Von Neumann Entropy Research Articles

Replenishment Model with Entropic Order Quantity for Deteriorating Items under Inflation

The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.

Quantum entropy‐based hierarchical strategy for inter‐shaft bearing fault detection

To effectively conduct the fault diagnosis of inter-shaft bearings in precision and stability, hierarchical quantum entropy (HQE) method is proposed by absorbing quantum theory into hierarchical entropy, to precisely extract the features of fault signals with strong robustness. Firstly, we investigate HQE method and HQE-based fault diagnosis thought based on quantum theory and hierarchical thought. Then the HQE method is validated by numerical simulation in feature extraction precision and stability (robustness) under the influence of key parameters. The HQE method is applied to the fault diagnosis of inter-shaft bearing based on the test data of four faults (i.e., normal state, inner ring fault, outer ring fault, and rolling ball fault) simulated in birotor experimental rig. As revealed in this study, (1) the HQE method can precisely extract and fully reflect the feature information of vibration signals by regarding the information of full-scale components comprising low- and high-frequency components and a series of bit ground states; (2) the HQE of signals is insensitive and stable against the key parameters (i.e., dimension number and data length), due to more scales acquired by quantum entropy and hierarchical decomposition, which is promising to improve the robustness and stability of fault diagnosis; (3) the proposed HQE possesses high diagnostic accuracy, high efficiency, and robustness under few experiment data, which indicates the good diagnostic performance of HQE method in the fault diagnosis of inter-shaft bearing. The efforts of this study provide a useful way to effectively conduct structural health monitoring besides inter-shaft bearing fault diagnosis.

Quantum and Classical Ergotropy from Relative Entropies.

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.

An oscillator with position-dependent mass exposed to a thermal bosonic bath

In this paper, we present the differential master equation (or Liouville–Von​ Neumann equation) for a harmonic oscillator with position-dependent mass (PDM) exposed to a thermal bosonic bath. Also, we obtain the density matrix of the system after time evolution. Using the density matrix, we consider the Von-Neumann entropy and Fisher Information (FI) as a function of temperature, time, and position. As a witness, we compare our results with an approximate relation for the lower bound of quantum Fisher information (QFI) which recently has been issued. Our work may be useful in quantum metrology.

Relating Entropies of Quantum Channels.

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.

Entropy-Like Properties and Lq-Norms of Hypergeometric Orthogonal Polynomials: Degree Asymptotics

In this work, the spread of hypergeometric orthogonal polynomials (HOPs) along their orthogonality interval is examined by means of the main entropy-like measures of their associated Rakhmanov’s probability density—so, far beyond the standard deviation and its generalizations, the ordinary moments. The Fisher information, the Rényi and Shannon entropies, and their corresponding spreading lengths are analytically expressed in terms of the degree and the parameter(s) of the orthogonality weight function. These entropic quantities are closely related to the gradient functional (Fisher) and the Lq-norms (Rényi, Shannon) of the polynomials. In addition, the degree asymptotics for these entropy-like functionals of the three canonical families of HPOs (i.e., Hermite, Laguerre, and Jacobi polynomials) are given and briefly discussed. Finally, a number of open related issues are identified whose solutions are both physico-mathematically and computationally relevant.

Thermodynamic and vortic structures of real Schur flows

A two-component-two-dimensional coupled with one-component-three-dimensional (2C2Dcw1C3D) flow may also be called a real Schur flow (RSF), as its velocity gradient is uniformly of real Schur form, the latter being the intrinsic local property of any general flows. The thermodynamic and “vortic” fine structures of RSF are exposed and, in particular, the complete set of equations governing a (viscous and/or driven) 2C2Dcw1C3D flow are derived. The Lie invariances of the decomposed vorticity 2-forms of RSFs in d-dimensional Euclidean space Ed for any interger d ≥ 3 are also proven, and many Lie-invariant fine results, such as those of the combinations of the entropic and vortic quantities, including the invariances of the decomposed Ertel potential vorticity (and their multiplications by any interger powers of entropy) 3-forms, then follow.

Real Space-Real Time Evolution of Excitonic States Based on the Bethe-Salpeter Equation Method.

We introduce a method for constructing localized excitations and simulating the real time dynamics of excitons at the Many-Body Perturbation Theory Bethe-Salpeter Equation level. We track, on the femto-seconds scale, electron injection from a photoexcited dye into a semiconducting slab. From the time-dependent many-body wave function we compute the spatial evolution of the electron and of the hole; full electron injection is attained within 5 fs. Time-resolved analysis of the electron density and electron-hole interaction energy hints at a two-step charge transfer mechanism through an intermediary partially injected state. We adopt the Von-Neumann entropy for analyzing how the electron and hole entangle. We find that the excitation of the dye-semiconductor model may be represented by a four-level system and register a decrease in entanglement upon electron injection. At full injection, the electron and the hole exhibit only a small degree of entanglement indicative of pure electron and hole states.

Numerical and experimental simulation of gas-liquid two-phase flow in 90-degree elbow

In the present research, the effects of four 90-degree horizontal elbows with different curvature radii (17, 34, 51, and 68 cm) and an identical rectangular cross-section (20 * 34 mm) on a gas–liquid slug flow pattern have been studied experimentally and numerically. Gas and liquid superficial velocities in numerical and experimental parts were set in 2.5 m/s and 0.44 m/s, respectively. In the computational fluid dynamics section, the distribution of volume fraction, velocity, pressure, turbulence intensity, and swirling intensity parameters were investigated using the VoF model and the SST k-ω method. Experimental studies were conducted utilizing pressure data and signal processing tools to study the dominant frequency of slug flow alongside bandwidth distribution as well as the Shannon entropy. The results exhibited that although the dominant frequency of slug flow did not change after passing the 90-degree elbow, the frequency signal's bandwidth increased. In this regard, the application of Shannon entropy quantity revealed that the frequency distribution signal experienced a greater increase in bandwidth as the elbows’ curvature radius increases. The turbulent intensity of the elbows’ outlet reveals that by increasing the curvature radius, the flow field behaves smoother. Also, swirling intensity distribution shows that decreasing the elbow radius leads to increment in the swirling intensity.

Aberration-corrected ultrafine analysis of miRNA reads at single-base resolution: a k-mer lattice approach.

Raw sequencing reads of miRNAs contain machine-made substitution errors, or even insertions and deletions (indels). Although the error rate can be low at 0.1%, precise rectification of these errors is critically important because isoform variation analysis at single-base resolution such as novel isomiR discovery, editing events understanding, differential expression analysis, or tissue-specific isoform identification is very sensitive to base positions and copy counts of the reads. Existing error correction methods do not work for miRNA sequencing data attributed to miRNAs’ length and per-read-coverage properties distinct from DNA or mRNA sequencing reads. We present a novel lattice structure combining kmers, (k – 1)mers and (k + 1)mers to address this problem. The method is particularly effective for the correction of indel errors. Extensive tests on datasets having known ground truth of errors demonstrate that the method is able to remove almost all of the errors, without introducing any new error, to improve the data quality from every-50-reads containing one error to every-1300-reads containing one error. Studies on experimental miRNA sequencing datasets show that the errors are often rectified at the 5′ ends and the seed regions of the reads, and that there are remarkable changes after the correction in miRNA isoform abundance, volume of singleton reads, overall entropy, isomiR families, tissue-specific miRNAs, and rare-miRNA quantities.

Witnessing negative conditional entropy

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.

Quantum corrections to the entropy in a driven quantum Brownian motion model

The quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. We obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy in the weak coupling limit. Moreover, we find that for the thermodynamic equilibrium initial state, all terms odd in ℏ are exactly zero. Our results bring important insights to the understanding of entropy in open quantum systems.

Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems

We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient features of localization, despite not being a proper entanglement measure. We numerically show that the OPDM entropy of the eigenstates obeys an area law. Similar to the von-Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well towards the transition into the ergodic phase. The computational cost to calculate the OPDM entropy scales only polynomially with the system size, suggesting that the OPDM provides a promising starting point for developing diagnostic tools for MBL in simulations and experiments.

Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches.

Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.

Spatial Entanglement of Fermions in One-Dimensional Quantum Dots.

The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree–Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible.

Schmidt decomposition analysis of normal- to local-mode transition in highly excited molecular vibration

The stretch vibrations SO2 are studied by the Schmidt decomposition focusing on the normal- to local-mode transition that takes place in the highly excited vibrational states. The von Neumann entropy is calculated from the eigenvalues of the reduced density matrices for the level sequences having excitations into the symmetric-stretch mode. The entropy shows significant increase as the typical trend, while those sequences with an even number of nonzero quanta in the antisymmetric-stretch mode show temporal decrease prior to the appearance of the local-mode bifurcation. The observed trends are rationalized on the basis of complexity or non-separability of the wave functions.

Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits

AbstractUsing the type-I SPDC process in BBO nonlinear crystal, we generate a polarization-entangled state near to the maximally-entangled Bell-state with high-visibility (high-brightness) 98.50 ± 1.33% (87.71 ± 4.45%) for HV (DA) basis. We calculate the CHSH version of the Bell inequality, as a nonlocal realism test, and find a strong violation from the classical physics or any hidden variable theory, S = 2.71 ± 0.10. Via measuring the coincidence count rate in the SPDC process, we obtain the quantum efficiency of single-photon detectors around (25.5 ± 3.4)%, which is in good agreement to their manufacturer company. As expected, we verify the linear dependency of the CC rate vs. pump power of input CW-laser, which may yield to find the effective second-order susceptibility crystal. Using the theory of the measurement of qubits, includes a tomographic reconstruction of quantum states due to the linear set of 16 polarization-measurement, together with a maximum-likelihood-technique, which is based on the numerical optimization, we calculate the physical non-negative definite density matrices, which implies on the non-separability and entanglement of prepared state. By having the maximum likelihood density operator, we calculate precisely the entanglement measures such as Concurrence, entanglement of formation, tangle, logarithmic negativity, and different entanglement entropies such as linear entropy, Von-Neumann entropy, and Renyi 2-entropy. Finally, this high-brightness and low-rate entangled photons source can be used for short-range quantum measurements in the Lab.

Fast and compact VCSEL-based quantum random number generator

Random number generators (RNGs) are an essential ingredient of modern cryptographic systems. Particular attention is paid today to a special class of RNGs – quantum RNGs, which are attracting close attention of researchers due to the explosive development of quantum key distribution systems, where the use of quantum randomness is a necessary security requirement. A large number of various quantum entropy sources have been proposed over the last 10-15 years. Most of them are based on the use of different quantum optics phenomena, particularly, on the effects occurring in semiconductor lasers. This choice is due to the relatively low cost and ease of use of such devices and the high random bit generation rate available with optical QRNGs. Motivated by these reasons, we study in the present research the QRNG based on variations of light polarization in a vertical-cavity surface-emitting laser (VCSEL). The scheme we propose allows creating an extremely compact and fast optical QRNG, consisting essentially of only a laser and a polarizing beam splitter. We revealed that it is possible to ensure the pulsed operation of a VCSEL in a bistable regime, which is characterized by random switch of light polarization. We show, however, that probabilistic properties of such laser pulses significantly depend on the internal laser parameters as well as on its operating mode. Understanding these properties is fundamentally important for the correct assessment of the quantum noise contribution and, consequently, for the subsequent post-processing of digitized random sequences.

The effect of GUP on thermodynamic phase transition of Rutz-Schwarzschild black hole

In this paper, considering the influence of generalized uncertainty principle, we explore phase transitions of the Rutz-Schwarzschild black hole based on the Parikh-Wilczek tunneling method. First, we obtain the corrected Hawking temperature, local temperature, remnant of black hole, entropy, heat capacity and other thermodynamic quantities. Then, we analyzed the effects of generalized uncertainty parameter β on phase transition. And we investigate thermodynamic stability, the critical behavior and phase transition structure under the influence of generalized uncertainty principle at last. The results show that there are first-order and second-order phase transitions in the Rutz-Schwarzschild black hole of the Finsler genometry framework. In addition, the generalized uncertainty parameter has great influence on the generation of black hole remnant.

Entropy of Badminton Strike Positions.

The aim of the current study was twofold: (i) to investigate the distribution of the strike positions of badminton players while quantifying the corresponding standard entropy and using an alternative metric (spatial entropy) related to winning and losing points and random positions; and (ii) to evaluate the standard entropy of the receiving positions. With the datasets of 259 badminton matches, we focused on the positions of players’ strokes and the outcome of each point. First, we identified those regions of the court from which hits were most likely to be struck. Second, we computed the standard entropy of stroke positions, and then the spatial entropy, which also considers the order and clustering of the hitting locations in a two-dimensional Euclidean space. Both entropy quantifiers revealed high uncertainty in the striking position; however, specific court locations (i.e., the four corners) are preferred over the rest. When the outcome of each point was taken into account, we observed that the hitting patterns with lower entropy were associated with higher probabilities of winning points. On the contrary, players striking from more random positions were more prone to losing the points.