Identifying non-k-separability of a class of N-qubit complete graph states using correlation tensors

TL;DR

This paper develops a criterion based on correlation tensors to identify non-k-separability in N-qubit complete graph states, including noisy states, using minimal local measurements.

Contribution

It introduces a new separability criterion utilizing correlation tensor norms for N-qubit complete graph states, including noisy variants.

Findings

The criterion effectively detects non-k-separability in complete graph states.

Few local measurements are sufficient to evaluate the criterion.

The method applies to noisy states with colored product noise.

Abstract

We derive a general expression for standard tensor norm of $N$-body correlation tensors for $N$-qubit complete graph states. With the help of this expression, we formulate a separability criterion that identifies non-$k$-separability of a class of $N$-qubit complete graph states, including GHZ state. We illustrate the performance of our criterion by considering the $N$-qubit complete graph states added with colored product noise. We also demonstrate that few local measurement settings are sufficient to evaluate our criterion.