A Construction of Linear Codes over \f_{2^t} from Boolean Functions

In this paper, we present a construction of linear codes over \f_{2^t} from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes \tilde{\C}_{f} and \C_f (see Theorem \ref{thm-maincode1} and Theorem \ref{thm-maincodenew}) over \f_{2^t} from a Boolean function f:\f_{q}\rightarrow \f_2, where $q=2^n$ and \f_{2^t} is some subfield of \f_{q}. The complete weight enumerator of \tilde{\C}_{f} can be easily determined from the Walsh spectrum of $f$, while the weight distribution of the code \C_f can also be easily settled. Particularly, the number of nonzero weights of \tilde{\C}_{f} and \C_f is the same as the number of distinct Walsh values of $f$. As applications of this construction, we show several series of linear codes over \f_{2^t} with two or three weights by using bent, semibent, monomial and quadratic Boolean function $f$

Linear codes with a few weights from inhomogeneous quadratic functions

Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes with a few weights are constructed from inhomogeneous quadratic functions over the finite field \gf(p), where $p$ is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined

A Class of Linear Codes with a Few Weights

Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of linear codes with a few weights over the finite field \gf(p) are presented and their weight distributions are also determined, where $p$ is an odd prime. Some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear codes.Comment: arXiv admin note: text overlap with arXiv:1503.06512 by other author

Realization of Probabilistic Identification and Clone of Quantum-States II Multiparticles System

We realize the probabilistic cloning and identifying linear independent quantum states of multi-particles system, given prior probability, with universal quantum logic gates using the method of unitary representation. Our result is universal for separate state and entanglement. We also provide the realization in the condition given $M$ initial copies for each state.Comment: 18 Pages, 3 Figures, ReVTe

Conditions for manipulation of a set of entangled pure states

We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical communication. If $k=N$, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states.Comment: 5 Pages, no Figure, REVTeX. The generalization of quant-ph/990801

Quantum authentication using entangled state

A scheme of quantum authentication is presented. Two parties share Einstein-Podolsky-Rosen (EPR) pairs previously as the authentication key which servers as encoder and decoder. The authentication is accomplished with local controlled-NOT operations and unitary rotations. It is shown that our scheme is secure even in the presence of an eavesdropper who has complete control over both classical and quantum channels. Another character of this protocol is that the EPR sources are reusable. The robustness of this protocol is also discussed.Comment: 5 Pages, no Figure, Eq.(7) is correcte

Spin dynamics in the XY model

We study the evolution of entanglement, quantum correlation and classical correlation for the one dimensional XY model in external transverse magnetic field. The system is initialized in the full polarized state along the z axis, after annealing, different sites will become entangled. We study the three kinds of correlation for both the nearest and the next-nearest neighbor sites. We find that for large anisotropy parameter the quantum phase transition can be indicated by the dynamics of classical correlation between the nearest neighbor sites. We find that the dynamics of entanglement for both the nearest and next-nearest neighbor sites show significantly different behaviors with different values of magnetic field. We also find that the evolution of quantum correlation and classical correlation of the nearest neighbor sites are obviously different from those of the next-nearest neighbor sites.Comment: 9 pages, new references added, some mistakes correcte

Unconditionally Secure Quantum Coin Tossing via Entanglement Swapping

An unconditionally secure quantum cion tossing protocol for two remote participants via entangled swapping is presented. The security of this protocol is guaranteed by the nonlocal property of quantum entanglement and the classical complexity.Comment: Withdraw. The scheme presented is insecur

Efficient Quantum Ratchet

Quantum resonance is one of the main characteristics of the quantum kicked rotor, which has been used to induce accelerated ratchet current of the particles with a generalized asymmetry potential. Here we show that by desynchronizing the kicked potentials of the flashing ratchet [Phys. Rev. Lett. 94, 110603 (2005)], new quantum resonances are stimulated to conduct directed currents more efficiently. Most distinctly, the missed resonances $\kappa=1.0\pi$ and $\kappa=3.0\pi$ are created out to induce even larger currents. At the same time, with the help of semiclassical analysis, we prove that our result is exact rather than phenomenon induced by errors of the numerical simulation. Our discovery may be used to realize directed transport efficiently, and may also lead to a deeper understanding of symmetry breaking for the dynamical evolution.Comment: 10 pages, 4 figures. Comments welcom

Engineering of multi-dimensional entangled states of photon pairs using hyper-entanglement

Multi-dimensional entangled states have been proven to be more powerful in some quantum information process. In this paper, down-converted photons from spontaneous parametric down conversion(SPDC) are used to engineer multi-dimensional entangled states. A kind of multi-degree multi-dimensional Greenberger-Horne-Zeilinger(GHZ) state can also be generated. The hyper-entangled photons, which are entangled in energy-time, polarization and orbital angular momentum (OAM), is proved to be useful to increase the dimension of systems and investigate higher-dimensional entangled states.Comment: 4pages,2figure