Data Compression Limit for an Information Source of Interacting Qubits

A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other. We establish the limit for the compression of information from such a source and show that asymptotically it is given by the von Neumann entropy rate. Our result can be viewed as a quantum ana-logue of Shannon's noiseless coding theorem for a class of non-i.i.d. quantum informa-tion sources. From the probabilistic point of view it is an analog of the Shannon-McMillan-Breiman theorem considered as a cornerstone of modern Information Theory. PACS: 03.67-a; 03.67.Lx     

Continuous-variable quantum network coding for coherent states

As far as the spectral characteristic of quantum information is concerned, the existing quantum network coding schemes can be looked on as the discrete-variable quantum network coding schemes. Considering the practical advantage of continuous variables, in this paper, we explore two feasible continuous-variable quantum network coding (CVQNC) schemes. Basic operations and CVQNC schemes are both provided. The first scheme is based on Gaussian cloning and ADD/SUB operators and can transmit two coherent states across with a fidelity of 1/2, while the second scheme utilizes continuous-variable quantum teleportation and can transmit two coherent states perfectly. By encoding classical information on quantum states, quantum network coding schemes can be utilized to transmit classical information. Scheme analysis shows that compared with the discrete-variable paradigms, the proposed CVQNC schemes provide better network throughput from the viewpoint of classical information transmission. By modulating the amplitude and phase quadratures of coherent states with classical characters, the first scheme and the second scheme can transmit \(4{\log _2}N\) and \(2{\log _2}N\) bits of information by a single network use, respectively.     

Experimental Demonstration of Quantum Lattice Gas Computation

We report an ensemble nuclear magnetic resonance (NMR) implementation of a quantum lattice gas algorithm for the diffusion equation. The algorithm employs an array of quantum information processors sharing classical information, a novel architecture referred to as a type-II quantum computer. This concrete implementa-tion provides a test example from which to probe the strengths and limitations of this new computation paradigm. The NMR experiment consists of encoding a mass density onto an array of 16 two-qubit quantum information processors and then following the computation through 7 time steps of the algorithm. The results show good agreement with the analytic solution for diffusive dynamics. We also describe numerical simulations of the NMR implementation. The simulations aid in determining sources of experimental errors, and they help define the limits of the implementation. PACS: 03.67.Lx; 47.11.+j; 05.60.-k     

How Do Two Observers Pool Their Knowledge About a Quantum System?

In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine independently obtained states of knowledge together to form a new state of knowledge, which is the state which would be possessed by someone having the combined information of both observers. Moreover, this combined state of knowledge can be found without reference to the manner in which the respective observers obtained their information. However, we show that in general this is not possible for quantum states of knowledge; in order to combine two quantum states of knowledge to obtain the state resulting from the combined information of both observers, these observers must also possess information about how their respective states of knowledge were obtained. Nevertheless, we emphasize this does not preclude the possibility that a unique, well motivated rule for combining quantum states of knowledge without reference to a measurement history could be found. We examine both the direct quantum analog of the classical problem, and that of quantum state-estimation, which corresponds to a variant in which the observers share a specific kind of prior information. PACS: 03.67.-a, 02.50.-r, 03.65.Bz     

Linking Classical and Quantum Key Agreement: Is There a Classical Analog to Bound Entanglement?

Abstract. After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocol is more powerful. We show that the limits of tolerable noise are identical for classical and quantum protocols in many cases. More specifically, we prove that a quantum state between two parties is entangled if and only if the classical random variables resulting from optimal measurements provide some mutual classical information between the parties. In addition, we present evidence which strongly suggests that the potentials of classical and of quantum protocols are equal in every situation. An important consequence, in the purely classical regime, of such a correspondence would be the existence of a classical counterpart of so-called bound entanglement, namely ``bound information' that cannot be used for generating a secret key by any protocol. This stands in contrast to what was previously believed.     

Public and private resource trade-offs for a quantum channel

Collins and Popescu realized a powerful analogy between several resources in classical and quantum information theory. The Collins?CPopescu analogy states that public classical communication, private classical communication, and secret key interact with one another somewhat similarly to the way that classical communication, quantum communication, and entanglement interact. This paper discusses the information-theoretic treatment of this analogy for the case of noisy quantum channels. We determine a capacity region for a quantum channel interacting with the noiseless resources of public classical communication, private classical communication, and secret key. We then compare this region with the classical-quantum-entanglement region from our prior efforts and explicitly observe the information-theoretic consequences of the strong correlations in entanglement and the lack of a super-dense coding protocol in the public-private-secret-key setting. The region simplifies for several realistic, physically-motivated channels such as entanglement-breaking channels, Hadamard channels, and quantum erasure channels, and we are able to compute and plot the region for several examples of these channels.     

N-qubit quantum teleportation, information splitting and superdense coding through the composite GHZ–Bell channel

We introduce a general odd qubit entangled system composed of GHZ and Bell pairs and explicate its usefulness for quantum teleportation, information splitting and superdense coding. After demonstrating the superdense coding protocol on the five qubit system, we prove that ‘2N + 1’ classical bits can be sent by sending ‘N + 1’ quantum bits using this channel. It is found that the five-qubit system is also ideal for arbitrary one qubit and two qubit teleportation and quantum information splitting (QIS). For the single qubit QIS, three different protocols are feasible, whereas for the two qubit QIS, only one protocol exists. Protocols for the arbitrary N-qubit state teleportation and quantum information splitting are then illustrated.     

Local controllability of quantum systems

We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.     

丢包环境中H.264视频编码的快速模式判决

目的 视频编码中传统的快速模式判决算法通常基于对视频源特性的分析,但如果考虑到信道传输中的差错,编码模式的率失真特性就会随之改变,快速模式判决算法的性能也会随之下降,需要考虑丢包环境对快速模式判决算法进行优化。方法 为了解决这一问题,首先分析了丢包环境下各种编码模式的端到端率失真特性,在此基础上提出了一个分层结构的快速模式判决算法。通过快速估计出丢包环境下skip和intra模式的编码率失真代价,进而将模式判决的路径划分为non-intra和non-skip。结果 将本文算法与基于遍历算法的容错视频编码算法进行对比实验,本文算法平均可以降低50%左右的编码时间,同时几乎不会降低率失真性能。结论 实验结果表明,在对丢包环境下端到端率失真代价进行估计的基础上,所提出的分层结构快速模式判决的算法,可以在保证解码端图像质量的同时,显著节省编码时间,满足实时视频通信中对低复杂度和鲁棒性的要求。     

Approximate Quantum Error Correction

The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate quantum error correction is possible. PACS: 03.67.H, 03.65.U     

Defining a test coverage criterion for model-level testing of FBD programs

ContextThe Programmable Logic Controller (PLC) is being integrated into the automation and control of computer systems in safety–critical domains at an increasing rate. Thoroughly testing such software to ensure safety is crucial. Function Block Diagram (FBD) is a popular data-flow programming language for PLC. Current practice often involves translating an FBD program into an equivalent C program for testing. Little research has been conducted on coverage of direct testing a data-flow program, such as an FBD program, at the model level. There are no commonly accepted structural test coverage criteria for data-flow programs. The objective of this study is to develop effective structural test coverage criterion for testing model-level FBD programs. The proposed testing scheme can be used to detect mutation errors at the logical function level.ObjectiveThe purpose of this study is to design a new test coverage criterion that can directly test FBD programs and effectively detect logical function mutation errors.MethodA complete test set for each function and function block in an FBD program are defined. Moreover, this method augments the data-flow path concept with a sensitivity check to avoid fault masking and effectively detect logical function mutation errors.ResultsPreliminary experiments show that this test coverage criterion is comprehensive and effective for error detection.ConclusionThe proposed coverage criterion is general and can be applied to real cases to improve the quality of data-flow program design.     

Quantum Erasure of Decoherence

We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the elements of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an example of environment-assisted correction, and present the generalization of the eraser setup for d-dimensional systems. Presented at the 38th Symposium on Mathematical Physics “Quantum Entanglement & Geometry”, Toruń, June 4–7, 2006.     

Quantum novel genetic algorithm based on parallel subpopulation computing and its application

A quantum novel genetic algorithm based on subpopulation parallel computing is presented, where quantum coding and rotation angle are improved to inspire more efficient genetic computing methods. In the algorithm, each axis of the solution space is divided into k parts, the individual (or chromosome) from each different subspace being coded differently, and the probability amplitude of each quantum bit or Q-bit is regarded as two paratactic genes. The basic quantum computing theory and classical quantum genetic algorithm are briefly introduced before a novel algorithm is presented for the function optimum and PID problem. Through a comparison between the novel algorithm and the classical counterpart, it is shown that the quantum inspired genetic algorithm performs better on running speed and optimization capability.     

基于蝶型网络模型的量子网络编码*

针对量子网络传输率低,信道利用率不高的问题,将经典网络编码的思想引入量子网络。基于蝶形网络模型,利用网络编码的思想,从经典信息和未知量子态两方面实现在量子网络上的最大流传输。而且在所提出的方案中,所有的信道都是量子信道,创新性的提出利用量子态作为“寄存器”实现经典信息的传递,有效的提高该方案的安全性。     

Thermodynamics and its prediction and CALPHAD modeling: Review,state of the art,and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2^nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.     

Quantum tasks using six qubit cluster states

The usefulness of the recent experimentally realized six photon cluster state by C. Y. Lu et al. (Nature 3:91, 2007) is investigated for quantum communication protocols like quantum teleportation and quantum information splitting (QIS) and dense coding. We show that the present state can be used for the teleportation of an arbitrary two qubit state deterministically. Later, we devise two distinct protocols for the QIS of an arbitrary two qubit state among two parties. We construct sixteen orthogonal measurement basis on the cluster state, which will lock an arbitrary two qubit state among two parties. The capability of the state for dense coding is investigated and it is shown that one can send five classical bits by sending only three qubits using this state as a shared entangled resource. We finally show that this state can also be utilised in the remote state preparation of an arbitrary two qubit state.     

CLASSICAL AND NONCLASSICAL REPRESENTATIONS IN PHYSICS: PHYSICS 1

Dynamical representations used in physics are analyzed from a “second-order” viewpoint, as distinction systems constructed by an observer in interaction with an object. The creation, conservation, and destruction of distinctions can be understood on the basis of a distinction dynamics. The fundamental mechanism is the variation through recombination and selective retention of closed combinations. The conservation of all distinctions is shown to provide a demarcation criterion, distinguishing classical from nonclassical representations. Different nonclassical representations (thermodynamics, quantum mechanics, relativity theory) are classified on the basis of distinctions they do not conserve. It is argued that the specific structures of these nonclassical representations can be reconstructed by studying the properties of nontrivial closure.     

On the second-order asymptotics for entanglement-assisted communication

The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon’s classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms of the quantum mutual information and does not increase in the presence of a noiseless quantum feedback channel from receiver to sender. In this work, we investigate second-order asymptotics of the entanglement-assisted classical communication task. That is, we consider how quickly the rates of entanglement-assisted codes converge to the entanglement-assisted classical capacity of a channel as a function of the number of channel uses and the error tolerance. We define a quantum generalization of the mutual information variance of a channel in the entanglement-assisted setting. For covariant channels, we show that this quantity is equal to the channel dispersion and thus completely characterize the convergence toward the entanglement-assisted classical capacity when the number of channel uses increases. Our results also apply to entanglement-assisted quantum communication, due to the equivalence between entanglement-assisted classical and quantum communication established by the teleportation and super-dense coding protocols.     

Fiber Optics Protocols for Quantum Communication

We show how the techniques developed for long distance quantum key distribution in optical fibers can be used to demonstrate other quantum information processing and communication protocols. We present a fiber optics realization of the Deutsch–Jozsa and Bernstein–Vazirani algorithms. We describe a method, called “error filtration”, for reducing errors in quantum communication channels, and present an experimental implementation thereof. We discuss the cryptographic primitive of string flipping, and present an experimental implementation which has higher security than achievable using any classical protocol.     

Certificateless network coding proxy signatures from lattice

Network coding can improve the information transmission efficiency and reduces the network resource consumption, so it is a very good platform for information transmission. Certificateless proxy signatures are widely applied in information security fields. However, certificateless proxy signatures based on classical number theory are not suitable for the network coding environment and cannot resist the quantum computing attacks. In view of this, we construct certificateless network coding proxy signatures from lattice (LCL-NCPS). LCL-NCPS is new multi-source signature scheme which has the characteristics of anti-quantum, anti-pollution and anti-forgery. In LCL-NCPS, each source node user can output a message vector to intermediate node and sink node, and the message vectors from different source nodes will be linearly combined to achieve the aim of improving the network transmission rate and network robustness. In terms of efficiency analysis of space dimension, LCL-NCPS can obtain the lower computation complexity by reducing the dimension of proxy key. In terms of efficiency analysis of time dimension, LCL-NCPS has higher computation efficiency in signature and verification.