Recovery of maximally entangled quantum states by weak-measurement reversal

Abstract

Maximal quantum entanglement provided by N00N states is a unique resource in the quest for the ultimate precision in physical measurements. Such states, however, are fragile and prone to decoherence. Even in weak-measurement schemes, as we demonstrate in this work, the phase super-resolution provided by N00N states is achieved at a cost of an N-fold enhancement of amplitude damping. Still, as the analysis presented here shows, a partial collapse of N00N states induced by weak measurements can be reversed, despite the dramatic, N-fold enhancement of amplitude damping, through appropriate reversal operations on the post-measurement state, enabling a full restoration of the Heisenberg-limit phase super-resolution of N00N states.