Quantum protocols at presence of nonabelian superselection rules in the framework of algebraic model

In this paper, we study the influence of nonabelian superselection rules on the transfer of quantum information with the help of qubits on the base of an algebraic model and formulate quantum protocols. We pay the main attention to the superselection structure of the algebra of observables [Formula: see text] defined by the Cuntz algebra [Formula: see text] (a field algebra) that contains [Formula: see text] as a pointwise fixed subalgebra with respect to the action of the gauge group [Formula: see text]. We prove that it is possible to code information only with the help of states such that projectors on them belong to the algebra of observables. These projectors commute with the elements of the representation of the group [Formula: see text], and therefore allow the recipient to restore the obtained information.

Design of Reed-Solomon Encoder for Error Detection in DRAM Cells

This paper investigates the design of Reed Solomon (RS) encoder. Based on the message symbols, the RS encoder generates the code-word. By carrying out a polynomial division using Galois Field algebra, the parity symbols are calculated. Reed-Solomon codes are one of the most effective and effective non-binary error codes to detect and correct burst errors. This is the focus work for my dissertation to implement RS encoder and decoder that is a complex algorithm and it is used for the reliable memory operation in a system. The RS Encoder and decoder are design in structural modeling and develop the hardware. The sift and multiplier type divider is used for Encoder and Syndrome module design.

Jones Type Basic Construction on Hopf Spin Models

Let H be a finite dimensional C∗-Hopf algebra and A the observable algebra of Hopf spin models. For some coaction of the Drinfeld double D(H) on A, the crossed product A⋊D(H)^ can define the field algebra F of Hopf spin models. In the paper, we study C∗-basic construction for the inclusion A⊆F on Hopf spin models. To achieve this, we define the action α:D(H)×F→F, and then construct the resulting crossed product F⋊D(H), which is isomorphic A⊗End(D(H)^). Furthermore, we prove that the C∗-basic construction for A⊆F is consistent to F⋊D(H), which yields that the C∗-basic constructions for the inclusion A⊆F is independent of the choice of the coaction of D(H) on A.

Improving Calculation Accuracy of Digital Filters Based on Finite Field Algebra

The applications of digital filters based on finite field algebra codes require their conjugation with positional computing structures. Here arises the task of algorithms and structures developed for converting the positional notation codes to finite field algebra codes. The paper proposes a method for codes conversion that possesses several advantages over existing methods. The possibilities and benefits of optimization of the computational channel structure for digital filter functioning based on the codes of finite field algebra are shown. The modified structure of computational channel is introduced. It differs from the traditional structure by the fact that there is no explicit code converter in it. The main principle is that the “reference” values of input samples, which are free from the error of the analog-digital converter, are used as input samples. The proposed approach allows achieving a higher quality of signal processing in advanced digital filters.

Optimization of the FIR Filter Structure in Finite Residue Field Algebra

This paper introduces a method for optimizing non-recursive filtering algorithms. A mathematical model of a non-recursive digital filter is proposed and a performance estimation is given. A method for optimizing the structural implementation of the modular digital filter is described. The essence of the optimization is that by using the property of the residue ring and the properties of the symmetric impulse response of the filter, it is possible to obtain a filter having almost a half the length of the impulse response compared to the traditional modular filter. A difference equation is given by calculating the output sample of modules p1 … pn in the modified modular digital filter. The performance of the modular filters was compared with the performance of positional non-recursive filters implemented on a digital signal processor. An example of the estimation of the hardware costs is shown to be required for implementing a modular digital filter with a modified structure. This paper substantiates the expediency of applying the natural redundancy of finite field algebra codes on the example of the possibility to reduce hardware costs by a factor of two. It is demonstrated that the accuracy of data processing in the modular digital filter is higher than the accuracy achieved with the implementation of filters on digital processors. The accuracy advantage of the proposed approach is shown experimentally by the construction of the frequency response of the non-recursive low-pass filters.

HADAMARD STATES FOR THE VECTOR POTENTIAL ON ASYMPTOTICALLY FLAT SPACETIMES

We develop a quantization scheme for the vector potential on globally hyperbolic spacetimes which realizes it as a locally covariant conformal quantum field theory. This result allows us to employ on a large class of backgrounds, which are asymptotically flat at null infinity, a bulk-to-boundary correspondence procedure in order to identify for the underlying field algebra a distinguished ground state which is of Hadamard form.