An Informational Approach to the Sinusoidal Law of Photon Polarization

The photon polarization law po ＝ sin2θ is derived from a simple informational consideration by twomethods: The first is via an intuitive principle of mininum Fisher information, the second is via a symmetry andinvariance argument. The results demonstrate that in photon polarization, Nature has a tendency to hide herselfas deepas possible while obeying some regular conditions.     

Uncertainty Relations for Coherence

Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables. In terms of the coherence measure based on the Wigner-Yanase skew information, we establish several uncertainty relations for coherence with respect to von Neumann measurements, mutually unbiased bases(MUBs), and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively. Since coherence is intimately connected with quantum uncertainties, the obtained uncertainty relations are of intrinsically quantum nature, in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties). From a dual viewpoint, we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement. In particular, it is shown that if the density operators representing the quantum states do not commute, then there is no measurement(reference basis) such that the coherence of these states can be simultaneously small.     

A Note on Fundamental Limit of Quantum Dynamics Rate

The unified bound on the fundamental limit of quantum dynamics rate, as quietly recently obtained by Levitin and Toffoli [Phys. Rev. Lett. 103 (2009) 160502], is improved and refined. The improvement may be arbitrarily large in certain cases. In particular, this puts a limit on the operation rate of quantumgates allowed by quantum mechanics.     

Uncertainty Relations in Terms of Fisher Information

By virtue of the well-known concept of Fisher information in the theory of statistical inference, we obtain an inequality chain which generalizes and refines the conventional Heisenberg uncertainty relations.     

Logarithm Versus Square Root： Comparing Quantum Fisher Information

In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.     

A Note on Fundamental Limit of Quantum Dynamics Rate

The unified bound on the fundamental limit of quantum dynamics rate, as quietly recently obtained by Levitin and Toffoli [Phys. Rev. Lett. 103 （2009） 160502], is improved and refined. The improvement may be arbitrarily large in certain cases. In particular, this puts a limit on the operation rate of quantum gates allowed by quantum mechanics.     

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.     

量子关联简介

量子纠缠作为一种非局域的关联,是一种重要的资源而被广泛应用于量子信息处理。然而,最近的研究结果发现,可分态中也可以存在非经典的关联,量子纠缠只是量子关联的一部分;非纠缠的量子关联在一些量子通信和量子计算任务中扮演着重要的角色。文章简要综述了量子关联的基本概念,描述了几种常见的量子关联度量,并介绍了量子关联在量子信息处理中的作用以及一些最新动态。     

Singularity of Farhi-Gutmann Analog Quantum Search

We show that the Farhi-Gutmann analog quantum search is a singular algorithm in the following sense: when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting state and to the target state with different energies, the maximum fidelity (transition probability) between the searching state and the target state is strictly less than 1 over the entire evolution period, and the first time to achieve this maximum fidelity is of order √(N)/√(1+cN), whose behavior depends crucially on whether c=0 or not (here N is the total number of items, and the original Farhi-Gutmann case corresponds to c=0). Moreover, when c≠ 0 and N tends to infinity, the maximum fidelity tends to zero, and the first time to achieve the maximum fidelity tends to a positive constant! The condition for guaranteeing the algorithm's efficiency is determined explicitly.     

Quantum Correlations Reduce Classical Correlations with Ancillary Systems

We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy. More precisely, we show that correlations in a bipartite state are classical if and only it each party ot the state can be perfectly correlated with other ancillary systems. In particular, this means that if there are quantum correlations between two parties, then the classical （as well as quantum） correlating capabilities of the two parties with other systems have to be strictly reduced.