Pure State Research Articles

Unveiling the Potential of Pt Nanoparticle-Decorated PEDOT:PSS Membranes for Efficient Gas Separation.

In the dynamic landscape of industrial processes, membrane technology offers a paradigm shift beyond energy-intensive separation techniques, exemplifying a progressive leap toward sustainability. In this regard, highly flexible and uniform poly(3,4-ethylenedioxythiophene)polystyrenesulfonate (PEDOT:PSS)-engineered membranes at a reduced thickness have been fabricated on track-etched poly(ethylene terephthalate) (PET) substrates. The membranes were functionalized and embedded with platinum nanoparticles (Pt NPs) having a higher affinity toward H2 gas. The materials and fabricated membranes were characterized by using high-resolution transmission electron microscopy (HRTEM) and field emission scanning electron microscopy (FESEM) techniques for morphological and structural analysis. FTIR and Raman characterizations were performed to study the characteristic bonds. The uniformity and quantification of Pt nanoparticle binding were tested through inductively coupled plasma mass spectrometry (ICP-MS) studies and FESEM with EDS mapping. The gas separation performance was studied using H2, N2, and CO2 gases in pure and mixed (H2/CO2 in 50:50) states. It was observed that the modified membrane showed a 116% increment in H2 permeability and 82 and 107% increment in H2/CO2 and H2/N2 selectivity values with pure gas, while a 121% increment in H2 permeability and 156% increment in H2/CO2 selectivity using mixed gas. The separation performance in pure and mixed gas states with repeated experiments conspicuously highlighted their prospective viability as prime contenders for gas separation applications.

Interpolation of positive matrices by quantum‐inspired optimal control

AbstractInterpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum‐inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open‐loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum‐inspired interpolation is shape‐preserving with applications to tensor field processing.

BCC-FCC transformation induced exchange bias effect in the Fe2MnGa alloys

Transformation from a body-centered cubic (BCC) to a face-centered cubic (FCC) phase has garnered substantial attention in materials design due to its capacity for adjustable properties. In this study, we investigated the magnetic behavior of stoichiometric Fe2MnGa during the BCC-FCC transformation. Our findings unveil that the Fe2MnGa alloy undergoes a gradual transformation from BCC to FCC phase. During this transformation, the proportion of FCC phase gradually increases, resulting in a dual-phase structure, until it ultimately reaches a pure FCC phase. Furthermore, as the cooling processes, a magnetic transition from ferromagnetic to weak magnetic state was observed within the FCC phase. Following this magnetic transition, the sample exhibits an exchange bias effect, indicating a mixed ferromagnetic/antiferromagnetic state rather than a pure antiferromagnetic state. The magnitude of the exchange bias field is directly proportional to the proportion of the FCC phase, suggesting a negligible contribution of the BCC phase to the exchange bias effect. The controllable dual-phase nature of Fe-Mn-Ga alloys holds significant potential for material design.

Average Rényi entropy of a subsystem in random pure state

Average Rényi entropy of a subsystem in random pure state

Orthonormal bases of extreme quantumness

Spin anticoherent states acquired recently a lot of attention as the most "quantum" states. Some coherent and anticoherent spin states are known as optimal quantum rotosensors. In this work, we introduce a measure of quantumness for orthonormal bases of spin states, determined by the average anticoherence of individual vectors and the Wehrl entropy. In this way, we identify the most coherent and most quantum states, which lead to orthogonal measurements of extreme quantumness. Their symmetries can be revealed using the Majorana stellar representation, which provides an intuitive geometrical representation of a pure state by points on a sphere. Results obtained lead to maximally (minimally) entangled bases in the 2j+1 dimensional symmetric subspace of the 22j dimensional space of states of multipartite systems composed of 2j qubits. Some bases found are iso-coherent as they consist of all states of the same degree of spin-coherence.

Facile green fabrication of copper/polyvinylidene fluoride nanocomposite for pathogens disinfection and dye degradation in wastewater

This study aimed to explore the production of valuable nanomaterials using natural waste-derived extracts through a green synthesis approach. Copper nanoparticles (CuNPs) were successfully fabricated using coffee grounds as a reducing agent. Characterization via TEM and DLS confirmed the small average size of the biogenic CuNPs, while XRD analysis indicated their formation in a pure state without impurities. To enhance effectiveness in bacterial disinfection, dye degradation, and conductivity, a CuNPs@polyvinylidene fluoride (PVDF) nanocomposite was developed. Various spectroscopic and microscopic methods validated CuNPs production. Experimental data demonstrated significant antibacterial activity in the CuNPs@PVDF nanocomposite, eliminating harmful bacteria (Salmonella enterica, Klebsiella pneumoniae, Bacillus subtilis, and Enterococcus faecalis) within 60 to 115 min. At concentrations of 50, 100, and 150 µg/mL, the nanocomposite notably accelerated Methyl Red (MR) dye degradation, achieving degradation rates of 68.72 %, 81.48 %, and 100 % after 150 min. These findings advocate for the potential use of the CuNPs@PVDF nanocomposite in eliminating pathogens and reducing organic dye pollution. Its eco-friendly synthesis, effective disinfection, and photocatalytic proficiency signify its wide applicability in water treatment, establishing it as a promising solution for tackling water contamination issues.

Fast New Method for Estimation of Captopril in Pure and Pharmaceutical Preparation by Reaction with Ammonium Ce (IV) Sulfate in Acid Medium

The determination of captopril (CAP) using a new continuous flow injection analysis (CFIA) method was given in this work CAP in its pure state and some of its pharmaceutical preparations. The technique can be described as simple, fast, sensitive, easy to operate, and low-cost. The CAP reacted with ammonium ceric(IV) sulfate (ACS)2(NH4 )2SO4Ce(SO4)2. 3 H2O in an acidic medium and the reaction led to the formation of a white, slightly yellowish precipitate. The formed precipitate was studied using Ayah 6S×1-ST-2D Solar cell-CFI Analyzer, a through the reflection of accident light on the surfaces of the precipitate particles at (0-1800), expressed as the response of the transducer measured in (mV). Some chemical and physical parameters were studied to provide the optimal conditions for the study. The calibration curve within the range of (0.07-3.0) mmol/L was linear, with a correlation coefficient (r) value equal to (0.9983), and the percentage value of linearity (R2%) was (99.65). The method's detection limit (L.O.D.) of the new method was 272.5 ng/25 µL; it was calculated by diluting the minimum concentration in the calibration curve gradually. RSD% was less than 0.2% for 0.9, 1.5, and 3.0 mmol/L concentrations of C.A.P. for n=8. The method was successfully applied to estimate C.A.P. in three pharmaceutical preparations, each produced by a different company. The new method was compared with the UV-Spectrophotometric method (classical method) at λmax= 207.2 nm by using the method of standard additions. Both the t-test and the F-test were conducted to ensure that there wasn't a significant difference between the new method and the conventional one. The results of both tests showed, at a confidence level of 95%, that there was no significant difference.

Quantifying Bell nonlocality of a pure two-qudit state via its entanglement

For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in Loubenets and Namkung (2022 J. Phys. A: Math. Theor. 55 285301) and also expressed via the concurrence, analytically quantify Bell nonlocality of a pure two-qudit state via its entanglement, in particular, prove explicitly that entanglement of a pure two-qudit state is necessary and sufficient for its Bell nonlocality. By re-visiting the pure two-qubit case, we also find and rigorously prove the new results on correlation properties of an arbitrary pure two-qubit state.

Update of [formula omitted]: Newly added functions and methods in versions 2 and 3

HΦ [aitch-phi] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal block preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the abinitio low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode—simplified input format in HΦ—to use these functions and methods. We explain the basics of the implemented methods and how to use them. Program summaryProgram Title:HΦ [aitch-phi]CPC Library link to program files:https://doi.org/10.17632/vnfthtyctm.2Developer's repository link:https://github.com/issp-center-dev/HPhiLicensing provisions: GPLv3Programming language: C, FortranJournal reference of previous version: Comput. Phys. Commun. 217 (2017) 180–192Does the new version supersede the previous version?: Yes. The latest version has compatibility with the old versions. Although most functions are available in newer versions, some redundant/unnecessary functions were abolished in newer versions.Reasons for the new version: Implementation of new functions and methods, development of utilities, and bug fixes.Summary of revisions: We added new functions to obtain excited spectrum, low-energy excited states, and time-dependent physical quantities. We also implemented the full diagonalization method by using MAGMA on GPGPUs and finite-temperature simulations by using the canonical thermal pure quantum state method. In addition, we developed utilities for connection with RESPACK and a submodule for a generator of input files.Nature of problem: Physical properties in quantum lattice models with finite system sizesSolution method: In HΦ, we implemented several numerical methods such as the Lanczos method, the full diagonalization method, the locally optimal block preconditioned conjugate gradient (LOBPCG) method, the real-time evolution method based on the Taylor expansion, the shifted Krylov method, and the microcanonical/canonical thermal pure quantum state method.

Impact dynamics of a free-falling reference test mass in space

Outer space may constitute a privileged environment for experiments involving impacts. In fact, disturbing phenomena like drag or weight forces are negligible and a nearly pure free-fall state may be achieved for the impacting bodies. The case analysed in this manuscript comes from the initialization of the science phase of a space mission (LISA Pathfinder, flown in 2015), in which an extended metallic body – starting from a caged configuration – was released to free-fall inside a spacecraft by a dedicated mechanism, the grabbing positioning and release mechanism (GPRM). During the release phase, the test mass (TM) experienced some impacts with the GPRM end effector, before being electrostatically controlled to its nominal position, i.e. still in the centre of the hosting electrode housing. The impact dynamics of the TM therefore resulted critical, since it helped reduce its kinetic energy with respect to the spacecraft. In this paper, the TM position and attitude telemetry signals are analysed, and the impacts coefficient of restitution is calculated, providing reference values for similar space instruments, where a free-falling reference body is used (for instance, for geodesy and/or spacecraft navigation).

Nonexpansive and noncontractive mappings on the set of quantum pure states

Wigner's theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In metric geometry, nonexpansive maps and noncontractive maps are well-studied generalizations of isometries. We show that under certain conditions Wigner symmetries can be characterized as nonexpansive or noncontractive maps on the set of all projections of rank one. The assumptions required for such characterizations are injectivity or surjectivity and they differ in the finite and the infinite-dimensional case. Motivated by a recently obtained optimal version of Uhlhorn's generalization of Wigner's theorem, we also give a description of nonexpansive maps which satisfy a condition that is much weaker than surjectivity. Such maps do not need to be Wigner symmetries. The optimality of all presented results is shown by counterexamples.

The photonic content of a transmission-line pulse

We develop a photonic description of short, one-dimensional electromagnetic pulses, specifically in the language of electrical transmission lines. Current practice in quantum technology, using arbitrary waveform generators, can readily produce very short, few-cycle pulses in a very-low-noise, low-temperature setting. We argue that these systems attain the limit of producing pure coherent quantum states, in which the vacuum has been displaced for a short time, and therefore over a short spatial extent. When the pulse is bipolar, that is, the integrated voltage of the pulse is zero, then the state can be described by the finite displacement of a single mode. Therefore there is a definite mean number of photons, but which have neither a well-defined frequency nor position. Due to the Paley-Wiener theorem, the two-component photon "wavefunction" of this mode, while somewhat localized, is not strictly bounded in space even if the vacuum displacement that defines it is bounded. When the pulse is unipolar, no photonic description is possible-the photon number can be considered to be divergent. We consider properties that photon counters and quantum non-demolition detectors must have to optimally convert and detect the photons in several example pulses. We develop a conceptual test system for implementing short-pulse quantum key distribution, building on the design of a recently achieved Bell's theorem test in a cryogenic microwave setup.

Endurance and durability in biodiesel powered engines

The use of fatty acids methyl esters either in mixtures with fossil diesel or in pure state in diesel engines is correlated to a series of technical problems which are to be taken into account in order to not spoil the important environmental and social advantages that this kind of biocombustibles reports. Throughout this work, in agreement with this fundamental premise and on the basis of the technical criteria of durability and resistance that so much affect engines, the most critical aspects of biodiesel use as well as their immediate consequences are introduced. Special emphasis is done on certain phenomena that condition the engine utility life, like the lubricating oil dilution and the deposits formation, as well as the storage and oxidative stability and finally the low temperature behaviour related to engine operation in greater or smaller degree incompatible with biodiesel (fatty acid methyl esters). To sum up, a study in depth will be realized about some of the most problematic aspects referred to biodiesel use, analysing its entire technical dimension and contributing possible solutions. In general, this work tries to be a guide, which allows to identify the most sensible areas within the engine, as well as the suitable means and solutions for the correct use of biodiesel in compression ignition engines (diesel engines).

Generalization of the Schrödinger Equation for Open Systems Based on the Quantum-Statistical Approach

Within the framework of the quantum-statistical approach, utilizing both non-Hermitian Hamiltonian and Lindblad’s jump operators, one can derive various generalizations of the von Neumann equation for reduced density operators, also known as hybrid master equations. If one considers the evolution of pure states only, i.e., disregarding the coherence between states and spontaneous transitions from pure to mixed states, then one can resort to quantum-mechanical equations of the Schrödinger type. We derive them from the hybrid master equations and study their main properties, which indicate that our equations have a larger range of applicability compared to other generalized Schrödinger equations proposed hitherto. Among other features, they can describe not only systems which remain in the stationary eigenstates of the Hamiltonian as time passes, but also those which evolve from those eigenstates. As an example, we consider a simple but important model, a quantum harmonic oscillator driven by both Hamiltonian and non-Hamiltonian terms, and derive its classical limit, which turns out to be the damped harmonic oscillator. Using this model, we demonstrate that the effects of dissipative environments of different types can cancel each other, thus resulting in an effectively dissipation-free classical system. Another discussed phenomenon is whether a non-trivial quantum system can reduce to a classical system in free motion, i.e., without experiencing any classical Newtonian forces. This uncovers a large class of quantum-mechanical non-Hamiltonian systems whose dynamics are not determined by conventional mechanics’ potentials and forces, but rather come about through quantum statistical effects caused by the system’s environment.

Square Root Statistics of Density Matrices and Their Applications.

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures-Hall ensemble, extending known results obtained recently over the Hilbert-Schmidt ensemble.

Comparing two entropy functions of a quantum channel

Inspired by a conjecture related to numerical investigations for a quantum channel in a system of large size, we shall study relations between two different entropies of a quantum channel. One of them is defined by Gour and Wilde as the generalization of quantum relative entropy and maximally mixed state. The second one is defined as the difference between the entropy of the Choi state of the quantum channel and a constant number. At first, we show that the latter entropy is an upper boundary of the former entropy. Moreover, we also give a sufficient and necessary condition that the two entropies are equal. That is, if and only if the relative entropy reaches its supremum on the maximal entangled pure state in the former entropy. At last, to study the difference between the two entropies, we expect to find some quantum channels in which their related entropies do not reach their supremum on the maximal entangled pure states for the former entropy. By calculating the two entropies, we find that amplitude-damping channels are desired examples.

Nonequilibrium Schwinger-Keldysh formalism for density matrix states: Analytic properties and implications in cosmology

Motivated by cosmological Hartle-Hawking and microcanonical density matrix prescriptions for the quantum state of the Universe we develop a Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with the initial density matrix. We build the generating functional of in-in Green’s functions and expectation values for a generic density matrix of the Gaussian type and show that the requirement of particle interpretation selects a distinguished set of positive/negative frequency basis functions of the wave operator of the theory, which is determined by the density matrix parameters. Then we consider a special case of the density matrix determined by the Euclidean path integral of the theory, which in the cosmological context can be considered as a generalization of the no-boundary pure state to the case of the microcanonical ensemble, and show that in view of a special reflection symmetry its Wightman Green’s functions satisfy Kubo-Martin-Schwinger periodicity conditions which hold despite the nonequilibrium and nonstationary nature of the physical setup. Rich analyticity structure in the complex plane of the time variable reveals the combined Euclidean-Lorentzian evolution of the theory, which depending on the properties of the initial density matrix can be interpreted as a decay of a classically forbidden quantum state. Published by the American Physical Society 2024

A Quantum-Like Tensor Compression Sentence Representation Based on Constraint Functions for Semantics Analysis

To emphasize the semantic impact of local semantic and grammatical information among adjacent words in the input text, we establish a constraint functions-based quantum-like tensor compression sentence representation model by integrating the concept of extending the pure state-based density matrix to the mixed-state projection operator in quantum mechanics. The provided model highlights the semantic significance of mixed word associations in the input text, simultaneously reducing the reliance on information derived solely from dictionary statistics. We combine the correlation coefficient with the attention mechanism to establish the correlation coefficient between words. The quantum-like sentence representation based on pure state density matrix is extended to the projection operator of mixed states. Combining the acquisition of maximum in convex optimization, a constraint functions-based quantum-like text representation pruning model is established to reduce redundant information caused by dimensional expansion of tensor operations. The experimental results on SICK-2014, STS-benchmark, and STS-companion show that the provided model is more effective than the mainstream models in mining semantic information, especially more sensitive to the negative semantics of sentences.

Probabilistic state synthesis based on optimal convex approximation

When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the circuit is probabilistically sampled, is able to reduce the approximation error compared to conventional deterministic synthesis. In this paper, we demonstrate that the optimal probabilistic synthesis quadratically reduces the approximation error. Moreover, we show that a deterministic synthesis algorithm can be efficiently converted into a probabilistic one that achieves this quadratic error reduction. We also numerically demonstrate how this conversion reduces the T-count and analytically prove that this conversion halves an information-theoretic lower bound on the circuit size. In order to derive these results, we prove general theorems about the optimal convex approximation of a quantum state. Furthermore, we demonstrate that this theorem can be used to analyze an entanglement measure.

Quantum Fisher information in moving reference frame

In the field of quantum metrology, an important application is quantum parameter estimation. As the fundamental theory of quantum parameter estimation, quantum Cramér-Rao inequality shows that the variance of parameter estimation is determined by the inverse of quantum Fisher information. Higher quantum Fisher information corresponds to a lower variance, thereby improving the precision of parameter estimation. Quantum Fisher information has been extensively investigated in many aspects of non-relativistic quantum mechanics, including entanglement structure detection, quantum teleportation, quantum phase transition, quantum chaos, and quantum computation. However, there are few researches considering the influence of relativistic effect on quantum Fisher information, and therefore, we attempt to investigate this topic in this work. The relativistic transformation of particle states is employed, and the quantum Fisher information about amplitude parameter <inline-formula><tex-math id="M3">\begin{document}$ \theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M3.png"/></alternatives></inline-formula> and phase parameter <inline-formula><tex-math id="M4">\begin{document}$\varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M4.png"/></alternatives></inline-formula> are investigated in moving reference frame. In this work, the parameters to be estimated are encoded into the spin degree of freedom, and the pure single-qubit state and the pure two-qubit state are both considered. The quantum Fisher information about <inline-formula><tex-math id="M5">\begin{document}$ \theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$\varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M6.png"/></alternatives></inline-formula> of single-qubit state and two-qubit state in moving reference frame are numerically calculated, respectively. It can be observed that the quantum Fisher information is associated with rapidity, amplitude parameter, and the ratio of the width to the particle mass <inline-formula><tex-math id="M7">\begin{document}${{{\sigma _r}} \mathord{\left/ {\vphantom {{{\sigma _r}} m}} \right. } m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M7.png"/></alternatives></inline-formula>. The quantum Fisher information of the estimated parameters decreases with rapidity increasing for both single-qubit state and two-qubit state. As rapidity approaches infinity, i.e. increases to the speed of light, the quantum Fisher information reaches to a constant which decreases as the ratio <inline-formula><tex-math id="M8">\begin{document}${{{\sigma _r}} \mathord{\left/ {\vphantom {{{\sigma _r}} m}} \right. } m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M8.png"/></alternatives></inline-formula> increases. More importantly, for the phase parameter <inline-formula><tex-math id="M9">\begin{document}$ \varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M9.png"/></alternatives></inline-formula>, it is observed that the quantum Fisher information of two-qubit state reduces more significantly than that of single-qubit state. While, for the amplitude parameter <inline-formula><tex-math id="M10">\begin{document}$\theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M10.png"/></alternatives></inline-formula>, the quantum Fisher information of two-qubit state is greater than that of single-qubit state. These results are useful and valuable for improving the precision of parameter estimation under the influence of relativistic effect.