Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

The entanglement-assisted classical capacity of a noisy quantum channel (C/sub E/) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity C/sub E/ is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs /spl rho/, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of /spl rho/ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency.     

The private classical capacity and quantum capacity of a quantum channel

A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities     

Partial recovery of quantum entanglement

Suppose Alice and Bob try to transform an entangled state shared between them into another one by local operations and classical communications. Then in general a certain amount of entanglement contained in the initial state will decrease in the process of transformation. However, an interesting phenomenon called partial entanglement recovery shows that it is possible to recover some amount of entanglement by adding another entangled state and transforming the two entangled states collectively. In this paper, we are mainly concerned with the feasibility of partial entanglement recovery. The basic problem we address is whether a given state is useful in recovering entanglement lost in a specified transformation. In the case where the source and target states of the original transformation satisfy the strict majorization relation, a necessary and sufficient condition for partial entanglement recovery is obtained. For the general case we give two sufficient conditions. We also give an efficient algorithm for the feasibility of partial entanglement recovery in polynomial time. As applications, we establish some interesting connections between partial entanglement recovery and the generation of maximally entangled states, quantum catalysis, mutual catalysis, and multiple-copy entanglement transformation.     

Quantum data hiding

We expand on our work on quantum data hiding - hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell (1964) states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data-hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme     

A tight lower bound on the classical communication cost of entanglement dilution

Suppose two distant observers, Alice and Bob, share some form of entanglement - quantum correlations - in some bipartite pure quantum states. They may apply local operations and classical communication to convert one form of entanglement to another. Since entanglement is regarded as a resource in quantum information processing, it is an important question to ask how much classical communication, which is also a resource, is needed in the inter-conversion process of entanglement. In this paper, we address this important question in the many-copy case. The inter-conversion process of entanglement is usually divided into two types: concentrating the entanglement from many partially entangled states into a smaller number of maximally entangled states (i.e., singlets) and the reverse process of diluting singlets into partially entangled states. It is known that entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of /spl radic/N. Our main result is to prove that this prior art result is optimal up to a constant factor; any procedure for approximately creating N partially entangled states from singlets requires /spl Omega/(/spl radic/N) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transformations. We also prove a lower bound on the inefficiency of the process: to dilute singlets to N copies of a partially entangled state, the entropy of entanglement must decrease by /spl Omega/(/spl radic/N). Moreover, we introduce two new tools - /spl delta/-significant subspaces and the standard form protocol reduction in entanglement manipulations. We hope that these two new tools will be useful in other work in quantum information theory.     

On quantum fidelities and channel capacities

For the discrete memoryless quantum channel, we show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion for success in transmission, and that which uses the minimum fidelity of pure states in a subspace of the input Hilbert space as its criterion. As a corollary, any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity. We also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel. This enables us to simplify a known upper bound for the channel capacity. It also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity     

Reversible simulation of bipartite product Hamiltonians

Consider two quantum systems A and B interacting according to a product Hamiltonian H=H/sub A//spl ominus/H/sub B/. We show that any two such Hamiltonians can be used to simulate each other reversibly (i.e., without efficiency losses) with the help of local unitary operations and local ancillas. Accordingly, all nonlocal features of a product Hamiltonian - including the rate at which it can be used to produce entanglement, transmit classical or quantum information, or simulate other Hamiltonians - depend only upon a single parameter. We identify this parameter and use it to obtain an explicit expression for the entanglement capacity of all product Hamiltonians. Finally, we show how the notion of simulation leads to a natural formulation of measures of the strength of a nonlocal Hamiltonian.     

量子通信的特色和局限性分析

利用量子纠缠粒子对的远程关联可以实现隐形传态,这是在经典物理现象中找不到的最奇妙的特性,它在量子通信中可能会扮演一个非常特殊的角色。但是利用隐形传态通信能否实现超光速通信、能否突破经典通信的距离和速率极限？通过从量子特性和通信系统工程角度对这些问题进行详细分析可知量子通信存在一些局限性,其在对潜通信和深空通信领域的应用前景有限,对量子通信系统的特色和局限性进行客观分析具有重要意义。     

量子纠缠联想记忆

提出一种基于量子纠缠的联想记忆神经网络(QuEAM).对比传统的联想记忆网络,QuEAM的存储容量得到了指数级的增大.学习算法是根据纠缠量度的性质,采用Grover量子迭代算法的基本原理局域放大量子位(qubit)的概率振幅,相当于传统计算机的按位操作,讨论了这个学习算法下的量子基本原理.最后给出具体的例子说明了算法的有效性.     

经典激光场驱动下的两量子比特纠缠动力学

利用超算符的方法研究了在经典激光场驱动下,分别囚禁在两个独立腔中的两个二能级原子的纠缠动力学。结果表明：两原子纠缠与腔场相干态的初始值无关,并且在腔场耗散比较小的时候,经典光驱动场会加速两原子的纠缠突然死亡,但是在腔场耗散比较大的时候,经典驱动场可以保护原子纠缠免于突然死亡。这说明即便在“坏”腔中,我们也可以通过加经典驱动场来避免原子纠缠突然死亡。     

Capacity of Wireless Communication Systems Employing Antenna Arrays,a Tutorial Study

A tutorial study is performed on thecapacity of multiple antenna wireless communication systems.Multiple antenna structures can be classified into single-inputmultiple-outputs (SIMO), multiple-inputs single-output (MISO), andmultiple-inputs multiple-outputs (MIMO) systems. Assuming that thechannel is known at receiver, capacity expressions are providedfor each structure, under the conditions of quasi-static flatfading. Also, information rate limits are provided in each casefor some suboptimal structures or detection techniques that may beused in practice. Using simulations for the case of flat Rayleighfading, capacities of optimal/suboptimal implementations arecontrasted for each multi-antenna structure. Discussions are madeon system design, regarding implementation complexity andpractical limitations on achieving these capacities. Inparticular, the problem of fading correlation and required antennaspacing, effect of fast channel fading, and lack of channelknowledge at receiver are discussed. Providing the results of themost recent researches considering the capacity of multi-antennasystems, as well as some new results, this paper can give a goodperspective for designing appropriate architectures in differentwireless communication applications.     

Quantum Secret Sharing Based on Multi-Particle Entanglement

1　Introduction　Classical secret sharing provides a way in which Alice canshare a secret with two parties, Bob and Charlie, such thatnone of them can recover her secret on his own, but they to gether can[1]. Again it can be generalized to [( m, n )threshold scheme] situations for any m≤n[2, 3]. However,with the advent of quantum computation, we need to protectthe communication data using quantum cryptography, whichhas unconditional security. The direct solution is to combinequantum…     

Counter-intuitive throughput behaviors in networks under end-to-end control

It has been shown that as long as traffic sources adapt their rates to aggregate congestion measure in their paths, they implicitly maximize certain utility. In this paper we study some counter-intuitive throughput behaviors in such networks, pertaining to whether a fair allocation is always inefficient and whether increasing capacity always raises aggregate throughput. A bandwidth allocation policy can be defined in terms of a class of utility functions parameterized by a scalar a that can be interpreted as a quantitative measure of fairness. An allocation is fair if /spl alpha/ is large and efficient if aggregate throughput is large. All examples in the literature suggest that a fair allocation is necessarily inefficient. We characterize exactly the tradeoff between fairness and throughput in general networks. The characterization allows us both to produce the first counter-example and trivially explain all the previous supporting examples. Surprisingly, our counter-example has the property that a fairer allocation is always more efficient. In particular it implies that maxmin fairness can achieve a higher throughput than proportional fairness. Intuitively, we might expect that increasing link capacities always raises aggregate throughput. We show that not only can throughput be reduced when some link increases its capacity, more strikingly, it can also be reduced when all links increase their capacities by the same amount. If all links increase their capacities proportionally, however, throughput will indeed increase. These examples demonstrate the intricate interactions among sources in a network setting that are missing in a single-link topology.     

Quantum information theory

We survey the field of quantum information theory. In particular, we discuss the fundamentals of the field, source coding, quantum error-correcting codes, capacities of quantum channels, measures of entanglement and quantum cryptography     

经典驱动J-C模型中的纠缠演化和转移特性研究

研究了受经典场驱动的两个二能级原子分别与两个单模腔场相互作用模型中两原子的纠缠动力学行为。该工作主要是对经典场驱动存在的J-C模型进行了研究,采用数值计算的方法,详细分析了纠缠初始状态以及经典场的驱动强度对原子纠缠和转移特性的影响。结果表明,适当调节经典场驱动强度,可以使原子的纠缠突然死亡现象得到抑制,同时实现原子与腔场间的最大转移。     

Asymptotic Ergodic Capacity of Multidimensional Vector-Sensor Array MIMO Channels

We analyze asymptotic ergodic capacity of multidimensional vector-sensor array MIMO (PMD-MIMO) channels established by the use of dual-polarized antennas in the form of 1D, 2D and/or 3D MIMO arrays. Based on the identification of the decomposition of PMD-MIMO channels into multiple independently-fading and scaled classical MIMO channels in parallel, we consequently derive corresponding asymptotic ergodic capacities analytically via tools out of free probability theory. The analysis of derived asymptotic ergodic capacity expressions in terms of antenna locus aspect ratio ?, average symbol SNR per antenna ˉ?s and cross-polar discrimination XPD as well as comparison with asymptotic ergodic capacity of classical MIMO channels present important gains in using compact multidimensional vector-sensor array MIMO systems in asymptotic regimes.     

腔QED系统中三体纠缠的转移和动力学特性研究

通过归纳法得到共振条件下k 个独立Jaynes-Cummings (J-C)模型系统 波函数概率幅的递推关系,给出了任意初态下波函数的解析解。在此基础上重点 研究了共振条件下三个独立J-C模型系统中的纠缠动力学特性。结果表明,系统 原子间的纠缠与子系统腔场光子数有关系,光子数越多,原子间纠缠第一次死亡 的时间越快。同时发现三个子系统的腔场处于真空态时,原子间的纠缠与腔场间 的纠缠随时间的演化呈现周期性的行为,并且原子间纠缠达到最小值0时,腔场 间纠缠达到最大值1,实现了原子与腔场之间纠缠的相互转移。     

Optimum profiles for dispersive multimode fibres

We give a simple closed-form expression for the index profile of multimode fibres with arbitrary dispersion that provides transmission capacities as large as 1.6/?2 Mbit/s×km, where ? ? ?n/n. Our result reduces to a recent result of Marcatili for the special case of circularly symmetric fibres. A transmission capacity of 150 Mbit/s over a 10 km-long fibre appears possible with l.e.d. sources     

Landau-Zener模型中纠缠演化及转移的研究

研究了受外场驱动的两个二能级系统分别与两个单模量子化光场相互作用模型中纠缠演化及转移问题。该工作主要是对外场驱动的Landau-Zener模型进行了研究，采用旋转波近似的方法，通过数值计算详细分析了二能级系统初始状态、能级间的耦合常数以及驱动外场的参数对子系统间纠缠和转移特性的影响。结果表明，适当调节模型中的参数，可以使系统初始纠缠完全转移为光腔场间的纠缠，实现二能级系统与光场间的最大纠缠转移。     

利用纠缠催化作用辅助恢复纠缠态转化中丢失的量子纠缠

利用局域操作的方法可以把一个初始纠缠态转化为一个目标纠缠态,在这个过程中会损失一定量的量子纠缠。文献[10]证明可以用一个附加纠缠态部分地恢复丢失的量子纠缠,但附加纠缠态的纠缠度必须大于目标纠缠态的纠缠度.本文证明当不满足这一条件时,可以用纠缠催化作用辅助恢复丢失的量子纠缠.我们发现催化剂纠缠态的纠缠度必须大于目标纠缠态的纠缠度。