Scalable self-testing of generic multipartite quantum states

TL;DR

This paper introduces a scalable protocol for self-testing almost all $n$-qubit states with polynomial sample complexity, enabling efficient device-independent certification of large quantum systems.

Contribution

It presents a novel, efficient scheme for self-testing multipartite quantum states using only polynomial resources, overcoming previous exponential scalability barriers.

Findings

Achieves robust self-testing of nearly all $n$-qubit states with polynomial sample complexity.

Uses a linear number of ancillary Bell pairs for multipartite Pauli measurements.

Provides a framework for scalable device-independent quantum state certification.

Abstract

Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed measurement statistics. However, existing self-testing methods for generic $n$-partite states face a scalability barrier, requiring exponentially many samples in the system size. In this work, we overcome this barrier by introducing a protocol that robustly self-tests almost all $n$-qubit states with only polynomial sample complexity. The key ingredient is an efficient scheme for device-independently evaluating multipartite Pauli measurements, which can be implemented using only a linear number of ancillary Bell pairs together with standard projective and Bell measurements, well within the reach of current quantum technology. Beyond self-testing states, our scheme provides a general framework for implementing a wide range of learning and certification protocols in the device-independent setting, thereby opening a scalable route to device-independent quantum information processing in large-scale quantum networks.