Pure State Research Articles

Influence of thickness scaling on the electronic structure and optical properties of oxygen deficient BaBiO3-δ thin films grown on SrTiO3-buffered Si(001) substrate

BaBiO3 has attracted a lot of research attention since it was discovered as the parent compound for the high-Tc superconducting BaPbxBi1–xO3 and Ba1–xKxBiO3. In its pure state, BaBiO3 is an insulator due to the presence of a breathing distortion of the BiO6 octahedra. The distortion is attributed to the valency of Bi in the compound being charge-ordered in the form of Bi3+ and Bi5+ along the lattice, resulting in alternating expanded or contracted BiO6 octahedra. The interaction between the electronic properties and the thickness of the thin film is crucial to study. We conducted a thorough study to investigate the effect of the thickness reduction of BaBiO3-δ grown on SrTiO3-buffered Si substrates on the optical properties as well as the Bi electronic structure of the thin films. We conclude that modifications in the valency of Bi in the ultra-thin film regime result in an optically conducting layer.

Fidelity Comparation of Two-Qubit Quantum Teleportation with Bit-Flip and Phase-Flip Channel

This study investigates the effect of noise on two-qubit quantum teleportation through a four-qubit entangled channel theoretically. Therefore, in this study a comparison of two states of teleportation through ideal and noisy channel was carried out. The noisy channel can have the effect of bit-flip channel and phase-flip channel. From these two effects, it is found that the channel transforms in-to a mixed state. If the noise is neglected, the channel is pure state. Then, this channel is measured and fidelity is calculated. The fidelity of an ideal environment is 1. This indicates that the teleportation was successfully sent and at the same time confirms the teleportation behavior under ideal conditions. In noisy environments, fidelity can be less than 1. Two factors in noisy environment that affect fidelity are noise factor (p) and the orginal parameter states (transmission coefficients). In this calculation, for the bit flip noise, we observed that as the values of the coefficient values of transmitted state increase, the fidelity value increases. Meanwhile, for the phase flip noise, we observed that as the values of the coefficient values of transmitted state increase, the fidelity value decreases.

A smooth horizon without a smooth horizon

Recent observations on type III algebras in AdS/CFT raise the possibility that smoothness of the black hole horizon is an emergent feature of the large-N limit. In this paper, we present a bulk model for the finite-N mechanism underlying this transition. We quantize a free scalar field on a BTZ black hole with a Planckian stretched horizon placed as a Dirichlet boundary for the field. This is a tractable model for the stretched horizon that does not ignore the angular directions, and it defines a black hole vacuum which has similarities to (but is distinct from) the Boulware state. Using analytic approximations for the normal modes, we first improve upon ’t Hooft’s brick wall calculation: we are able to match both the entropy and the temperature, exactly. Emboldened by this, we compute the boundary Wightman function of the scalar field in a typical pure state built on our stretched horizon vacuum, at an energy sliver at the mass of the black hole. A key result is that despite the manifest lack of smoothness, this single-sided pure state calculation yields precisely the Hartle-Hawking thermal correlator associated to the smooth horizon, in the small-GN limit. At finite GN, there are variance corrections that are suppressed as Oe−SBH/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({e}^{-{S}_{BH}/2}\\right) $$\\end{document}. They become important at late times and resolve Maldacena’s information paradox. Highly excited typical pure states on the stretched horizon vacuum are therefore models for black hole microstates, while the smooth horizon describes the thermal state. We note that heavy excited states on the stretched horizon are better defined than the vacuum itself. These results suggest that complementarity in the bulk EFT could arise from a UV complete bulk description in which the black hole interior is not manifest.

Quantum algorithms for matrix operations and linear systems of equations

Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the ‘sender-receiver’ model, we propose quantum algorithms for matrix operations such as matrix-vector product, matrix-matrix product, the sum of two matrices, and the calculation of determinant and inverse matrix. We encode the matrix entries into the probability amplitudes of the pure initial states of senders. After applying proper unitary transformation to the complete quantum system, the desired result can be found in certain blocks of the receiver’s density matrix. These quantum protocols can be used as subroutines in other quantum schemes. Furthermore, we present an alternative quantum algorithm for solving linear systems of equations.

Qudit Concurrence and Monogamy

It is well known that entanglement is one of the distinctive aspects of the quantum world. The measurement and quantification of entanglement is one of the major problems in understanding and applying this resource. This research aims to investigate entanglement measures and their properties in high-dimensional systems. One such property is entanglement monogamy, viz. quantum correlations are not shareable, different from the classical ones. On the other hand, the study of entanglement depends on the definitions of its measures. Here we examine the applicability of concurrence, an entanglement measure known for its effectiveness in the analysis of qubit entanglement. While the entanglement of two-level systems or qubits is widely understood, its extension to higher dimensions remains challenging. Our research establishes equivalence between different concurrence definitions for bipartite qubit pure states and extends them to qudits. Subsequently, we investigate the monogamous relations of these measurements to explore their characteristics. This approach might enhance our comprehension of quantum traits in qudit systems and advance our understanding of entanglement in broader quantum contexts.

Maximum Geometric Quantum Entropy.

Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally-suitable, possibilities. Following Jaynes' information-theoretic perspective, this can be framed as an inference problem. We propose the Maximum Geometric Quantum Entropy Principle to exploit the notions of Quantum Information Dimension and Geometric Quantum Entropy. These allow us to quantify the entropy of fully arbitrary ensembles and select the one that maximizes it. After formulating the principle mathematically, we give the analytical solution to the maximization problem in a number of cases and discuss the physical mechanism behind the emergence of such maximum entropy ensembles.

Elastic bit and Berry phase: Investigating topological phenomena in a classical granular network

This study investigates the Berry phase, a key concept in classical and quantum physics, and its manifestation in a classical system. We achieve controlled accumulation of the Berry phase by manipulating the elastic bit (a classical analogue to a quantum bit) in an externally driven, homogeneous, spherical, nonlinear granular network. This is achieved through the classical counterpart of quantum coherent superposition of states. The elastic bit's state vectors are navigated on the Bloch sphere using external drivers' amplitude, phase, and frequency, yielding specific Berry phases. These phases distinguish between trivial and nontrivial topologies of the elastic bit, with the zero Berry phase indicating pure states of the linearized granular system and the nontrivial π phase representing equal superposed states. Other superposed states acquire different Berry phases. Crucially, these phases correlate with the structure's eigenmode vibrations: trivial phases align with distinct, in-phase, or out-of-phase eigenmodes, while nontrivial phases correspond to coupled vibrations where energy is shared among granules, alternating between oscillation and rest. Additionally, we explore Berry's phase generalizations for non-cyclic evolutions. This research paves the way for advanced quantum-inspired sensing and computation applications by utilizing and controlling the Berry phase.

Optimality conditions for bilevel optimal control problems with non-convex quasi-variational inequalities

We establish Pontryagin optimality conditions for a generalized bilevel optimal control problem in which the leader is subject to a pure state inequality constraint, while the follower is governed by a non-convex quasi-variational inequality parameterized by the final state. To simplify the problem at hand, we convert it into a single-level optimal control problem by mapping the solution set of the quasi-variational inequality to a parametric optimization problem and employing the value function reformulation. Furthermore, we introduce certain regularity conditions to ensure that the derived maximum principle remains non-degenerate. Finally, we provide an illustrative example to elucidate our research findings.

Identifying families of multipartite states with non-trivial local entanglement transformations

The study of state transformations by spatially separated parties with local operations assisted by classical communication (LOCC) plays a crucial role in entanglement theory and its applications in quantum information processing. Transformations of this type among pure bipartite states were characterized long ago and have a revealing theoretical structure. However, it turns out that generic fully entangled pure multipartite states cannot be obtained from nor transformed to any inequivalent fully entangled state under LOCC. States with this property are referred to as isolated. Nevertheless, multipartite states are classified into families, the so-called SLOCC classes, which possess very different properties. Thus, the above result does not forbid the existence of particular SLOCC classes that are free of isolation, and therefore, display a rich structure regarding LOCC convertibility. In fact, it is known that the celebrated n-qubit GHZ and W states give particular examples of such classes and in this work, we investigate this question in general. One of our main results is to show that the SLOCC class of the 3-qutrit totally antisymmetric state is isolation-free as well. Actually, all states in this class can be converted to inequivalent states by LOCC protocols with just one round of classical communication (as in the GHZ and W cases). Thus, we consider next whether there are other classes with this property and we find a large set of negative answers. Indeed, we prove weak isolation (i.e., states that cannot be obtained with finite-round LOCC nor transformed by one-round LOCC) for very general classes, including all SLOCC families with compact stabilizers and many with non-compact stabilizers, such as the classes corresponding to the n-qunit totally antisymmetric states for n≥4. Finally, given the pleasant feature found in the family corresponding to the 3-qutrit totally antisymmetric state, we explore in more detail the structure induced by LOCC and the entanglement properties within this class.

Overlap structure and free energy fluctuations in short-range spin glasses

We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on Gibbs states whose edge overlap values with a reference state fall within a specified range. Using this metastate we show that, in any dimension, the variance of free energy difference fluctuations between pure states within a single mixed Gibbs state with multiple edge overlap values diverges linearly with the volume. We discuss some implications of these results.

From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part I. Stationary Hamiltonians

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text] and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector [Formula: see text], orthogonal to both [Formula: see text] and [Formula: see text]. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit [Formula: see text] and [Formula: see text] states under evolution by a quantum Heisenberg Hamiltonian.

Analysis of the physical chemistry of domestic water supply sources in choba, Port Harcourt, rivers state

Water are used for several important purposes but the most essential use considered on the basis of social and economic significance as it relates to the health of the population is human consumption and sanitation. Man needs constant and accessible supply of water to provide necessary prerequisite for important physiological and biochemical processes. On account of the general contention that water is more basic than all other critical stuff to life and in its pure state is commended key to health. This study aimed at to examine the physical characteristics of the water supply sources in Choba as a crucial factor for development and upon which the quality of life depends. Thus, water samples were collected from borehole and well water sources being the only available major sources of water supply in Rumuokocha, Rumuchakara, Igbogo, Owhipa, Ndudor and Rumualoghu communities that make Choba and the parameters investigated include pH, Temperature, Dissolved oxygen (DO), Conductivity, Total Dissolved Solid (TDS) and Salinity. The results of the analyses for temperature was t= 0.751 and t= 0.547 both at p<0.05 for borehole and well water sources implying no significant difference from the allowable limit by WHO whereas for DO, pH, salinity, TDS and conductivity, t= -51.966; -24.027; -24.796, -19.546 ;2.321and t= -51.966; -24.027; -16.966, -20.024; 2.272 for borehole and well water sources respectively indicating a statistically significant difference between the parameters investigated and the allowable limits. Similarly, the ANOVA result shows F= 400.384; 23.262; 19.997; 8502.215at p<0.05 for parameters like temperature, salinity, TDS and conductivity of the available water sources do not vary significantly in the area. Therefore, constant monitoring and assessment of physical water quality parameters, water treatment and assessment of bacteriological content and other relevant water parameters to holistically ascertain it suitability for adequate human use were recommended.

Interlayer Coupling Controlled Ordering and Phases in Polar Vortex Superlattices.

The recent discovery of polar topological structures has opened the door for exciting physics and emergent properties. There is, however, little methodology to engineer stability and ordering in these systems, properties of interest for engineering emergent functionalities. Notably, when the surface area is extended to arbitrary thicknesses, the topological polar texture becomes unstable. Here we show that this instability of the phase is due to electrical coupling between successive layers. We demonstrate that this electrical coupling is indicative of an effective screening length in the dielectric, similar to the conductor-ferroelectric interface. Controlling the electrostatics of the superlattice interfaces, the system can be tuned between a pure topological vortex state and a mixed classical-topological phase. This coupling also enables engineering coherency among the vortices, not only tuning the bulk phase diagram but also enabling the emergence of a 3D lattice of polar textures.

Single-Molecule Magnet Behavior of Confined Dy(III) in a Mixed Heteroatom-Substituted Polyoxotungstate.

Two heteroatom-templated Dy(III)-confined polyoxotungstates [H2N(CH3)2]7Na7[Dy2(H2O)7(W4O9)(HPSeW15O54)(α-SeW9O33)2]·31H2O (1) and [H2N(CH3)2]14K2Na18{[Dy2(H2O)13W14O40]2[α-SeW9O33]4[HPSeW15O54]2}·44H2O (2) were synthesized by a one-pot aqueous reaction and structurally characterized. The most distinctive structural feature of complexes 1 & 2 is the simultaneous presence of both trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building blocks containing P(III)-Se(IV) heteroatoms. The trimeric polyanion of 1 can be represented as a fusion of two trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units encapsulating the [Dy2(H2O)7(W4O9)]12+ cluster. On the other hand, hexameric polyoxoanions of 2 are described as four trivacant Keggin [α-SeW9O33]8- and two Dawson [HPSeW15O54]10-, building units anchoring a [Dy4(H2O)26W28O80]20+ cluster. The magnetic investigation revealed the presence of significant magnetic anisotropy and slow relaxation of magnetization behavior for complex 1 with a phenomenological energy barrier, Ueff = 13.58 K in the absence of an external magnetic field, and Ueff = 24.57 K in the presence of a 500 Oe external dc magnetic field. On the other hand, complex 2 favors the QTM relaxation process in the absence of an external magnetic field and shows field-induced slow relaxation of magnetization with Ueff = 11.11 K at 1500 Oe applied dc field. The in-depth analysis of magnetic relaxation dynamics shows that the relaxation process follows the Orbach as well as Raman relaxation pathways. Further, the ab initio calculation of the studied complexes confirms that the highly axial ground and first excited energy states (containing pure highest mJ states) are responsible for the observed single-molecule magnet (SMM) behavior. Remarkably, this is the first example of a mixed heteroatom-based Dy(III)-substituted polyoxotungstate with both trimeric Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units showing SMM behavior.

Investigating entangled photons to quantify quantum correlations in dual optomechanical cavities.

Quantum correlations that go beyond quantum entanglement have a significant role in the fields of quantum information processing and quantum computation. In essence, when we describe a quantum system using pure states, quantum entanglement and quantum correlation are essentially indistinguishable. However, this equivalence breaks down when dealing with general mixed states. To contribute to understanding this distinction, we have considered a straightforward model for both generating and measuring these quantum correlations. We focus on two macroscopic mechanical resonators situated in separate Fabry–Perot cavities and coupled through the photon hopping process. Our model allows us to conduct a comprehensive examination and quantification of quantum correlations that extend beyond entanglement between these mechanical modes. Our approach begins with the determination of the global covariance matrix, serving as the foundation for calculating two key metrics: the Entropy of Formation and the Gaussian quantum Discord. These metrics enable us to quantify the extent of quantum entanglement and quantum correlations, respectively. Our analysis, based on these quantifiers, reveals that quantum discord serves as a more appropriate metric for characterizing the quantum correlations between the mechanical modes in an optomechanical quantum system, especially in the presence of robust photon hopping.

Sodium-rich solid state reaction synthesis of sodium tri-titanate for AMTEC application

Alkali-Metal-Thermal-Electric-Converter systems (AMTEC-systems) pose a promising approach for energy conversion, e.g. from waste heat. Central components are a gas-tight ion-conductive solid membrane and an enclosed porous electrode. The presented study covers an adapted synthesis routine for single-phase sodium-tritanate (Na2Ti3O7) and its assessment as an alternative AMTEC-membrane-material. In contrast to the conventional stoichiometric solid state reaction between sodium carbonate and titania, the adapted synthesis reaction was performed with sodium excess. Up to 900 °C, the as-synthesised material evinced both, a constant thermal expansion behaviour over various thermal cycles and an expected electric conductivity. More important, phase stability either in pure state as well as in contact with a potential electrode material (La0.8Sr0.2)0.98MnO3 was demonstrated by long term exposure at 900 °C over 240 h. According to those findings the synthesised Na2Ti3O7 is considered to be an alternative membrane-material for AMTEC-application.

Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized.

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( ENm ) and the Gaussian interferometric power ( PGm ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( PGm ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.

Engineered Chimera Protein Constructs to Facilitate the Production of Heterologous Transmembrane Proteins in E. coli.

To delve into the structure-function relationship of transmembrane proteins (TMPs), robust protocols are needed to produce them in a pure, stable, and functional state. Among all hosts that express heterologous TMPs, E. coli has the lowest cost and fastest turnover. However, many of the TMPs expressed in E. coli are misfolded. Several strategies have been developed to either direct the foreign TMPs to E. coli's membrane or retain them in a cytosolic soluble form to overcome this deficiency. Here, we summarize protein engineering methods to produce chimera constructs of the desired TMPs fused to either a signal peptide or precursor maltose binding protein (pMBP) to direct the entire construct to the periplasm, therefore depositing the fused TMP in the plasma membrane. We further describe strategies to produce TMPs in soluble form by utilizing N-terminally fused MBP without a signal peptide. Depending on its N- or C-terminus location, a fusion to apolipoprotein AI can either direct the TMP to the membrane or shield the hydrophobic regions of the TMP, maintaining the soluble form. Strategies to produce G-protein-coupled receptors, TMPs of Mycobacterium tuberculosis, HIV-1 Vpu, and other TMPs are discussed. This knowledge could increase the scope of TMPs' expression in E. coli.