Robustness of multi-qubit entanglement in the independent decoherence model

Abstract

We study the robustness of the GHZ (or ``cat'') class of multi-partite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of N-party entanglement is studied in the large N limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes large (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.