Quantum networks for concentrating entanglement

Abstract

If two parties, Alice and Bob, share some number, n, of partially entangled pairs of qubits, then it is possible for them to concentrate these pairs into some smaller number of maximally entangled states. We present a simplied version of the algorithm for such entanglement concentration, and we describe ecient networks for implementing these operations. 1 Introduction The state of a single pure quantum bit, or qubit, is described by a vector in a 2-dimensional Hilbert space spanned by basis vectors j0i and j1i. The state of n pure qubits (i.e. an n-qubit register) is described by a vector in a 2 n - dimensional Hilbert space which is the tensor product of the 2-dimensional spaces for the states of each of the n qubits. Consider a 2-qubit register in a state described by the vector j\ti = 1 p 2 j00i + 1 p 2 j11i. We call a pair of particles in this state an EPR pair, named after Einstein, Podolsky and Rosen, who discussed such particle pairs in their 1935 paper [EPR35]. It ca...