Pure State Research Articles

State-dependent and state-independent uncertainty relations for skew information and standard deviation

In this work, we derive state-dependent uncertainty relations (uncertainty equalities) in which commutators of incompatible operators (not necessarily Hermitian) are explicitly present and state-independent uncertainty relations based on the Wigner-Yanase (-Dyson) skew information. We derive uncertainty equality based on standard deviation for incompatible operators with mixed states, a generalization of previous works in which only pure states were considered. We show that for pure states, the Wigner-Yanase skew information based state-independent uncertainty relations become standard deviation based state-independent uncertainty relations which turn out to be tighter uncertainty relations for some cases than the ones given in previous works, and we generalize the previous works for arbitrary operators. As the Wigner-Yanase skew information of a quantum channel can be considered as a measure of quantum coherence of a density operator with respect to that channel, we show that there exists a state-independent uncertainty relation for the coherence measures of the density operator with respect to a collection of different channels. We show that state-dependent and state-independent uncertainty relations based on a more general version of skew information called generalized skew information which includes the Wigner-Yanase (-Dyson) skew information and the Fisher information as special cases hold. In qubits, we derive tighter state-independent uncertainty inequalities for different form of generalized skew informations and standard deviations, and state-independent uncertainty equalities involving generalized skew informations and standard deviations of spin operators along three orthogonal directions. Finally, we provide a scheme to determine the Wigner-Yanase (-Dyson) skew information of an unknown observable which can be performed in experiment using the notion of weak values.

The Medical Professional Elimination Program and the Ideology and Motivation of Nazi Physicians

The appointment of a new chancellor in 1933 marked the beginning of the Third Reich in Germany. The ideology of the Nazi Party focused on establishing a pure Aryan state characterized by nationalism and racial superiority. Their goals would be achieved through a totalitarian form of government that enforced the subjugation, exclusion, and elimination of those they defined as inferior minorities, particularly Jews, who were depicted as non-human. Implementation of the Nazi ideology required the exclusion of Jewish people and other dissenters, particularly Jewish physicians, from their professions. The exclusion of Jewish physicians, referred to herein as a “Medical Professional Elimination Program,” was gradually imposed on other Jewish professions in nations absorbed by the Third Reich, and particularly enforced by incorporated Austria. Why did German and Austrian doctors support the Nazi racial ideology, the removal of Jewish physicians from every possible sphere of influence, and subsequently participate in criminal medical research and experimentation, as well as euthanasia of perceived non-contributors to society, and become involved in refining the effectiveness of the death camps? Was the Medical Professional Elimination Program an opportunistic political concept, or was it part of an entrenched ideology? With these questions in mind, the lives of four key Nazi physicians and two institutions are examined.

Multiqubit quantum state preparation enabled by topology optimization

Using topology optimization, we inverse-design nanophotonic cavities enabling the preparation of pure states of pairs and triples of quantum emitters. Our devices involve moderate values of the dielectric constant, operate under continuous laser driving, and yield fidelities to the target (Bell and W) states approaching unity for distant qubits (several natural wavelengths apart). In the fidelity optimization procedure, our algorithm generates entanglement by maximizing the dissipative coupling between the emitters, which allows the formation of multipartite pure steady states in the driven-dissipative dynamics of the system. Our findings open the way toward the efficient and fast preparation of multiqubit quantum states with engineered features, with potential applications for nonclassical light generation, and quantum sensing and metrology.

Using linear and nonlinear entanglement witnesses to generate and detect bound entangled states on an IBM quantum processor

Abstract We investigate bound entanglement in three-qubit mixed states which are diagonal in the Greenberger-Horne-Zeilinger (GHZ) basis. Entanglement in these states is detected using entanglement witnesses and the analysis focuses on states exhibiting positive partial transpose (PPT). We then compare the detection capabilities of optimal linear and nonlinear entanglement witnesses. In theory, both linear and nonlinear witnesses produce non-negative values for separable states and negative values for some entangled GHZ diagonal states with PPT, indicating the presence of entanglement. Our experimental results reveal that in cases where linear entanglement witnesses fail to detect entanglement, nonlinear witnesses are consistently able to identify its presence. Optimal linear and nonlinear witnesses were generated on an IBM quantum computer and their performance was evaluated using two bound entangled states (Kay and Kye states) from the literature, and randomly generated entangled states in the GHZ diagonal form. Additionally, we propose a general quantum circuit for generating a three-qubit GHZ diagonal mixed state using a six-qubit pure state on the IBM quantum processor. We experimentally implemented the circuit to obtain expectation values for three-qubit mixed states and compute the corresponding entanglement witnesses.

Extracting dynamical maps of non-Markovian open quantum systems.

The most general description of quantum evolution up to a time τ is a completely positive tracing preserving map known as a dynamical mapΛ̂(τ). Here, we consider Λ̂(τ) arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales, Λ̂(τ) is generically expected to be non-Markovian; however, we do assume the ensuing dynamics has a unique steady state, implying the baths possess a finite memory time τm. By combining several techniques within a tensor network framework, we directly and accurately extract Λ̂(τ) for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. First, we use an orthogonal polynomial mapping and thermofield doubling to arrive at a purified chain representation of the baths whose length directly equates to a time over which the dynamics of the infinite baths is faithfully captured. Second, we employ the Choi-Jamiolkowski isomorphism so that Λ̂(τ) can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxiliary modes up to time τ. From Λ̂(τ), we also compute the time local propagator L̂(τ). By examining the convergence with τ of the instantaneous fixed points of these objects, we establish their respective memory times τmΛ and τmL. Beyond these times, the propagator L̂(τ) and dynamical map Λ̂(τ) accurately describe all the subsequent long-time relaxation dynamics up to stationarity. These timescales form a hierarchy τmL≤τmΛ≤τre, where τre is a characteristic relaxation time of the dynamics. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where τre ≫ τm, where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit. Our results also show that having access to Λ̂(τ) affords a number of insightful analyses of the open system thus far not commonly exploited.

Pour Point Depression of Waxy Crude Oil Using Unmodified African Pear (Dacryodes edulis) Seed Oil

The pour point depression of a Nigeria waxy crude oil was investigated using unmodified African pear seed oil. Crude oil sample collected from a marginal field in Delta state was analyzed for its physiochemical parameters such as; specific gravity, API, kinematic viscosity, pour point and wax content. African pear seeds sourced from choba Port Harcourt were extracted of their oil content and the oil was analyzed for some oil quality parameters such as; free fatty acid (FFA), acid value, saponification value and iodine value. The results showed a crude oil of high wax content and extracted oil of low FFA and high saponification and iodine values. The waxy crude oil was dosed with the unmodified African pear seed oil of concentrations 0.1ml, 0.2ml and 0.3 ml. The result showed no reduction in the pour point of the crude oil at all concentrations. Therefore the African pear seed oil cannot be used as a pour point depressant in its pure state.

The quantum uncertainty relation for skew information of coherence

Abstract The quantum uncertainty relation characterizes the restriction of the quantum coherence on different measurement bases. The skew information of coherence is a coherence measure both operationally and informatically. We study the quantum uncertainty relation for the skew information of coherence under any two orthonormal bases. In qubit and qutrit systems, we derive the quantum uncertainty relations with the lower bounds in the factorized forms by the purity of quantum states and the incompatibility between two orthonormal bases. Especially the lower bound in qubit systems is strictly positive for non-maximally mixed states and incompatible orthonormal bases. These quantum uncertainty relations reveal the intrinsic relation among the coherence, the purity and the incompataibility between two orthonormal bases quantitatively. The advantages of these quantum uncertainty relations are illustrated by some specific examples. This method we developed here is beneficial to some other quantum uncertainty relations.

Universal Time-Entanglement Trade-Off in Open Quantum Systems

We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B, interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024

Thermal experiment study on the self-luminous properties of metallic iron during solid–liquid phase transition

According to the thermal experiment study of the self-luminescence spectrum of industrially pure iron (DT8) at a heating and cooling rate of 5 °C/min, at the moment of 0 (800 °C), DT8 had no significant self-luminescence characteristics in the wavelength range of 200–1100 nm. At the same time, the first-order differentiation of the spectral intensity versus time was equal to zero at the beginning and end moments of the solid-liquid phase transition. When the solid-liquid melt temperatures are equal (i.e. 1531 °C), there are two sharp peaks at wavelengths of 589.1 nm and 766.7 nm of the self-luminous spectrum in the pure liquid state compared to the self-luminous spectrum in the pure solid state. The intensity of the spectrum decreases significantly as the metallic iron changes from the pure solid phase to the pure liquid phase, with a reduction rate greater than 20%. The appearance of the fitted peaks at 589.1 nm and 769 nm was found by XPS fitting analysis to be a significant feature of the difference in the auto-luminescence spectra of pure solid phase and pure liquid phase metallic iron at a constant melt pool temperature. After the transformation of pure solid phase into pure liquid phase, the decay rate of the self-luminous spectrum in the long-wave direction at wavelengths greater than 762 nm is greater than that in the short-wave direction at wavelengths less than 625 nm.

Novel eco-friendly HPTLC method using dual-wavelength detection for simultaneous quantification of duloxetine and tadalafil with greenness evaluation and application in human plasma

A novel, environmentally friendly, and sensitive HPTLC method has been developed and validated for simultaneous quantification of duloxetine (DLX) and tadalafil (TDL) in their pure state, laboratory-prepared mixtures, and spiked human plasma. This method is particularly important for patients dealing with depression and sexual issues, as it allows for the measurement of these co-administered antidepressant and sexual stimulant drugs in biological fluids. The separation process employed a stationary phase of pre-coated silica gel 60 F254 and a mobile phase consisting of ethyl acetate, acetonitrile, and 33% ammonia (8:1:1, v/v). The optimized mobile phase resulted in well-defined bands for DLX and TDL, with Rf values of 0.3 and 0.8, respectively with dual-wavelength detection at 232 nm for DLX and 222 nm for TDL. Polynomial regression analysis revealed exceptional linearity for both drugs, with correlation coefficients of 0.9999 over concentration ranges of 10–900 ng/band for DLX and 10-1200 ng/band for TDL. The quantitation limits were 8.2 ng/band for DLX and 8.6 ng/band for TDL, while the detection limits (LOD) were 2.7 ng/band for DLX and 2.8 ng/band for TDL. The validation of this method followed the guidelines set by the International Council for Harmonization (ICH). Additionally, the suggested method’s greenness was assessed by means of four up-to-date ecological tools, namely the Eco-Scale, the National Environmental Method Index (NEMI), the Green Analytical Procedure Index (GAPI), and the Analytical Greenness metric approach (AGREE). The proposed method was also assessed using the Blue Applicability Grade Index (BAGI), a recently developed metric for assessing the practicality (blueness) of procedures.

The Effects of Loading Angles on the Failure of Cross-Ply Notched Bio-Basalt Composites

A cross-ply basalt V-notched butterfly specimens were subjected to pure tension, combined tension-shear, and shear stress-strain state using a modified Arcan test fixture with loading angles from 0° to 90° with 15° increment. Multiaxial stress and strain states were studied using the principal stress and strain ratio, from which the principal angle was determined and used to represent principal states in the gauge section. The quasi-elastic to non-linear transition stresses were determined for each loading angle. In biaxial stress-strain states and pure shear, the deformation and consequently the shear-induced damage start to accumulate significantly. Also, in biaxial stress-strain states between 15°-75°, the shift from tension-shear to pure shear was observed after the transition to the non-linear part of the stress-strain curve. The digital image correlation (DIC) images and microscopic evaluation show that a large extent of damage is the consequence of the shear deformation after the rotation of 0° clamped fibres, while the 90° fibres maintained their original straight form. In off-axis tests, the principal strain axis rotates towards the weakest material axis even at small off-axis angles. This causes a transition from a tension-shear biaxial state in the linear loading part to shear in the non-linear part, leading to irreversible damage beyond the transition point.

Quantum state tomography with locally purified density operators and local measurements

Understanding quantum systems is of significant importance for assessing the performance of quantum hardware and software, as well as exploring quantum control and quantum sensing. An efficient representation of quantum states enables realizing quantum state tomography with minimal measurements. In this study, we propose an alternative approach to state tomography that uses tensor network representations of mixed states through locally purified density operators and employs a classical data postprocessing algorithm requiring only local measurements. Through numerical simulations of one-dimensional pure and mixed states and two-dimensional pure states up to size 8 × 8, we demonstrate the efficiency, accuracy, and robustness of our proposed methods. Experiments on the IBM and Quafu Quantum platforms complement these numerical simulations. Our study opens avenues in quantum state tomography for two-dimensional systems using tensor network formalism.

Relation of acrylic acid polymerization behavior in deep eutectic solvent to water content: Computer simulation and experiment

Polymerizable deep eutectic solvents (DES) are promising starting materials for preparation of eutectogels and hydrogels that can be applied in drug delivery, as strain sensors and various components of soft electronics. However, the understanding of relationship between the molecular structure, physicochemical properties and polymerization behavior of such systems in pure state and in their mixtures with water is not well studied yet. In this work we report the results of both computer simulation and experimental investigations for polymerizable choline chloride/acrylic acid DES and its mixtures with water. Molecular dynamics was applied to reveal the influence of water on the structure of polymerizable DES at the molecular and supramolecular levels. The diffusion coefficients of DES components with different water content were measured using NMR. The course of photoinduced polymerization of DES/water mixtures was traced using FTIR spectroscopy, while the molar mass and hydrodynamic characteristics of obtained polyacrylic acid were studied by means of static and dynamic light scattering. It was found that addition of water leads to a gradual decrease in size of the acrylic acid clusters that exist in pure DES and is accompanied by an increase in orientation mobility and diffusion coefficients of components. The maximal molar mass was obtained for the polymer prepared by polymerization of DES with 5 wt% of water. This can be attributed to the optimal combination of acrylic acid clusters size and increased mobility of components.

Information theoretic measures for Lifshitz system

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in 3 + 1-dimensions. This geometry is the gravity dual to a class of 2 + 1-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent (z) present in the Lifshitz field theory.

Quantum Rabin oblivious transfer using two pure states

Oblivious transfer between two untrusting parties is an important primitive in cryptography. There are different variants of oblivious transfer. In Rabin oblivious transfer, the sender Alice holds a bit, and the receiver Bob either obtains the bit, or obtains no information with probability p?. Alice should not know whether or not Bob obtained the bit. We examine a quantum Rabin oblivious transfer (OT) protocol that uses two pure states. Investigating different cheating scenarios for the sender and for the receiver, we determine optimal cheating probabilities in each case. Comparing the quantum Rabin oblivious transfer protocol to classical Rabin oblivious transfer protocols, we show that the quantum protocol outperforms classical protocols, which do not use a third party, for some values of p?. We find that quantum Rabin OT protocols that use mixed states can outperform quantum Rabin OT protocols that use pure states for some values of p?. Published by the American Physical Society 2024

A novel multifunctional naphthalene triazole columnar liquid crystal: synthesis, self-assembly and application in silicon solar cells

Herein, click reaction was used as a crucial step to effectively synthesize a new multifunctional naphthalene triazole columnar liquid crystal ICm/n. The properties of liquid crystal and gel in ICm/n were investigated using POM, DSC, XRD and SEM. ICm/n can self-assemble into square columnar liquid crystals in their pure state and form organogels in N,N-dimethylformamide (DMF). In addition, ICm/n can be used as a Fe3+ chemosensor. Interestingly, the addition of lithium salts has a significant impact on the self-assembly, molecular dynamics and ionic conductivity of the compounds, thus potentially providing nanostructured LC electrolytes with continuous substrate ionic conductivity. Additionally, the use of ICm/n as a dopant in the poly (3,4-ethylenedioxythiophene): polystyrene (PEDOT: PSS) hole injection layer greatly enhanced the photoelectric conversion efficiency (PCE) of Si/PEDOT: PSS heterojunction solar cells, boosting it from 2.08 % to 8.10 %. The current work offers a novel method for creating liquid crystal (LC) materials with several uses for naphthalene triazoles.

Two novel pure-state coherence measures in quantifying coherence

Quantification is one of the primary goals of quantum coherence resource theory. Here, we put forward two coherence measures, analytically prove their validity in the pure-state regime following the axiomatic definition of a legitimate pure-state coherence measure (PSCM), and provide their general normalized forms. We further discuss their extensions in the domain of mixed states with the assistance of the convex roof of coherence, and top coherence (quantification in terms of pure state coherence) and define their classes (coherence \emph{monotone} or \emph{measure}); in this regard, we thoroughly investigate the top coherence class. For the quantitative demonstration, we pick up different laser pulse-two-qubit interaction scenarios and compare the evolutions of these two coherence measures along with \(l_{1}\)-norm of coherence and relative entropy of coherence; this study also signifies the importance of coherence in probing an atomic or molecular system.

A new class of distances on complex projective spaces

The complex projective space P(Cn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the ‘earth mover problem’. We show that this construction leads to a quantity satisfying the triangle inequality, which yields a true distance on complex projective space belonging to the family of quantum 2-Wasserstein distances.

Azo Coupling Reaction for Spectrophotometric Determination of Sulfanilamide Using β -Naphthol as a Reagent

This research is based on one simple and good method for determining sulfanilamide in its pure state and in pharmaceutical preparations. Spectrophotometric determination of Sulfanilamide using the azo coupling reaction in an aqueous solution and several standard solutions were prepared. The optimal conditions were also studied. The effects of the type of acid and its volume, the influence of the base type and its volume, the effect of reagent volume (100 µg/ml), the effect of reaction time on the color stability of the product, the effect of adding sequence, the solvent effect, and the effect of temperature on the formation and stability of the colored product. The product for the Sulfanilamide drug is auburn at a wavelength of 489 nm; the method obeyed Beer's law in a range of concentrations ranging from 1–12 µg/ml; and the molar absorptivity was 28840.76 L/mol.cm. Sandal's sensitivity (0.00091 μg/cm), detection limit (0.2472 µg/ml), correlation coefficient value 0.9984, and RSD% value 0.01365, By applying the method to a pharmaceutical preparation containing Sulfanilamide, the recovery value ranged between 102.1306%.

One sided sequential sharing of tripartite nonlocality for pure and mixed three-qubit states

One sided sequential sharing of tripartite nonlocality for pure and mixed three-qubit states