Entangled bases with fixed Schmidt number

Unextendible maximally entangled bases and mutually unbiased bases

Equi-entangled bases in arbitrary dimensions

For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many ...

Generation of entangled states of two traveling modes for fixed number of photon

We present an scheme to generate entangled state between two traveling modes for fixed number of photon, which is based on beam splitter transformation and conditional zero photon counters. PACS number(s): 42.50.Dv, 03.67.-a It has long realized that the striking nature of entanglement lies at the heart of study of the fundamental issues in quantum mechanics as witnessed by Einstein-PodolskyRos...

Arithmetics on number systems with irrational bases

For irrational β > 1 we consider the set Fin(β) of real numbers for which |x| has a finite number of non-zero digits in its expansion in base β. In particular, we consider the set of β-integers, i.e. numbers whose β-expansion is of the form ∑n i=0 xiβ , n ≥ 0. We discuss some necessary and some sufficient conditions for Fin(β) to be a ring. We also describe methods to estimate the number of fra...

On the fixed number of graphs

‎A set of vertices $S$ of a graph $G$ is called a fixing set of $G$‎, ‎if only the trivial automorphism of $G$ fixes every vertex in $S$‎. ‎The fixing number of a graph is the smallest cardinality of a fixing‎ ‎set‎. ‎The fixed number of a graph $G$ is the minimum $k$‎, ‎such that ‎every $k$-set of vertices of $G$ is a fixing set of $G$‎. ‎A graph $G$‎ ‎is called a $k$-fixed graph‎, ‎if its fix...