arXiv subjects

Mohammad Ali Jafarizadeh

Publications and source records attributed to Mohammad Ali Jafarizadeh.

4 recordsLinked to original sources

arXiv2019

Continuous k-frames and their duals

k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by continuous super positions. We construct a continuous k-frame, so called ck-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a ck-frame and we prove some new results about it.

math.FA↗

arXiv2015

Construction of quantum codes based on self-dual orientable embeddings of complete multipartite graphs complete multipartite graphs

This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the com- plete graphs K4r+1 and K4s and by current graphs and rotation schemes. and s are both divisible by 4.

quant-ph↗

arXiv2015

Topological quantum codes from self-complementary self-dual graphs

In this paper we present two new classes of binary quantum codes with minimum distance of at least three, by self-complementary self-dual orientable embeddings of voltage graphs and Paley graphs in the Galois field GF(pr), where p is a prime number and r is a positive integer. The parameters of two new classes of quantum codes are [[(2k+2)(8k+ 7); 2(8k^2+7k); d]] and [[(2k+2)(8k+9); 2(8k^2+9k+1); d]] respectively, where d>=3. For these quantum codes, the code rate approaches 1 as k goes to infinity.

quant-ph↗

arXiv2010

Generating maximally entangled distant pair in invariant stratification spin networks

In this paper we study the generation of Bell states between distant vertices in a permanently coupled quantum spin network, interacting via invariant stratification graphs. To begin with we establish a class of upper bounds over achievable entanglement between the reference site and various vertices. We observe that the maximum of these upper bounds is 1 e-bit. We conclude that the reference site can generate a Bell state with a vertex if the corresponding upper bound of the vertex is 1 e-bit. Thus for generation of a Bell state this upper bound must be saturated. Taking this into account, we obtain the characteristic constraint of the proper graphs. We introduce a special class of antipodal invariant stratification graphs, which is called reflective, whereas the antipode vertex obeys the characteristic constraint. We also show that the antipodal association scheme graphs are reflective so Bell states can be generated between the antipodal vertices. Moreover we observe that in such graphs the proper Hamiltonian that enables creation of Bell state is the Heisenberg interaction between vertex pairs.

quant-ph↗