Determination of stabilizer states

TL;DR

This paper proves that all n-qubit stabilizer states can be uniquely identified by their reduced density matrices on the supports of their generators, aiding quantum error correction and state characterization.

Contribution

It establishes that stabilizer states are uniquely determined by specific reduced density matrices, a novel result in quantum state determination.

Findings

Stabilizer states are uniquely determined by their reduced density matrices.

This applies to both pure and mixed states.

Supports of generators suffice for state identification.

Abstract

The determination of many special types of quantum states has been studied thoroughly, such as the generalized |GHZ> states, |W> states equivalent under stochastic local operations and classical communication and Dicke states. In this paper, we are going to study another special entanglement states which is stabilizer states. The stabilizer states and their subset graph states play an important role in quantum error correcting codes, multipartite purification and so on. We show that all n- qubit stabilizer states are uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices for systems which are the supports of n independent generators of the corresponding stabilizer formalisms.