Decoherence of an n-qubit quantum memory

Abstract

We analyze decoherence of a quantum register in the absence of nonlocal operations, i.e., n noninteracting qubits coupled to an environment. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: first, decoherence must be small, and second, the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to a random matrix model, and illustrate its reach considering a Greenberger-Horne-Zeilinger state coupled to a spin bath. � 2007 The American Physical Society.