New Optimal Asymmetric Quantum Codes Derived from Negacyclic Codes

The construction of quantum maximum-distance-separable (MDS) codes have been studied by many researchers for many years. Here, by using negacyclic codes, we construct two families of asymmetric quantum codes. The first family is the asymmetric quantum codes with parameters $[[q^{2}+1,q^{2}+1-2(t+k+1),(2k+2)/(2t+2)]]_{q^{2}}$ , where 0≤t≤k≤(q?1)/2, $q \equiv1(\operatorname{mod} 4)$ , and k, t are positive integers. The second one is the asymmetric quantum codes with parameters $[[(q^{2}+1)/2,(q^{2}+1)/2-2(t+k),(2k+1)/(2t+1)]]_{q^{2}}$ , where 1≤t≤k≤(q?1)/2, and k, t are positive integers. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.     

Some Families of Asymmetric Quantum MDS Codes Constructed from Constacyclic Codes

Quantum maximal-distance-separable (MDS) codes that satisfy quantum Singleton bound with different lengths have been constructed by some researchers. In this paper, seven families of asymmetric quantum MDS codes are constructed by using constacyclic codes. We weaken the case of Hermitian-dual containing codes that can be applied to construct asymmetric quantum MDS codes with parameters \([[n,k,d_{z}/d_{x}]]_{q^{2}}\). These quantum codes are able to correct quantum errors with greater asymmetry. Moreover, these quantum codes constructed in this paper are different from the ones in the literature.     

Quantum Codes Derived from Cyclic Codes

In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical) cyclic codes whose defining set consists of only one cyclotomic coset containing at least two consecutive integers.     

X-ray spectra and valence states of cations in nanostructured half-doped $$\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}$$ manganite

Soft X-ray absorption (XAS) and emission (XES) spectroscopies were applied to determine valence states of manganese ions in nanostructured powder of half-doped \(\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}\) manganite obtained by milling in a ball mill. XAS spectra were measured both in surface-sensitivity total electron-yield and in bulk-sensitivity total fluorescence-yield modes. O K\(_{\upalpha }\) XES and O 1s XAS spectra characterized the occupied and unoccupied partial O 2p densities of states are compared with band-structure calculations made using the TB-LMTO-ASA codes. Experimental Mn 2p, Ca 2p, and La 3\(d\) XAS spectra are compared with results of crystal field atomic multiplet calculations. For the nanostructured system of \(\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}\), concentrations of Mn\(^{4+}\) ions are found to be increased with increasing the time of milling.     

Synthesis and Study the Effect of Donor-Acceptor Substituent on Fluorescence Behavior of Thieno[3, 2-c]pyridine Derivatives

4-Hetero-1-yl-2-bromothieno[3,2-c]pyridines 3(a–d) were synthesized by the reaction of 2-bromo-4-chlorothieno[3,2-c]pyridine (1) and cyclic amine 2(a–d), which on Suzuki coupling with substituted boronic acids 4(a–f) exclusively converted to corresponding 4-hetero -1-yl-2-arylthieno[3,2-c]pyridine 5(a–x) in good yields. The effect of donor-acceptor substituent on absorption emission properties and fluorescent quantum yield of new thienopyridine derivatives 5(a-x) were studied.     

A Topos for Algebraic Quantum Theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos \({\mathcal{T}(A)}\) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra \({\underline{A}}\) . According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum \({\underline{\Sigma}(\underline{A})}\) in \({\mathcal{T}(A)}\) , which in our approach plays the role of the quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on \({\underline{\Sigma}}\) , and self-adjoint elements of A define continuous functions (more precisely, locale maps) from \({\underline{\Sigma}}\) to Scott’s interval domain. Noting that open subsets of \({\underline{\Sigma}(\underline{A})}\) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos \({\mathcal{T}(A)}\).These results were inspired by the topos-theoretic approach to quantum physics proposed by Butterfield and Isham, as recently generalized by Döring and Isham.     

Some Families of Quantum BCH Codes

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have been studied extensively. The Calderbank-Shor-Steane (CSS) construction, especially Steane’s enlargement, and Hermitian construction are the most widely used methods in design of quantum codes. The BCH codes containing their Euclidean dual or Hermitian dual codes can be used to generate good stabilizer codes. Therefore, we can construct quantum codes by classical BCH codes over finite fields in this paper. Firstly, we study the properties of such classical BCH codes in terms of the cyclotomic cosets. It is convenient to compute the dimension of new quantum BCH codes. Meanwhile, it ensures that classical BCH codes are Euclidean dual-containing or Hermitian dual-containing. These results about suitable cyclotomic cosets make it possible to construct several new families of nonbinary quantum BCH codes with a given parameter set. Compared with the ones available in the literature, the quantum BCH codes in our schemes have good parameters. In particular, we extend to more general cases than known results.

     

Physics Without Physics

David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D’Ariano et al., 2017) and of free quantum field theory (D’Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a re-foundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the currently observed regime where discreteness is not visible is the so-called “relativistic regime” of small wavevectors, which holds for all energies ever tested (and even much larger), where the usual free quantum field theory is perfectly recovered. In the present quantum discrete theory Einstein relativity principle can be restated without using space-time in terms of invariance of the eigenvalue equation of the automaton/walk under change of representations. Distortions of the Poincaré group emerge at the Planck scale, whereas special relativity is perfectly recovered in the relativistic regime. Discreteness, on the other hand, has some plus compared to the continuum theory: 1) it contains it as a special regime; 2) it leads to some additional features with GR flavor: the existence of an upper bound for the particle mass (with physical interpretation as the Planck mass), and a global De Sitter invariance; 3) it provides its own physical standards for space, time, and mass within a purely mathematical adimensional context. The paper ends with the future perspectives of this project, and with an Appendix containing biographic notes about my friendship with David Finkelstein, to whom this paper is dedicated.     

List Decoding of Arıkan’s PAC Codes

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2.     

Deformations of spectral triples and their quantum isometry groups via monoidal equivalences

In this paper, we propose a new procedure to deform spectral triples and their quantum isometry groups. The deformation data are a spectral triple \((\mathcal {A},\mathcal {H}, D)\), a compact quantum group \({\mathbb {G}}\) acting algebraically and by orientation-preserving isometries on \((\mathcal {A},\mathcal {H},D)\) and a unitary fiber functor \(\psi \) on \({\mathbb {G}}\). The deformation procedure is a proper generalization of the cocycle deformation of Goswami and Joardar.     

Optical wireless quantum communication coding system using decimal convertor

In this study, a system of microring resonators and an add/drop filter are used to generate a large bandwidth signal as a localized multi wavelength, applicable for continuous dense coding and continuous variable encoding generation. This technique uses the Kerr nonlinear type of light in the MRR to generate multi wavelength of bright and dark soliton for quantum network cryptography. Afterwards, generated bright and dark optical pulses are converted into digital logic quantum codes using a decimal convertor system in which transmission of secured information are performed via an optical wireless communication system. Results show that ranges of multi bright and dark soliton wavelengths from 1.45 to $1.65\,\upmu \mathrm{m}$ with central wavelength of $1.55\,\upmu \mathrm{m}$ could be simulated, where the FWHM and FSR of 50 and 1,440 pm are obtained, respectively.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Concentration of Measure for Quantum States with a Fixed Expectation Value

Given some observable H on a finite-dimensional quantum system, we investigate the typical properties of random state vectors \({|\psi\rangle}\) that have a fixed expectation value \({\langle\psi|H|\psi\rangle=E}\) with respect to H. Under some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We discuss the implications of our results as new proof tools in quantum information theory and to study phenomena in quantum statistical mechanics. As a by-product, we derive a method to sample the resulting distribution numerically, which generalizes the well-known Gaussian method to draw random states from the sphere.     

Spectral Properties of Quantum Walks on Rooted Binary Trees

We define coined quantum walks on the infinite rooted binary tree given by unitary operators $U(C)$ on an associated infinite dimensional Hilbert space, depending on a unitary coin matrix $C\in U(3)$ , and study their spectral properties. For circulant unitary coin matrices $C$ , we derive an equation for the Carathéodory function associated to the spectral measure of a cyclic vector for $U(C)$ . This allows us to show that for all circulant unitary coin matrices, the spectrum of the quantum walk has no singular continuous component. Furthermore, for coin matrices $C$ which are orthogonal circulant matrices, we show that the spectrum of the Quantum Walk is absolutely continuous, except for four coin matrices for which the spectrum of $U(C)$ is pure point.     

Local-Entire Cyclic Cocycles for Graded Quantum Field Nets

In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over ${\mathbb{R}}$ , and we carried out a detailed analysis of these objects on certain models of superconformal nets. In the present article, we show that these locally bounded functionals give rise to local-entire cyclic cocycles (generalized JLO cocycles) which are homotopy-invariant for a suitable class of perturbations of the dynamical system. Thus we can associate meaningful noncommutative geometric invariants to those graded quantum dynamical systems.     

Euler’s Theorem for Homogeneous White Noise Operators

In this paper we introduce a new notion of λ ?order homogeneous operators on the nuclear algebra of white noise operators. Then, we give their Fock expansion in terms of quantum white noise (QWN) fields \(\{a_{t},\: a^{*}_{t}\, ; \; t\in \mathbb {R}\}\). The quantum extension of the scaling transform enables us to prove Euler’s theorem in quantum white noise setting.     

General quantum field theories and strict locality

A class of general quantum field theories without explicit use of fieldsA(x) is defined by a set of postulates for the von Neumann algebras ? _C of local observables. The vacuum state is cyclic with respect to any ? _C , and the Borchers tube theorem is shown to hold. Some ? _C are factors and not of finite type. A property of local observables called strict locality is formulated and expressed by means of a necessary and sufficient condition for the algebras ? _C . It is proved for finite regions.     

Dynamical behaviors of FRW universe containing a positive/negative potential scalar field in loop quantum cosmology

The dynamical behaviors of FRW Universe containing a posivive/negative potential scalar field in loop quantum cosmology scenario are discussed. The method of the phase-plane analysis is used to investigate the stability of the Universe. It is found that the stability properties in this situation are quite different from the classical cosmology case. For a positive potential scalar field coupled with a barotropic fluid, the cosmological autonomous system has five fixed points and one of them is stable if the adiabatic index $\gamma $ satisfies $0<\gamma <2$ . This leads to the fact that the universe just have one bounce point instead of the singularity which lies in the quantum dominated area and it is caused by the quantum geometry effect. There are four fixed points if one considers a scalar field with a negative potential, but none of them is stable. Therefore, the universe has two kinds of bounce points, one is caused by the quantum geometry effect and the other is caused by the negative potential, the Universe may enter a classical re-collapse after the quantum bounce. This hints that the spatially flat FRW Universe containing a negative potential scalar field is cyclic.     

A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems

In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.