Abstract
Self-testing is a method to infer the underlying physics of a quantum experiment in a black box scenario. As such it represents the strongest form of certification for quantum systems. In recent years a considerable self-testing literature has developed, leading to progress in related device-independent quantum information protocols and deepening our understanding of quantum correlations. In this work we give a thorough and self-contained introduction and review of self-testing and its application to other areas of quantum information.
Highlights
In contrast to classical theories, states in quantum physics can be entangled and sets of measurements can be incompatible
The outcomes of incompatible measurements made on the local subsystems of an entangled quantum state can exhibit correlations that are provably stronger than any resulting from a classical theory, a phenomenon known as Bell nonlocality
These works have since given birth to the field of self-testing, which broadly speaking aims to understand the structure of the set of quantum correlations and identify those correlations that admit a unique physical realisation
Summary
In contrast to classical theories, states in quantum physics can be entangled and sets of measurements can be incompatible. As more was understood about Bell nonlocality, a number of works [SW87, PR92, BMR92, Tsi93] eventually pointed out that there exist Bell nonlocal correlations that—as well as requiring entanglement and incompatibility—can only be produced by making particular sets of incompatible measurements on particular entangled states These works have since given birth to the field of self-testing, which broadly speaking aims to understand the structure of the set of quantum correlations and identify those correlations that admit a unique physical realisation. A similar idea was already present in [MY98] in a cryptographic context, using the term ‘self-checking’ instead of ‘self-testing’ These early works introduced the paradigm of device-independence, to which self-testing is intimately related. We recommend [McK10, Kan, Kan16] as valuable texts for first time readers
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