The Elusive Source of Quantum Speedup

We discuss two qualities of quantum systems: various correlations existing between their subsystems and the distinguishability of different quantum states. This is then applied to analysing quantum information processing. While quantum correlations, or entanglement, are clearly of paramount importance for efficient pure state manipulations, mixed states present a much richer arena and reveal a more subtle interplay between correlations and distinguishability. The current work explores a number of issues related with identifying the important ingredients needed for quantum information processing. We discuss the Deutsch-Jozsa algorithm, the Shor algorithm, the Grover algorithm and the power of a single qubit class of algorithms. In the latter, a quantity called discord is seen to be more important than entanglement. One section is dedicated to cluster states where entanglement is crucial, but its precise role is highly counter-intuitive. Here we see that the notion of distinguishability becomes a more useful concept.     

Controllable Quantum Network Coding Scheme Based on Quantum Walk

Quantum entanglement is one of the key methods in quantum information processing, but it is difficult to prepare quantum entanglement. Quantum walk is widely used in quantum computation and quantum simulation, it can be applied to the preparation of quantum entangled states. In this paper, a controllable quantum network coding scheme based on quantum walk is proposed. With the help of quantum walk, the scheme preliminary realized the entanglement distribution of butterfly network, reduced entanglement resources and enhanced scalability. According to the existing technology, it is feasible to implement the quantum network coding scheme proposed in this paper.

     

利用多光子相互作用实现量子信息传递

利用全量子理论,研究了多原子-腔场系统中多光子相互作用的过程,给出了不同情况下系统的一般演化式,发现利用此过程可实现量子纠缠信息的传递:只要控制腔场与原子相互作用的时间即原子以特定速度通过腔场时,处于基态的原子与存储纠缠信息的腔场相互作用的结果使原子获得量子纠缠信息;相反,纠缠原子中的量子纠缠信息也可传递给处于真空态的腔场;基态原子作为"飞行的量子比特"还可将量子纠缠信息从一个腔场传递到另一个腔场。该结论适应于讨论任意多个原子-腔场系统中任意多个光子相互作用的普遍情形。     

Quantum Communication with Continuous Variables

Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous‐variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous‐variable entanglement and show how to make it. The members of a family of multi‐mode states are found to be truly multi‐party entangled with respect to all their modes. These states also violate multi‐party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi‐party continuous‐variable entanglement. Various quantum communication protocols based on the continuous‐variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous‐variable entanglement swapping. We highlight the similarities and differences between continuous‐variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi‐party generalization of quantum teleportation. This so‐called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no‐cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase‐insensitive amplifier and beam splitters.     

Characterizing Quantum Correlations in Arbitrary-Dimensional Bipartite Systems Using Hurwitz's Theory

Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord （QD） and entanglement of formation （EOF） axe two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of chaxaeterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in axbitraxy-dimensionM bipaxtite quantum systems in terms of Hurwitz＇s theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of axbitraxy-dimensional bipaxtite quantum states via purification, and the relations.hip between QD and EOF.     

Nondestructive Probing Scheme of Quantum State Without Quantum Correlation

We study a scheme that an auxiliary qubit is introduced for probing the information of the given bipartite quantum state, while the correlations of the probed quantum state and even the probed state itself are not disturbed after the probing, which means nondestructive probing. We find that, in order to guarantee the invariance of the correlations of the probed state, neither quantum entanglement nor quantum discord between the auxiliary qubit and the probed states can be present. This could make us reconsider the role of quantum correlation in some quantum information processing tasks.     

Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics

We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice.Starting from an unentangled initial state associated with the regular 'island' of classical phase space,it is demonstrated that the quantum resonance leads to entanglement generation,the chaotic parameter region results in the increase of the generation speed,and the symmetries of the initial probability distribution determine the final degree of entanglement.The entangled initial states are associated with the classical 'chaotic sea',which do not affect the final entanglement degree for the same initial symmetry.The results may be useful in engineering quantum dynamics for quantum information processing.     

多模简并多光子Tavis-Cummings模型中的量子纠缠特性

利用冯·纽曼约化熵理论研究了多模相干态光场与两等同二能级原子简并多光子相互作用系统量子纠缠演化特性,得到了多模光场量子纠缠的解析表达式,并给出了双模光场与两原子相互作用时量子纠缠的数值计算结果.结果表明:量子纠缠随着光子简并度的增大而增强;随着初始平均光子数的增加,量子纠缠演化的周期性变得越来越明显;当场与原子远离共振时,量子纠缠随着频率失谐量的增大而减弱;当失谐量足够大时,场与原子几乎总是处于纠缠状态.这些结论对于纠缠态或纯态的制备及获取光学系统中的量子信息研究中有一定参考价值.     

Quantum Entanglement Swapping in a Non-Markovian Environment

We propose an entanglement swapping scheme for mixed states in a classical non-Markovian noises, which is modelled as the so-called Ornstein-Uhlenbeck processes. The two mixed states before entanglement swapping are two X-type mixed states, which are caused by the environment-induced decoherence on the initially Bell states. This is more practical than the pure state case in quantum information processing. The fidelity and concurrence of the post-swapping states are discussed.     

Quantum and classical correlations in quantum Brownian motion

We investigate the entanglement properties of the joint state of a distinguished quantum system and its environment in the quantum Brownian motion model. This model is a frequent starting point for investigations of environment-induced superselection. Using recent methods from quantum information theory, we show that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment. If the distinguished system has been initially prepared in a pure Gaussian state, then entanglement is created immediately, regardless of the temperature of the environment and the nonvanishing coupling.     

Quantum Information in the Frame of Coherent States Representation

In this paper we have showed that the qubit can be expressed through the coherent states. Consequently, a message, i.e. a sequence of qubits, is expressed as a tensor product of coherent states. In the quantum information theory and practice, only the code and key message are expressed as a sequence of qubits, i.e. through a quantum channel, the properly information will be transmitted by using a classical channel. Even if the most used coherent states in the quantum information theory are the coherent states of the harmonic oscillator (particularly, expressing by them the Schrödinger “cat states” and the Bell states), several authors have been demonstrated that other kind of coherent states may be used in quantum information theory. For the ensembles of qubits, we must use the density operator, in order to describe the informational content of the ensemble. The diagonal representation of the density operator, in the coherent state representation, is also useful to examine the entanglement of the states.     

非马尔科夫环境下耦合超导量子系统纠缠演化的数值研究

基于耦合超导量子比特系统模型下,在非马尔科夫环境中利用共生纠缠的方法分析了耦合系统纠缠的产生及其动力学的演化。研究了不同初始纠缠态下的纠缠猝死(ESD)和纠缠再生(ESB)现象;主要分析了系统耦合强度、库的截止频率与系统的振荡频率间的比值、温度和约瑟夫森能级差对纠缠演化的影响。结果表明:系统纠缠取决于初始纠缠态和系统的耦合强度J,并且通过调节以上非马尔科夫环境的相干参数可以延长解纠缠时间来确保量子计算过程中的应用和量子信息的实现。     

Symmetric Telecloning and Entanglement Distribution of Spin Quantum States

We propose a physical realization of symmetric telecloning machine for spin quantum states. The concept of area average fidelity is introduced to describe the telecloning quality. It is indicated that for certain input states this quantity may come to an enough high level to satisfy the need of quantum information processing. We also study the properties of entanglement distribution via the spin chain for arbitrary two-qubit entangled pure states as inputs and find that the decay ratio of entanglement for the output states is only determined by the parameters of spin chain and waiting time, independent of the initial input states.     

Entanglement Dynamics in a Model Tripartite Quantum System

A Λ-type atom interacting with two radiation fields exhibits electromagnetically induced transparency and other nonclassical effects that appear in the entanglement dynamics of the atomic subsystem and in appropriate field observables. Both EIT and field-atom entanglement are important for quantum information processing. We investigate the roles played by specific initial field states, detuning parameters, field nonlinearities and intensity-dependent field-atom couplings on EIT and the entanglement between subsystems. Departure from coherence of the initial field states produces significant effects. We investigate these aspects in a model that exhibits the salient features of entangled tripartite systems. For initial photon-added coherent states, collapses and revivals of the atomic subsystem von Neumann entropy appear as the intensity parameter varies over a narrow range of values. These features could be useful in enabling entanglement.     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

Three-Party Quantum Network Communication Protocols Based on Quantum Teleportation

By utilizing the delocalized correlation of entangled states in quantum information theory, a novel method on acknowledgments of quantum information among three-party is presented, and then two three-party quantum network communication protocols based on quantum teleportation are presented, namely, three-party stop-wait quantum communication protocol and three-party selective automatic repeat quantum communication protocol. In the two proposed protocols, the data frames composed of qubits are teleported via three-party quantum teleportation, the two receivers simultaneously receive quantum frames from the sender, and then return quantum acknowledgment frames or quantum negative acknowledgment frames via quantum entanglement channels. The sender simultaneously receives and deals with quantum acknowledgment frames and quantum negative acknowledgment frames from the two receivers, thus the processing delay on returning quantum frames is reduced. And due to the transience of transferring quantum information, the returning of quantum acknowledgment frames and quantum negative acknowledgment frames are completed instantaneously, the proposed protocols reduce the transmission delay and improve the communication efficiency. During the whole course of communications, the classical channels are only used to transmit the measurement message, so the burdens of classical channels are reduced.     

Quantum computing based on space states without charge transfer

An implementation of a quantum computer based on space states in double quantum dots is discussed. There is no charge transfer in qubits during a calculation, therefore, uncontrolled entanglement between qubits due to long-range Coulomb interaction is suppressed. Encoding and processing of quantum information is merely performed on symmetric and antisymmetric states of the electron in double quantum dots. Other plausible sources of decoherence caused by interaction with phonons and gates could be substantially suppressed in the structure as well. We also demonstrate how all necessary quantum logic operations, initialization, writing, and read-out could be carried out in the computer.     

量子纠缠与宇宙学弗里德曼方程

量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球（a geodesic ball）的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.