A Simple Example of “Quantum Darwinism”: Redundant Information Storage in Many-Spin Environments

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence.     

An Exact and Practical Classical Strategy for 2D Graph State Sampling

Constant-depth quantum circuits that prepare and measure graph states on 2D grids are proved to possess a computational quantum advantage over their classical counterparts due to quantum nonlocality and are also well suited for demonstrations on current superconducting quantum processor architectures. To simulate the partial or full sampling of 2D graph states, a practical two-stage classical strategy that can exactly generate any number of samples (bit strings) from such circuits is proposed. The strategy is inspired by exploiting specific properties of a hidden linear function problem solved by the target quantum circuit, which in particular combines traditional classical parallel algorithms and an explicit gate-based constant-depth classical circuit together. A theoretical analysis reveals that on average each sample can be obtained in nearly constant time for sampling specific circuit instances of large size. Moreover, the feasibility of the theoretical model is demonstrated by implementing typical instances up to 25 qubits on a moderate field programmable gate array platform. Therefore, the strategy can be used as a practical tool for verifying experimental results obtained from shallow quantum circuits of this type.     

Quantum Pseudo-Telepathy

Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required. Pseudo-telepathy is a surprising application of quantum information processing to communication complexity. Thanks to entanglement, perhaps the most nonclassical manifestation of quantum mechanics, two or more quantum players can accomplish a distributed task with no need for communication whatsoever, which would be an impossible feat for classical players. After a detailed overview of the principle and purpose of pseudo-telepathy, we present a survey of recent and not-so-recent work on the subject. In particular, we describe and analyse all the pseudo-telepathy games currently known to the authors. Supported in Part by Canada’s Natural Sciences and Engineering Research Council (NSERC), the Canada Research Chair programme and the Canadian Institute for Advanced Research (CIAR). Supported in part by a scholarship from Canada’s NSERC. Supported in part by Canada’s NSERC Québec’s Fonds de recherche sur la nature et les technologies (FQRNT), the CIAR and the Mathematics of Information Technology and Complex Systems Network (MITACS).     

Analysis of the role of von Neumann’s projection postulate in the canonical scheme of quantum teleportation

Modern development of quantum technologies based on quantum information theory (in particular, laser-based quantum-information technologies) stimulated the analysis of proposed computational, cryptographic, and teleportational schemes from the viewpoint of quantum foundations. It is evident that not all mathematical calculations performed in the complex Hilbert space can directly be realized in the physical space. Recently, analyzing the original EPR paper, we found that their argument was based on the misuse of von Neumann’s projection postulate. In contrast to von Neumann, Einstein, Podolsky, and Rosen (EPR) applied this postulate to the observables represented by the operators with degenerate spectra. It was completely forbidden by von Neumann’s axiomatics of quantum mechanics. It is impossible to repeat the EPR considerations within the von Neumann’s framework. We analyze here quantum teleportation by taking into account von Neumann’s projection postulate. Our analysis shows that the so-called quantum teleportation is impossible within the von Neumann’s framework.     

Variational quantum support vector machine based on Hadamard test

Classical machine learning algorithms seem to be totally incapable of processing tremendous amounts of data, while quantum machine learning algorithms could deal with big data with ease and provide exponential acceleration over classical counterparts. Meanwhile, variational quantum algorithms are widely proposed to solve relevant computational problems on noisy, intermediate-scale quantum devices. In this paper, we apply variational quantum algorithms to quantum support vector machines and demonstrate a proof-of-principle numerical experiment of this algorithm. In addition, in the classification stage, fewer qubits, shorter circuit depth, and simpler measurement requirements show its superiority over the former algorithms.     

A prototype of quantum von Neumann architecture

A modern computer system, based on the von Neumann architecture, is a complicated system with several interactive modular parts. It requires a thorough understanding of the physics of information storage, processing, protection, readout, etc. Quantum computing, as the most generic usage of quantum information, follows a hybrid architecture so far, namely, quantum algorithms are stored and controlled classically, and mainly the executions of them are quantum, leading to the so-called quantum processing units. Such a quantum–classical hybrid is constrained by its classical ingredients, and cannot reveal the computational power of a fully quantum computer system as conceived from the beginning of the field. Recently, the nature of quantum information has been further recognized, such as the no-programming and no-control theorems, and the unifying understandings of quantum algorithms and computing models. As a result, in this work, we propose a model of a universal quantum computer system, the quantum version of the von Neumann architecture. It uses ebits (i.e. Bell states) as elements of the quantum memory unit, and qubits as elements of the quantum control unit and processing unit. As a digital quantum system, its global configurations can be viewed as tensor-network states. Its universality is proved by the capability to execute quantum algorithms based on a program composition scheme via a universal quantum gate teleportation. It is also protected by the uncertainty principle, the fundamental law of quantum information, making it quantum-secure and distinct from the classical case. In particular, we introduce a few variants of quantum circuits, including the tailed, nested, and topological ones, to characterize the roles of quantum memory and control, which could also be of independent interest in other contexts. In all, our primary study demonstrates the manifold power of quantum information and paves the way for the creation of quantum computer systems in the near future.     

Quantum secure direct communication over the collective amplitude damping channel

An efficient quantum secure direct communication protocol is presented over the amplitude damping channel. The protocol encodes logical bits in two-qubit noiseless states, and so it can function over a quantum channel subjected to collective amplitude damping. The feature of this protocol is that the sender encodes the secret directly on the quantum states, the receiver decodes the secret by performing determinate measurements, and there is no basis mismatch. The transmission’s safety is ensured by the nonorthogonality of the noiseless states traveling forward and backward on the quantum channel. Moreover, we construct the efficient quantum circuits to implement channel encoding and information encoding by means of primitive operations in quantum computation. Supported by the National Natural Science Foundation of China (Grant Nos. 60873191 and 60821001), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200800131016), the Natural Science Foundation of Beijing (Grant No. 4072020), the National Laboratory for Modern Communications Science Foundation of China (Grant No. 9140C1101010601), and the ISN Open Foundation     

Realizing number recognition with simulated quantum semi-restricted Boltzmann machine

Quantum machine learning based on quantum algorithms may achieve an exponential speedup over classical algorithms in dealing with some problems such as clustering. In this paper, we use the method of training the lower bound of the average log likelihood function on the quantum Boltzmann machine (QBM) to recognize the handwritten number datasets and compare the training results with classical models. We find that, when the QBM is semi-restricted, the training results get better with fewer computing resources. This shows that it is necessary to design a targeted algorithm to speed up computation and save resources.     

The 50% Advanced Information Rule of?the?Quantum Algorithms

The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function (e.g. its period) through function evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. This requires representing physically, besides the solution algorithm, the possible choices of the oracle. Here we check that this 50% rule holds for the main quantum algorithms. In structured problems, a classical algorithm with the advanced information, to identify the missing information should perform one function evaluation. The speed up is exponential since a classical algorithm without advanced information should perform an exponential number of function evaluations. In unstructured database search, a classical algorithm that knows in advance n/2 bits of the database location, to identify the n/2 missing bits should perform O(2 ^n/2) function evaluations. The speed up is quadratic since a classical algorithm without advanced information should perform O(2 ⁿ ) function evaluations. The 50% rule allows to identify in an entirely classical way the problems solvable with a quantum sped up. The advanced information classical algorithm also defines the quantum algorithm that solves the problem. Each classical history, corresponding to a possible way of getting the advanced information and a possible result of computing the missing information, is represented in quantum notation as a sequence of sharp states. The sum of the histories yields the function evaluation stage of the quantum algorithm. Function evaluation entangles the oracle’s choice register (containing the function chosen by the oracle) and the solution register (in which to read the solution at the end of the algorithm). Information about the oracle’s choice propagates from the former to the latter register. Then the basis of the solution register should be rotated to make this information readable. This defines the quantum algorithm, or its iterate and the number of iterations.     

Directional quantum random walk induced by coherence

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution.     

玻色-爱因斯坦凝聚系统的量子Fisher信息与混沌

量子Fisher信息作为经典Fisher信息的自然推广,与量子信息中的纠缠判断具有密切联系.在表现为典型量子混沌特征的受击两分量玻色-爱因斯坦凝聚系统中,研究了与经典相空间对应的纠缠和量子Fisher信息动力学性质. 结果表明,初次撞击后的系统量子态是纠缠的,与初态所处相空间中的混乱程度无关.而量子Fisher信息的动力学演化对系统初态非常敏感,当初态处于混沌区域时,量子Fisher信息值比初态处于规则区域时大.利用这种较好的量子-经典对应关系,得到量子Fisher信息可以刻画量子混沌的结论. 关键词： 量子Fisher信息 玻色-爱因斯坦凝聚 量子混沌 量子-经典对应     

基于量子隐形传态的量子保密通信方案

量子保密通信包括量子密钥分发、量子安全直接通信和量子秘密共享等主要形式.在量子密钥分发和秘密共享中,传输的是随机数而不是信息,要再经过一次经典通信才能完成信息的传输.在量子信道直接传输信息的量子通信形式是量子安全直接通信.基于量子隐形传态的量子通信(简称量子隐形传态通信)是否属于量子安全直接通信尚需解释.构造了一个量子隐形传态通信方案,给出了具体的操作步骤.与一般的量子隐形传态不同,量子隐形传态通信所传输的量子态是计算基矢态,大大简化了贝尔基测量和单粒子操作.分析结果表明,量子隐形传态通信等价于包含了全用型量子密钥分发和经典通信的复合过程,不是量子安全直接通信,其传输受到中间介质和距离的影响,所以不比量子密钥分发更有优势.将该方案与量子密钥分发、量子安全直接通信和经典一次性便笺密码方案进行对比,通过几个通信参数的比较给出各个方案的特点,还特别讨论了各方案在空间量子通信方面的特点.     

Dicke模型的量子经典对应关系

非旋波近似条件下Dicke模型表现为量子混沌动力学特征.在详细考察Dicke模型经典相空间结构特点的基础上,采用经典-量子"一对多"的思想,即经典相空间中的一点对应于量子体系两个初始相干态的演化,利用对两个初态量子纠缠动力学演化取统计平均的方法,得到了与经典相空间对应非常好的量子相空间结构.数值计算结果表明:经典混沌有利地促进系统两体纠缠的产生,平均纠缠可以作为量子混沌的标识,利用平均纠缠可以得到一种较好的量子动力学与经典相空间的对应关系. 关键词： Dicke模型 非旋波近似 量子混沌 经典量子对应     

Renormalization and Quantum Scaling of Frenkel–Kontorova Models

We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel–Kontorova models studied by Aubry and others to non-zero Planck’s constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman’s functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay’s renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime     

The effect of quantum noise on the restricted quantum game

It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of 0 〈 p ≤ 0.422 （p is the quantum noise parameter）, while two special Nash equilibria appear in the range of 0.422 〈 p 〈 1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player＇s payoff and the reduction of the quantum player＇s payoff, but is helpful in forming two Nash equilibria.     

Quantum algorithms in one-way quantum computation

Cluster states are the fundamental resource for the one-way model of quantum computation. In this paper we show the realization of a two-photon four-qubit cluster state. The qubits are encoded in the polarization and the linear momentum of the particles. By using this state we realized two important quantum algorithms, namely the Grover’s search and the Deutsch’s algorithm.     

Equivalent programmable quantum processors

Programmable quantum circuits, or processors, have the advantage over single-purpose quantum circuits that they can be used to perform more than one function. The inputs of a quantum processor consist of two quantum states, the first, the data register, is a state on which an operation is to be performed, and the second, the program, determines the operation to be performed on the data. In this paper we study how to determine whether two different quantum processors perform the same set of operations on the data. We define an equivalence between quantum processors that is quite natural in a circuit model of quantum information processing. Two processors are equivalent if one can be converted into the other by inserting fixed unitary gates at the input and the output of the program register. We then use this definition to find a necessary condition for two processors to be equivalent. We also study the beam splitter as an example of a quantum processor and find that this example suggests that as well as there being an equivalence relation on processors, there may also be a partial ordering.     

A quantum encryption scheme using d-level systems

Using the generalized Bell states and quantum gates, we introduce a quantum encryption scheme of d-level states （qudits）. The scheme can detect and correct arbitrary transmission errors using only local operations and classical communications between the communicators. In addition, the entanglement key used to encrypt can be recycled. The protocol is informationally secure, because the output state is a totally mixed one for every input state p.     

Superadditivity of Wigner-Yanase-Dyson Information Revisited

The Wigner-Yanase-Dyson information is an important variant of quantum Fisher information. Two fundamental requirements concerning this notion of information content originally postulated by Wigner and Yanase are convexity and superadditivity. The former was fully established by Lieb in 1973, and led to the first proof of the strong subadditivity of quantum entropy. The latter, although widely believed to be true, was quite recently disproved by Hansen. Nevertheless, superadditivity has also been established in two extreme cases, i.e., when the states are pure or classical. In this paper, we first review a scheme to classify bipartite states into a hierarchy of classical, semi-quantum, and quantum states, which are arranged in the order of increasing quantumness. We then prove the superadditivity of the Wigner-Yanase-Dyson information for all semi-quantum states. The convexity of the Wigner-Yanase-Dyson information plays a crucial role here.     

连续变量无条件纠缠交换 --纠缠态的量子离物传送

利用自行设计的两台非简并光学参量放大器，获得了一对具有经典相干性且量子起伏相互独立的连续变量纠缠态光场，并用它完成了连续变量的无条件纠缠交换，即纠缠态的量子离物传送．通过联合贝尔态探测与纠缠塌缩，使两个初始不纠缠而又从未发生过直接相互作用的光场产生了量子纠缠，其正交振幅和位相分量的量子起伏关联方差被直接测量，其测量值分别低于散离噪声极限1．23dB和1．12dB．理论计算与实验结果基本符合．