A Class of Linear Positive Maps in Matrix Algebras II

We provide a class of linear trace preserving positive maps on matrix algebras which is a generalization of that in [7]. A systematic construction by means of spectra of generators of SU(n) is discussed.Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004.Supported by the Grant-in-Aid for JSPS Research Fellows.Supported by the Grant PBZ-MIN-008/P03/2003.     

Entanglement,Purity, and Information Entropies in Continuous Variable Systems

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particu-lar, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entan-glement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.Presented at the International Conference “Entanglement, Information & Noise”, Krzyżowa, Poland, June 14–20, 2004.     

Codes for Copyright Protection: The Case of Two Pirates

The problem of finding so-called pirates via the minimum Hamming distance decoding is considered for the simplest case of two pirates. We prove that for all q ≥ 3 there exist “good” _q-ary codes capable of finding at least one pirate by the minimum distance decoding in the Hamming metric.__________Translated from Problemy Peredachi Informatsii, No. 2, 2005, pp. 123–127.Original Russian Text Copyright © 2005 by Kabatiansky.Supported in part by the Russian Foundation for Basic Research, project no. 03-01-00098.     

A Note on Positive Maps and Classification of States

The relation between positive maps on M_n and subsets of self-adjoint elements from M_n ⊗ M_n is investigated. It has been shown that there exists the isomorphism between the set of all positive normalized maps on M_n and the subset of separable states on M_n ⊗ M_n.Presented at the International Conference “Entanglement, Information & Noise”, Krzyżowa, Poland, June 14-20, 2004.Supported by the Grant-in-Aid for JSPS Research Fellows.Supported by the Grant PBZ-MIN-008/P03/2003.     

Experimental investigation of forecasting methods based on data compression algorithms

We suggest and experimentally investigate a method to construct forecasting algorithms based on data compression methods (or the so-called archivers). By the example of predicting currency exchange rates we show that the precision of thus obtained predictions is relatively high.Translated from Problemy Peredachi Informatsii, No. 1, 2005, pp. 74–78.Original Russian Text Copyright © 2005 by Ryabko, Monarev.Supported in part by the Russian Foundation for Basic Research, project no. 03-01-00495, and INTAS, Grant 00-738.     

Tensor Product Decomposition,Entanglement, and Bogoliubov Transformations for Two Fermion System

We consider the two-fermion system whose states are subjected to the superselection rule forbidding the superposition of states with fermionic and bosonic statistics. This implies that separable states are described only by diagonal density matrices. Moreover, we find the explicit formula for the entanglement of formation, which in this case cannot be calculated properly using Wootters’s concurrence. We also discuss the problem of the choice of tensor product decompo-sition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators. Finally, we show that there exist states which are separable with respect to all tensor product decompositions of the underlying Hilbert space.Presented at the 36th Symposium on Mathematical Physics, “Open Systems & Quantum Information”, Toruń, Poland, June 9–12, 2004.     

Spin-Based Quantum Information Processing in Magnetic Quantum Dots

We define the qubit as a pair of singlet and triplet states of two electrons in a He-type quantum dot (QD) placed in a diluted magnetic semiconductor (DMS) medium. The molecular field is here essential as it removes the degeneracy of the triplet state and strongly enhances the Zeeman splitting. Methods of qubit rotation as well as two-qubit operations are suggested. The system of a QD in a DMS is described in a way which allows an analysis of the decoherence due to spin waves in the DMS subsystem.on leave from Institute of Physics, Odessa UniversityPresented at the 36th Symposium on Mathematical Physics, “Open Systems & Quantum Information”, Toruń, Poland, June 9–12, 2004.     

Code bounds for multiple packings over a nonbinary finite alphabet

The problem of constructing asymptotic bounds for multiple packings in the space of q-ary sequences of length n is considered. For the zero rate, tightness of the expurgation bound is proved.Translated from Problemy Peredachi Informatsii, No. 1, 2005, pp. 28–38.Original Russian Text Copyright © 2005 by Blinovsky.Supported in part by the Russian Foundation for Basic Research, project nos. 03-01-00592 and 03-01-00098.     

Some Remarks on the Role of Minimal Length of Positive Maps in Constructing Entanglement Witnesses

The main objective of this paper is to discuss correspondence between the concept of entanglement witnesses (self-adjoint operators on a composite Hilbert space that are, in general, not positive, but are positive on separable states) and positive maps which are not completely positive. The notion of minimal length of linear positive map is introduced and the role of this quantity in the constructing of entanglement witnesses is explained.Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004.Supported by the Grant PBZ-MIN-008/P03/2003.     

Cooperative multiple access channels: Achievable rates and optimal resource allocation

We investigate the multiple access channels (MAC) where sources can cooperate via half-duplex relaying and refer to it as cooperative MAC channels (CMAC). Assuming perfect channel state information (CSI) at the transmitters and the receivers, we determine the bounds on the achievable rate region of a Gaussian CMAC channel and an inner bound on the outage capacity region of a fading CMAC channel. Based on superposition modulation, a half-duplex cooperative relay scheme with optimal resource allocation is proposed to achieve the bounds of capacity region. Analytical results and simulation results show that the achievable rate region of a Gaussian CMAC channel is larger than that of a Gaussian MAC channel with direct transmission (DT) schemes. But they have the same achievable sum rate. Moreover, the proposed scheme can provide higher outage capacity region than DT schemes in a fading MAC channel due to the fact that sources can share the resources with each other to reduce outages. Supported partially by the National Natural Science Foundation of China (Grant No. 60672079), the Natural Science Foundation of Jiangsu Province (Grant No. BK2006701), and the Natinoal High-Tech Research & Development Program of China (Grant No. 2007AA01Z267)     

Nonbinary Error-Correcting Codes with One-Time Error-Free Feedback

We show that, using one-time error-free feedback, it is possible to attain the asymptotic Hamming bound if the number of errors is fixed.__________Translated from Problemy Peredachi Informatsii, No. 2, 2005, pp. 63–67.Original Russian Text Copyright © 2005 by Bassalygo.Supported in part by the Russian Foundation for Basic Research, project no. 03-01-00098.     

Data flow analysis of distributed communicating processes

Data flow analysis is a technique essential to the compile-time optimization of computer programs, wherein facts relevant to program optimizations are discovered by the global propagation of facts obvious locally. This paper extends several known techniques for data flow analysis of sequential programs to the static analysis of distributed communicating processes. In particular, we present iterative algorithms for detecting unreachable program statements, and for determining the values of program expressions. The latter information can be used to place bounds on the size of variables and messages. Our main innovation is theevent spanning graph, which serves as a heuristic for ordering the nodes through which data flow information is propagated. We consider bothstatic communication, where all channel arguments are constants, and the more difficultdynamic communication, where channel arguments may be variables and channels may be passed as messages.A preliminary version of this paper appeared in the proceedings of the Sixth Annual ACM Symposium on Principles of Programming Languages, pp. 257–268, June 1979.Supported by National Science Foundation Grant NSF MCS82-00269 and the Office of Naval Research Contract N00014-80-C-0647.Supported by National Science Foundation Grants NSF DCR-8505873 and NSF CCR-8704309.     

Non-Decomposable Quantum Dynamical Semigroups and Bound Entangled States

We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4 × 4 bipartite system.Presented at the International Conference “Entanglement, Information & Noise”, Krzyżowa, Poland, June 14–20, 2004.     

Superselection Sectors,Pure States,Bose and Fermi Distributions by Completely Positive Quantum-Motions

The connection of the operators V, building up the Kossakowski-Lindblad generator, with the asymptotic states of the corresponding completely positive quantum-maps is discussed. Maps leading to decoherence are constructed, the importance of zero-modes in the absolute value of V for the generation of pure states from arbitrary mixed states is illustrated. The universal rôle of equipartite states appears when unitary V are chosen. The ‘damped oscillator model’ is generalized to yield Bose and Fermi distributions as asymptotic states for systems described by a Hamiltonian and other constants of motion. Calculations are performed in .nite dimensional Hilbert spaces.Presented at the International Conference “Entanglement, Information & Noise“, Krzyżowa, Poland, June 14-20, 2004.     

A 485ps 64-Bit Parallel Adder in 0.18$\mu$m CMOS

This paper presents an optimized 64-bit parallel adder. Sparse-tree architecture enables low carry-merge fan-outs and inter-stage wiring complexity. Single-rail and semi-dynamic circuit improves operation speed. Simulation results show that the proposed adder can operate at 485ps with power of 25.6mW in 0.18μm CMOS process. It achieves the goal of higher speed and lower power.     

System reduction via truncated Hankel matrices

The problem of approximating Hankel operators of finite or infinite rank by lower-rank Hankel operators is considered. For efficiency, truncated Hankel matrices are used as the intermediate step before other existing algorithms such as theCF algorithms are applied to yield the desirable approximants. If the Hankel operator to be approximated is of finite rank, the order of approximation by truncated Hankel operators is obtained. It is also shown that when themths-number is simple, then rational symbols of the best rank-m Hankel approximants of thenth truncated Hankel matrices converge uniformly to the corresponding rational symbol of the best rank-m Hankel approximant of the original Hankel operator asn tends to infinity. Supported by SDIO/IST managed by the U.S. Army under Contract No. DAAL03-87-K-0025 and also supported by the National Science Foundation under Grant No. DMS 8602337. Supported by SDIO/IST managed by the U.S. Army under Contract No. DAAL03-87-K-0025. Supported by the National Science Foundation under Grant No. DMS 8602337.     

A bandwidth efficient two-user cooperative diversity system with limited feedback

A two-user cooperative diversity system based on Alamouti signaling was proposed, which utilizes the orthogonal structure of Alamouti signaling to make cooperative users relay on the shared channel resources so that the spectral efficiency of the traditional cooperative system can be improved. When M-ary phase shift keying (M-PSK) modulation and an improved selection decode-and-forward (SDF) relaying protocol with limited feedback are used at the users and m(m ⩾1) receive antennas are configured at the base station, the average bit-error-rate (BER) system performance for statistically similar uplink channels was derived and it was verified by simulations. Under various channel scenarios of interest, numerical and simulation results show that the diversity gain achieved and the BER performance of the proposed system increase with the interuser channel quality, and the full transmit diversity order of two can be obtained for sufficiently high interuser signal-to-noise ratios (SNRs). Supported by the National High-Tech Research & Development Program of China (Grant No. 2006AA01Z270), the National Natural Science Foundation of China-Guangdong (Grant No. U0635003), the Natural Science Foundation of Shaanxi Province (Grant No. 2007F07), the “111” Project (Grant No. B08038), and the Open Research Fund of State Key Laboratory of Rail Traffic Control and Safety, Bejing Jiaotong University (Grant No. RCS2008K003)     

A Simple Proof of the Jamiołkowski Criterion for Complete Positivity of Linear Maps

We give a simple direct proof of the Jamiołkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accessible for physicists than other ones found in the literature and provides a systematic method to give any set of Kraus matrices of the Kraus decomposition.Presented at the 36th Symposium on Mathematical Physics, “Open Systems & Quantum Information”, Toruń, Poland, June 9-12, 2004.     

Decay of Entanglement Due to Pure Dephasing: the Role of Geometry of Entangled States

The study of the effect that pure dephasing has on the entanglement of a pair of two-level systems shows that complete disentanglement may be caused by partial pure dephasing for some initial entangled states. We examine the behaviour of the entanglement of two confined charge states under the influence of partial pure dephasing introduced by a super-Ohmic reservoir (typical for semiconductors). We classify the set of completely dephasible states and provide an explanation of this effect. Presented at the 38th Symposium on Mathematical Physics “Quantum Entanglement & Geometry”, Toruń, June 4–7, 2006.