A Note of Coherence for Duality Quantum Computers Acting on Pure States

In this paper, we discuss the coherence for duality quantum computers under taking different unitary operators acting on pure states. Firstly, for arbitrary unitary operators, we give some general quantitative results of the coherence of output states. Secondly, for incoherence unitary operators, we obtain that the coherence of output states satisfies an inequality. In addition, we also give a conclusion of the coherence of output states under unitary permutation operators.     

A Note on Quantum Entropy

Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.     

Quantum Coherence in Non-Markovian Quantum Channels

We numerically simulate quantum coherence in a system of two qubits interacting with a reservoir for non-Markovian channels. The explicit form of the master equation is taken in terms of density-operator elements and is solved according to the initial conditions. In particular, we consider the effect of an Ohmic reservoir (OR) with Lorentz–Drude regularization (LDR) on the extent of coherence during dynamics. We describe the dynamical behavior of the coherence for low, intermediate, and high-temperature reservoirs. We explain the effect of the ratio of the cutoff frequency (CF) to the quantum system frequency and the effect of temperature on the quantum coherence. We show that a decreasing ratio enhances coherence, while an increasing temperature decreases it.

     

Protecting Qutrit Quantum Coherence

High dimensional quantum system plays a vital role in quantum information processing. However, decoherence induced by the coupling between quantum system and environment often destroys quantum resource. In this paper, we study the dynamics and protection of qutrit quantum coherence (QC) under amplitude damping (AD) decoherence. We propose two schemes to protect QC. We find that the first scheme can not always protect QC and the second scheme has prominent advantage over the first scheme. In addition, better protection requires lower success probability (SP).     

A Note on Quantum Bell Nonlocality and Quantum Entanglement for High Dimensional Quantum Systems

We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.

     

A Note on Polarization Vectors in Quantum Electrodynamics

A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence-free in the Coulomb gauge. These facts are normally taken into account in QED by introducing two polarization vectors (k) with {1,2}, which are orthogonal to the wave-vector k. These vectors must be very discontinuous functions of k and, consequently, their Fourier transforms have bad decay properties. Since these vectors have no physical significance there must be a way to eliminate them and their bad decay properties from the theory. We propose such a way here.Dedicated to Freeman Dyson on the occasion of his eightieth birthdayWork partially supported by U.S. National Science Foundation grant PHY 01-39984.Work partially supported by U.S. National Science Foundation grant DMS 03-00349. 2003 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.Acknowledgement We thank Herbert Spohn and Jakob Yngvason for many useful discussions about this work. After completing this work and submitting it to CMP it was brought to our attention that the last section, 10.3, of the paper [2] by Fröhlich, Griesemer and Schlein contains the same idea in the context of Rayleigh scattering in the dipole approximation. The three-component concept enables them to extend the results in the rest of their paper from scalar fields to vector fields, but, as we see here, the concept works in much greater generality.     

Estimation on Geometric Measure of Quantum Coherence

We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115(2015)020403]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states—maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.     

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.     

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.     

A Note on the Relationship Between Genuinely Coherence and Generalized Entanglement Monotones

International Journal of Theoretical Physics - We find a one to one mapping between genuinely incoherent operations and special one-way local operations and classical communication(LOCC) for...     

A Note on the Time Development of Quantum Lattice Systems

The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group _t for which is a KMS state are constructed.     

A Note on the Stochastic Nature of Feynman Quantum Paths

We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.     

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.     

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix （CM） separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.     

Quantum Work Statistics with Initial Coherence

The two-point measurement scheme for computing the thermodynamic work performed on a system requires it to be initially in equilibrium. The Margenau–Hill scheme, among others, extends the previous approach to allow for a non-equilibrium initial state. We establish a quantitative comparison between both schemes in terms of the amount of coherence present in the initial state of the system, as quantified by the l1-coherence measure. We show that the difference between the two first moments of work, the variances of work, and the average entropy production obtained in both schemes can be cast in terms of such initial coherence. Moreover, we prove that the average entropy production can take negative values in the Margenau–Hill framework.     

Quantum Coherence in Loopless Superconductive Networks

Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific branches of the networks and sharp increases in pair currents are the main signatures of the coherent states. In order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent—but isolated—counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases in the Josephson currents, along the above-mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks, and in both cases, the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.     

"量子相干性跟踪控制"的鲁棒性分析

文献[Quantum Information and Computation,2005,5(4):350-363]提出量子相干性跟踪控制策略以保持量子位的相干性,该策略本质是开环控制,而开环控制的缺陷就是严重依赖于精确地了解系统的初始条件和模型参数。然而,我们对于系统的知识总是存在不确定性的。本文从鲁棒性的角度分析了量子相干性跟踪控制策略的局限性。首先,我们对该方法的鲁棒性进行了理论分析;接着用仿真实例定量说明了:量子初始条件和模型参数的精度对保持相干性的影响。根据相干性的精度要求,我们可以利用仿真分析的手段,来确定对模型参数和初始状态必须满足的精度条件。总之,我们在应用中必须谨慎采用量子相干性跟踪控制策略。     

Note on Entropies of Quantum Dynamical Systems

We review some techniques and notions for quantum information theory. It is shown that the dynamical entropies is discussed and some numerical computations of these entropies are carried for several states.