Sharif Digital Repository

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 the achievable entanglement between the reference site and various vertices. We observe that the maximum of these upper bounds is one 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 one 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... 

The effective resistance or two-point resistance between two nodes of a resistor network is the potential difference that appears across them when a unit current source is applied between the nodes as terminals. This concept arises in problems which deal with graphs as electrical networks including random walks, distributed detection and estimation, sensor networks, distributed clock synchronization, collaborative filtering, clustering algorithms and etc. In the previous paper (Jafarizadeh et al. in J. Math. Phys. 50:023302, 2009) a recursive formula for evaluation of effective resistances on the so-called distance-regular networks was given based on the Christoffel-Darboux identity. In this... 

We investigate the creation of optimal entanglement in axially symmetric networks. The proposed network is one in which the connections are organized using a group table - in other words, using group association schemes. We show that optimal entanglement can be provided on such networks by adjusting couplings and the initial state. We find that the optimal initial state is a simple locally excited state. Moreover we obtain an analytic formula for the entanglement achievable between vertex pairs located in the same or conjugate strata and calculate their relevant optimal couplings. For those pairs located in non-conjugate strata, two upper bounds are presented. These results are also checked...