fully and strictly incoherent operations

Quantum coherence plays an important role in quantum resource theory, which is strongly related with entanglement. In order to quantify the full coherence of qudit states, we define G-coherence and convex roof of G-coherence, and prove that the G-coherence is a strong coherence monotone and the convex roof of G-coherence is a coherence measure under fully and strictly incoherent operation (FSIO), respectively. Similar to the entanglement factorization law, we prove a coherence factorization law for arbitrary d-dimensional quantum pure and mixed states under FSIO channels, which generalizes the entanglement factorization law for bipartite pure states. Our results will play an important role in the simplification of dynamical coherence measure.

Quantifying the quantumness of pure-state ensembles via coherence of Gram matrix

The Gram matrix of a set of pure states plays a crucial role in exploring the information content of quantum states. Since the Gram matrix of a pure-state ensemble can be regarded as a quantum state, we can quantify the quantumness of the corresponding quantum ensemble by means of the coherence of the Gram matrix. In particular, we introduce two natural measures of quantumness of an ensemble by means of the coherence of the Gram matrix based on Hilbert-Schmidt distance and skew information, respectively, and investigate their fundamental properties. In addition, notice that the average coherence and the maximum coherence are independent of the choice of a reference basis, we further propose to use the average coherence and the maximum coherence of the Gram matrix to quantify the generalized quantumness of the corresponding ensemble, and find that the generalized quantumness is not only related to the quantum states in the ensemble, but also to the probability distribution. We discuss the validity of these quantumness measures by calculating some important pure-state ensembles in quantum measurement and quantum cryptography. Finally, we compare these quantifiers with other existing quantifiers in the literatures and illustrate that different quantifiers can yield different features and quantumness orderings for quantum ensembles.

Entanglement preservation in tripartite quantum systems under dephasing dynamics

Abstract Protecting entanglement from decoherence is a critical aspect of quantum information processsing. For many-body quantum systems evolving under decoherence, estimating multipartite entanglement is challenging. This challenge can be met up by considering distance based measure such as relative entropy of entanglement which decisively measures entanglement in both pure as well as mixed states. In this work, we investigate the tripartite entanglement dynamics of pure and mixed states in the presence of a structured dephasing environment at finite temperature. We show that the robustness of the quantum system to decoherence is dependent on the distribution of entanglement and its relation to different configurations of the bath. If the bath is structured individually such that each qubit has its own environment, the system has different dynamics compared to when the bath is common to all the three qubits. From the results we conjecture that there is a connection between the distribution of entanglement among the qubits and the distribution of bath degrees of freedom, and the interplay of these two distributions determines the decay rate of the entanglement dynamics. The sustainability of tripartite entanglement is shown to be enhanced significantly in presence of reservoir memory.

MesoHOPS: Size-invariant scaling calculations of multi-excitation open quantum systems.

The photoexcitation dynamics of molecular materials on the 10-100nm length scale depend on complex interactions between electronic and vibrational degrees of freedom, rendering exact calculations difficult or intractable. The adaptive Hierarchy of Pure States (adHOPS) is a formally exact method that leverages the locality imposed by interactions between thermal environments and electronic excitations to achieve size-invariant scaling calculations for single-excitation processes in systems described by a Frenkel-Holstein Hamiltonian. Here, we extend adHOPS to account for arbitrary couplings between thermal environments and vertical excitation energies, enabling formally exact, size-invariant calculations that involve multiple excitations or states with shared thermal environments. In addition, we introduce a low-temperature correction and an effective integration of the noise to reduce the computational expense of including ultrafast vibrational relaxation in Hierarchy of Pure States (HOPS) simulations. We present these advances in the latest version of the open-source MesoHOPS library and use MesoHOPS to characterize charge separation at a one-dimensional organic heterojunction when both the electron and hole are mobile.

Euclidean wormholes for individual 2d CFTs

We interpret appropriate families of Euclidean wormhole solutions of AdS3 gravity in individual 2d CFTs as replica wormholes described by branching around the time-symmetric apparent horizons of black holes sourced by the backreaction of heavy point particles. These wormholes help describe a rich formalism to coarse grain pure states in 2d CFTs dual to the black hole geometries because the wormhole amplitudes match with the Renyi entropies of CFT states obtained by decohering the pure states in a specific way. This formalism can be generalised to coarse grain pure states in several copies of the CFT dual to multi-boundary black holes using wormhole solutions with higher genus boundaries using which we illustrate that coarse graining away the interior of multi-boundary black holes sets the mutual information between any two copies of the dual CFT to zero. Furthermore, this formalism of coarse graining pure states can be extended to decohere transition matrices between pure states which helps interpret more general families of wormhole solutions including those with non replica-symmetric boundary conditions in individual CFTs. The pseudo entropy of the decohered transition matrices has interesting holographic interpretation in terms of the area of minimal surfaces on appropriate black hole or wormhole geometries. The wormhole solutions which show up in the coarse graining formalism also compute the Renyi entropies of Hawking radiation after the Page time in a setup which generalizes the West Coast model to 3d gravity. Using this setup, we discuss the evaporation of one-sided black holes sourced by massive point particles and multi-boundary black holes in 3d gravity.

Hypoglycemia during hyperosmolar hyperglycemic crises is associated with long-term mortality

BackgroundPrevious research has indicated that hypoglycemia during hospitalization is a predictor of unfavorable outcomes in patients with diabetes. However, no studies have examined the long-term impact of hypoglycemia in adults admitted for hyperglycemic crises. The study was aimed to investigate the long-term implications of hypoglycemia during hyperosmolar hyperglycemic crises, particularly in terms of all-cause mortality.MethodsThis retrospective cohort study included 170 patients (82 men [48.2%], median age 72 years) admitted to a university hospital for hyperosmolar hyperglycemic crises, including pure hyperosmolar hyperglycemic states and hyperosmolar diabetic ketoacidoses. We separately investigated the prognostic significance of hypoglycemia on mortality during the initial intravenous insulin therapy phase and during the later subcutaneous insulin therapy phase, both during hospitalization and in the long term (median follow-up, 652 days; range 2–3460 days).ResultsBoth hypoglycemia during the initial intravenous insulin therapy phase (observed in 26.5% of patients) and hypoglycemia during the later subcutaneous insulin therapy phase (observed in 52.7% of patients) were associated with long-term mortality. After adjusting for potential confounders, hypoglycemia during the initial intravenous insulin therapy phase remained associated with mortality (hazard ratio 2.10, 95% CI 1.27–3.46, p = 0.004).ConclusionsHypoglycemia during hyperosmolar hyperglycemic crises is a marker of long-term mortality, especially when it occurs during the initial intravenous insulin therapy phase.

Exact exponent for atypicality of random quantum states

We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of ‘concentration of measure’ and have focused on the behavior of the states close to the average. In contrast, we investigate the large deviation regime, where the states may be far from the average. We prove the following results: first, the probability that the induced random state is within a given set decreases no slower or faster than exponential in the dimension of the subsystem traced out. Second, the exponent is equal to the quantum relative entropy of the maximally mixed state and the given set, multiplied by the dimension of the remaining subsystem. Third, the total probability of a given set strongly concentrates around the element closest to the maximally mixed state, a property that we call conditional concentration. Along the same line, we also investigate an asymptotic behavior of coherence of random pure states in a single system with large dimensions.

Pickl’s proof of the quantum mean-field limit and quantum Klimontovich solutions

This paper discusses the mean-field limit for the quantum dynamics of N identical bosons in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{R}}^3$$\\end{document} interacting via a binary potential with Coulomb-type singularity. Our approach is based on the theory of quantum Klimontovich solutions defined in Golse and Paul (Commun Math Phys 369:1021–1053, 2019) . Our first main result is a definition of the interaction nonlinearity in the equation governing the dynamics of quantum Klimontovich solutions for a class of interaction potentials slightly less general than those considered in Kato (Trans Am Math Soc 70:195–211, 1951). Our second main result is a new operator inequality satisfied by the quantum Klimontovich solution in the case of an interaction potential with Coulomb-type singularity. When evaluated on an initial bosonic pure state, this operator inequality reduces to a Gronwall inequality for a functional introduced in Pickl (Lett Math Phys 97:151-164, 2011), resulting in a convergence rate estimate for the quantum mean-field limit leading to the time-dependent Hartree equation.

Distinguishing pure and thermal states by Landauer’s principle in open systems

Starting from Polchinski’s thought experiment on how to distinguish between pure and thermal states, we construct a specific system to study the interaction between qubit and cavity quantum field theory (QFT) in order to provide a more operational point of view. Without imposing any restrictions on the initial states of qubit and cavity QFT, we compute the evolution of the system order by order by the perturbation method. We choose Landauer’s principle, an important bound in quantum computation and quantum measurement, as the basis for the determination of the thermal state. By backtracking the initial state form, we obtain the conditions that must be satisfied by the cavity QFT: the expectation value of the annihilation operator should be zero, and the expectation value of the particle number operator should satisfy the Bose–Einstein distribution. We also discuss the difference between the thermal state and a possible alternative to the thermal state: the canonical thermal pure quantum (CTPQ) state.

Realization of IR Photodetector based on AGNRs operating in the Atmospheric Windows

Nowadays, the importance of Atmospheric windows in optoelectronic industries is not hidden from anyone. On the other hand, using graphene nanoribbons widely has been applied in optical devices. So, armchair graphene nanoribbons (AGNRs) from three different families as IR photodetectors are proposed and modeled, in this work. Our results show that the energy gap of AGNRs has been in the 1–3 μm and 8–14 μm atmospheric windows in the pure state and with nitrogen (N)/boron (B) substitutional doping. Also, responsivity and specific detectivity (D*) have been calculated, by introducing a simple structure as an IR photodetector. The energy gap and dark current (Jdark) calculations have been done by density functional theory (DFT) and non-equilibrium Green's function (NEGF) formalism, respectively. The specific detectivity peaks on the order of 109 cmHz1/2/W for 9-AGNR and 10-AGNR at 1–3 μm atmospheric window have been concluded. Furthermore, our results show that 11-AGNR with B dopants can be used to design dual-band detectors in the 1–3 μm and 8–14 μm atmospheric windows.