Quantification of Entanglement Entropy in Helium by the Schmidt–Slater Decomposition Method

In this work, we present an investigation on the spatial entanglement entropies in the helium atom by using highly correlated Hylleraas functions to represent the S-wave states. Singlet-spin 1sns ¹ S ^e states (with n = 1 to 6) and triplet-spin 1sns ³ S ^e states (with n = 2 to 6) are investigated. As a measure on the spatial entanglement, von Neumann entropy and linear entropy are calculated. Furthermore, we apply the Schmidt–Slater decomposition method on the two-electron wave functions, and obtain eigenvalues of the one-particle reduced density matrix, from which the linear entropy and von Neumann entropy can be determined.     

Differential Entropy and Dynamics of Uncertainty

We analyze the functioning of Gibbs-type entropy functionals in the time domain, with emphasis on Shannon and Kullback-Leibler entropies of time-dependent continuous probability distributions. The Shannon entropy validity is extended to probability distributions inferred from L ²(R ⁿ ) quantum wave packets. In contrast to the von Neumann entropy which simply vanishes on pure states, the differential entropy quantifies the degree of probability (de)localization and its time development. The associated dynamics of the Fisher information functional quantifies nontrivial power transfer processes in the mean, both in dissipative and quantum mechanical cases. PACS NUMBERS: 05.45.+b, 02.50.-r, 03.65.Ta, 03.67.-a     

Perturbation theory of von Neumann entropy

In quantum information theory, von Neumann entropy plays an important role; it is related to quantum channel capacities. Only for a few states can one obtain their entropies. In a continuous variable system, numeric evaluation of entropy is not easy due to infinite dimensions. We develop the perturbation theory for systematically calculating von Neumann entropy of a non-degenerate system as well as a degenerate system.     

Entropy of Quantum States

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to its possible decompositions into pure states, we give a purely algebraic definition of entropy for states of an algebra of observables, thus solving the above ambiguity. The entropy so-defined satisfies all the desirable thermodynamic properties and reduces to the von Neumann entropy in the quantum mechanical case. Moreover, it can be shown to be equal to the von Neumann entropy of the unique representative density matrix belonging to the operator algebra of a multiplicity-free Hilbert-space representation.     

A New Inequality for the von Neumann Entropy

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of strong subadditivity: it is an inequality which is true for any four party quantum state, provided that it satisfies three linear relations (constraints) on the entropies of certain reduced states.     

Uniform Estimates on the Tsallis Entropies

By means of a probabilistic coupling technique, we establish some tight upper bounds on the variations of the Tsallis entropies in terms of the uniform distance. We treat both classical and quantum cases. The results provide some quantitative characterizations of the uniform continuity and stability properties of the Tsallis entropies. As direct consequences, we obtain the corresponding results for the Shannon entropy and the von Neumann entropy, which are stronger than the conventional ones.      

两格点两电子Hubbard-Holstein模型极化子的量子纠缠特性

本文利用相干态正交化展开方法, 对两格点两电子Hubbard-Holstein极化子模型的能谱以及动力学特性进行了精确求解. 讨论了耦合强度g、平均声子数n以及电子 初态对纠缠演化特性及系统冯诺依曼熵的影响. 数值计算结果表明: 1)纠缠度随时间的演化呈现出良好的周期性, 当其他的参数固定时, 演化周期随耦合强度g增大逐渐减小, 与平均声子数n无关; 2)系统冯诺依曼熵同电子状态占有率表现出严格的同步演化特性; (3) 在弱耦合强度和低平均声子数下, 初始电子态c_2↑⁺ c_2↓⁺|O>_e或c_1↑⁺ c_1↓⁺ |O>_e较c_1↑⁺c_2↓⁺—c_1↓⁺ c_2↑⁺具有更大的最大冯诺依曼熵, 并随耦合强度增大、平均声子数的增加而逐渐接近.     

Distribution of Mutual Information in Multipartite States

Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations.     

Laser Desorption Mass Spectrometry of Some Organic Acids

Abstract

Positive and negative ion laser desorption (LD) mass spectra of organic acids are characterized by the emission of the quasimolecular ions (M+H)⁺ and (M-H)^?. Generation of (M+H)⁺ ions is interpreted as evidence for the occurence of high pressure proton transfer reactions in LD. Fragment ions can be rationalized by loss of stable neutral molecules from quasimolecular ions although decomposition may also be occuring prior to ionization. Features unique to LD, including the detection of pyrolysis products along with ions characteristic of the sample, are discussed in terms of the internal energy distribution in the irradiated microvolume. Negative ion mass spectra of acids are dominated by (M-H)^?, while positive ion spectra contain abundant fragment ions, underlining the utility of detecting negative ions for acidic compounds.     

Notes on entropic characteristics of quantum channels

One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss a few channel characteristics expressed by means of generalized entropies. Such characteristics can often be treated in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the q-average output entropy of degree q ≥ 1 is bounded from above by the q-entropy of the input density matrix. The concavity properties of the (q, s)-entropy exchange are considered. Fano type quantum bounds on the (q, s)-entropy exchange are derived. We also give upper bounds on the map (q, s)-entropies in terms of the output entropy, corresponding to the completely mixed input.     

The effect of atomic motion and two-quanta JCM on the information entropy

We study the interaction between a moving two-level atom and a single-mode field. The coupled atom-cavity system with atomic center-of-mass motion included is modeled by considering the dependence of the atomic motion along z-axis. At exact resonance between the internal atomic transition and the cavity eigenfrequency, an exact solution of the system is obtained and periodically modulated Rabi oscillations and regular translational motion are observed. We focused on the dynamics of both field Wehrl entropy and Wehrl phase distribution. The influence of the atomic motion on the evolution of von Neumann entropy and Wehrl entropy is examined. The results show that the atomic motion and the field-mode structure play important roles in the evolution of the von Neumann entropy, Wehrl entropy and Wehrl PD.     

Entropy scaling and simulability by matrix product states

We investigate the relation between the scaling of block entropies and the efficient simulability by matrix product states (MPSs) and clarify the connection both for von Neumann and Rényi entropies. Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPSs. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian.     

Sheath characteristics in multi-component plasma with negative ions

Properties of steady state ion sheath formed in front of a negatively biased metal plate under the influence of negative ions have been investigated in collisionless argon/SF₆ plasma. This experiment is carried out at a fixed discharge voltage and fixed filament heating power. In this experiment, the decrement in plasma pre-sheath potential drop as well as positive ion drift velocity toward the plate is experimentally recorded in the presence of negative ions. It is also found that the plasma positive ion density and plasma electron temperature decrease in the presence of negative ions. These factors attribute to the decrease of ion current toward the plate. Hence the usual ion sheath expands. Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Correlation Effects in the Moshinsky Model

We investigate quantum correlations in the ground state of the Moshinsky model formed by N harmonically interacting particles confined in a harmonic potential. The model is solvable which allows an exact determination of entanglement between the subset of p particles and the remaining N ? p particles. We study linear entropies and von Neumann entropies of the bipartitions and compare their behavior with that of the relative correlation energy and of the statistical Kutzelnigg coefficient.     

Quantum Entanglement and Normal-to-Local Transition in Molecule H2

Quantum entanglement of two stretches in molecule H2S is investigated for various initial states in terms of the reduced-density yon Neumann entropy and the mean entropy defined by average over time. It is shown that the maximal and the mean entropies of an initial state with local-mode character are smaller than those with normal-mode character, and the mean entropy displays a maximum near the position of the normal-to-local transition.     

Entanglement Entropies in the Ground States of Helium-Like Atoms

We examine the entanglement in the ground states of helium and helium-like ions using an original Hylleraas expansion. The von Neumann and linear entropies of the reduced density matrix are accurately computed by performing the Schmidt decomposition of the S singlet spatial wavefunctions. The results presented are more accurate than currently available in published literature.     

The entropy of entangled three-level atoms interacting with entangled cavity fields: Entanglement swapping

The dynamics of an entangled atomic system, partially interacting with entangled cavity fields and characterizing an entanglement swapping, has been studied through their von Neumann entropies. The aforementioned interaction is implemented via a two-photon process, given by either the full microscopical Hamiltonian approach or the two-photon Jaynes-Cummings model. Numerical simulations furnish the explicit expressions for each sub-system entropy, which allow us to estimate the multiperiodicity in the evolution of the entangled atom-field system. The effects of the detuning parameter upon the period and the amplitude of the entropies are also discussed as well as the power spectrum of the entropy.     

Some Aspects of Quantum Entanglement for CAR Systems

We show some distinct features of quantum entanglement for bipartite CAR systems such as the failure of triangle inequality of von Neumann entropy and the possible change of our entanglement degree under local operations. Those are due to the nonindependence of CAR systems and never occur in any algebraic independent systems. We introduce a new notion half-sided entanglement.     

Real and spurious contributions for the Shannon, Rényi and Tsallis entropies

A two-parameter probability distribution is constructed by dilatation (or contraction) of the escort probability distribution. This transformation involves a physical probability distribution P associated with the system under study and an almost arbitrary reference probability distribution P^′. In contrast to the Shannon and Rényi entropies, the Tsallis entropy does not decompose as the sum of the physical contribution due to P and the reference or spurious part owing to P^′. For solving this problem, a slight modification to the relation between Tsallis and Rényi entropies must be introduced. The procedure in this paper gives rise to a nonconventional one-parameter Shannon entropy and to two-parameter Rényi and Tsallis entropies associated with P. It also contributes to clarify the meaning and role of the escort probabilities set.     

Spin Entropy

Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states.