Quantum tensor product structures are observable-induced
Paolo Zanardi, Daniel Lidar, Seth Lloyd
TL;DR
A general algebraic framework aimed to formalize the partition of a quantum system into subsystems and the emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are developed.
Abstract
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the associated notion of quantum entanglement are then relative and observable-induced. We develop a general algebraic framework aimed to formalize this concept. We discuss several cases relevant to quantum information processing and decoherence control.