Quantum Gaussian memory channels

We study the information transmission through two different models of Gaussian memory channels: an additive Gaussian channel and a lossy bosonic memory channel. We then show that entangled inputs can enhance the transmission rate in such channels. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 390–404, August, 2007.     

Metric adjusted skew information and uncertainty relation

We show that an uncertainty relation for Wigner-Yanase-Dyson skew information proved by Yanagi (2010) [10] can hold for an arbitrary quantum Fisher information under some conditions. This is a refinement of the result of Gibilisco and Isola (2011) [4].     

A note on a generalization of the Luo's uncertainty relation

We give the trace inequalities as a generalization of the uncertainty relation improved by S. Luo. These inequalities are refinements of the trace inequality conjectured by Furuichi et al.     

Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case

We show that in contrast to a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. We consider an approximation based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the second-order term. To escape technical difficulties related to the infinite dimensionality of the phase space for quantum mechanics, we consider finite-dimensional quantum mechanics. On one hand, this is a simple example with high pedagogical value. On the other hand, quantum information operates in a finite-dimensional state space. Therefore, our investigation can be considered a construction of a classical statistical model for quantum information. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 278–291, August, 2007.     

Quantum teleportation

In the framework of an algebraic approach, we consider a quantum teleportation procedure. It turns out that using the quantum measurement nonlocality hypothesis is unnecessary for describing this procedure. We study the question of what material objects are information carriers for quantum teleportation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 79–98, October, 2008.     

Trace inequalities on a generalized Wigner-Yanase skew information

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S. Luo for the quantum uncertainty quantity excluding the classical mixture. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued.     

Sharper uncertainty principles in quaternionic Hilbert spaces

The uncertainty principle for quaternionic linear operators in quaternionic Hilbert spaces is established, which generalizes the result of Goh-Micchelli. It turns out that there appears an additional term given by a commutator that reflects the feature of quaternions. The result is further strengthened when one operator is self-adjoint, which extends under weaker conditions the uncertainty principle of Dang-Deng-Qian from complex numbers to quaternions. In particular, our results are applied to concrete settings related to quaternionic Fock spaces, quaternionic periodic functions, quaternion Fourier transforms, quaternion linear canonical transforms, and nonharmonic quaternion Fourier transforms.     

Existence of uncertainty minimizers for the continuous wavelet transform

Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time-scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.     

量子环面上斜导子李代数的表示

记L为量子环面上的斜导子李代数，本文构造了一族从sl2-模到L-模的函子F^αg，并对L-模F^αg（V）的结构进行了完全刻画，最后给出了L-模F^αg1（V）与F^βg2（W）同构的充分必要条件。     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

Stronger uncertainty principles for hypercomplex signals

In this paper, for real para-vector-valued signals, we obtain stronger uncertainty principles in terms of covariance and absolute covariance based on Fourier transform in both directional and the spatial cases. We provide certain conditions that give rise to the equal relation between the two uncertainty principles. Examples are presented to verify the results.     

基于异质预期的量子伯川德博弈复杂动力机制分析

针对伯川德双寡头垄断博弈经济系统中出现的混沌现象,利用量子博弈论,构建了基于有限理性与天真预期行为的量子伯川德动态博弈模型,分析了量子纠缠度对纳什均衡点稳定性及复杂动力行为的影响。结果表明:量子纠缠度能增强该系统的稳定性,企业价格调整速度达到某一程度时会导致该系统的复杂混沌特性,纠缠度可以有效控制混沌状态。最后利用数值模拟从分岔、最大李雅普诺夫指数、奇怪吸引子、初始条件敏感性及分数维数方面验证了理论准确性。     

Inhomogeneous Quantum Codes （III）： The Asymmetric Case

The stabilizer （additive） method and non-additive method for constructing asymmetric quantum codes have been established. In this paper, these methods are gen- eralized to inhomogeneous quantum codes.     

Quantum trajectories of an oscillator interacting with an electromagnetic field, a classical force, and a heat bath

We consider a solvable problem describing the dynamics of a quantum oscillator interacting with an electromagnetic field, a classical force, and a heat bath. We propose a general method for solving Markovian master equations, the method of quantum trajectories. We construct the stochastic evolution operator involving the stochastic analogue of the Baker-Hausdorff formula and calculate the system density matrix for an arbitrary initial state. As a physical application, we evaluate the influence of the environment at a finite temperature on the accuracy of measuring a weak classical force by the interference method. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 444–459, March, 2009.     

Novel uncertainty principles associated with 2D quaternion Fourier transforms

The quaternion Fourier transform has been widely employed in the colour image processing. The use of quaternions allow the analysis of colour images as vector fields. In this paper, the right-sided quaternion Fourier transform and its properties are reviewed. Using the polar form of quaternions, two novel uncertainty principles associated with covariance are established. They prescribe the lower bounds with covariances on the products of the effective widths of quaternionic signals in the space and frequency domains. The results generalize the Heisenberg's uncertainty principle to the 2D quaternionic space.     

Wigner-Yanase skew information vs. quantum Fisher information

Among concepts describing the information contents of quantum mechanical density operators, both the Wigner-Yanase skew information and the quantum Fisher information defined via symmetric logarithmic derivatives are natural generalizations of the classical Fisher information. We will establish a relationship between these two fundamental quantities and show that they are comparable.

     

Quantum electronic transport in graphene: A kinetic and fluid‐dynamic approach

We derive a fluid‐dynamic model for electron transport near a Dirac point in graphene. Starting from a kinetic model, based on spinorial Wigner functions, the derivation of the fluid model is based on the minimum entropy principle, which is exploited to close the moment system deduced from the Wigner equation. To this aim we make two main approximations: the usual semiclassical approximation (??1) and a new one, namely, the ‘strongly mixed state’ approximation, which allow to compute the closure explicitly. Particular solutions of the fluid‐dynamic equations are discussed which are of physical interest because of their connection with the Klein paradox phenomenon. Copyright © 2010 John Wiley & Sons, Ltd.