Sample-efficient device-independent quantum state verification and certification

TL;DR

This paper introduces a new, sample-efficient method for device-independent quantum state verification and certification that does not rely on IID assumptions, enhancing reliability in quantum information processing.

Contribution

It develops a systematic, finite-copy, device-independent verification approach that is optimal in sample efficiency, advancing beyond asymptotic and IID limitations.

Findings

Verification can be performed without IID assumptions.

Achieves optimal sample efficiency in device-independent verification.

Provides a protocol for quantum state certification using a subset of resources.

Abstract

Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. Steady progress vis-\`{a}-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years. When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce. Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource. Such strong assumptions deprive the verification procedure of its truly device-independent character. In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime. Remarkably, we show that device-independent verification can be performed with optimal sample efficiency. Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.