Abstract
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell’s theorem, one can infer the appearance of certain entangled state when the maximum violation is observed, e.g., to self-test singlet state using CHSH inequality. In this work, by constructing a versatile entanglement source, we experimentally demonstrate a generalized self-testing proposal for various bipartite entangled states up to four dimensions. We show that the high-quality generated states can approach the maximum violations of the utilized Bell inequalities, and thus, their Schmidt coefficients can be precisely inferred by self-testing them into respective target states with near-unity fidelities. Our results indicate the superior completeness and robustness of this method and promote self-testing as a practical tool for developing quantum techniques.
Highlights
In contrast to theoretical schemes of quantum information processing (QIP), where the imperfections of the involved devices are generally not taken into account, practically we often do not have sufficient knowledge of the internal physical structure, or the used devices cannot be trusted
The researches on this topic open a new realm of quantum science, namely, “device-independent” science,[1,2,3,4,5,6,7,8,9] in which no assumptions are made about the states under observation, the experimental measurement devices, or even the dimensionality of the Hilbert spaces where such elements are defined
Such a device-independent certification of quantum systems is titled “self-testing”, which was first proposed by Mayers and Yao to certify the presence of a quantum state and the structure of a set of experimental measurement operators.[13]
Summary
In contrast to theoretical schemes of quantum information processing (QIP), where the imperfections of the involved devices are generally not taken into account, practically we often do not have sufficient knowledge of the internal physical structure, or the used devices cannot be trusted. A self-testing criterion underlies the entire protocol, with which one can uniquely infer the presence of a particular ensemble of entangled states, when observing the maximal violation of certain Bell inequality These states should be different from each other by only a local unitary transformation, which does not change the Bell correlations. Coladangelo et al.[36] have provided a general method to self-test all pure bipartite entangled states by constructing explicit correlations, which can be achieved excluwhere 0p≤ffiffiffiffiαffiffiffi≤ffiffiffiffi2ffiffiffiffi and the maximum quantum violation of it is bðαÞ 1⁄4 8 þ 2α2 If such Bell correlations are duplicated by Alice and Bob on an unknown state |φ〉, it is possible to construct an isometry satisfying that follows equations[23]. It is still unclear whether arbitrary pure bipartite entangled state is self-testable
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