Multipartite Entanglement and Global Information

TL;DR

This paper characterizes maximally entangled multipartite qubit states, such as stabilizer states, showing how they can encode maximum local information, be uniquely identified by observables, and be prepared for quantum computing applications.

Contribution

It provides a simple characterization of maximally entangled states and constructs a complete set of observables to uniquely identify them, advancing understanding of quantum entanglement.

Findings

States can be maximally entangled with local auxiliary systems

A basis can be constructed via local unitaries from these states

Complete set of observables uniquely characterizes the states

Abstract

We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this property iff one can construct out of it an orthonormal basis by applying independent local unitary operations. This implies that those states can be used to encode locally the maximum amount of $n$ bits. Examples of these states are the so--called stabilizer states, which are used for quantum error correction and one--way quantum computing. We give a simple characterization of these states and construct a complete set of commuting unitary observables which characterize the state uniquely. Furthermore we show how these states can be prepared and discuss their applications.