The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Here, we have shown that any bipartite pure entangled state can be self-tested through Quantum Steering. Analogous to the tilted CHSH inequality, we have established a new steering inequality called Tilted Steering Inequality for self-testing any pure two-qubit entangled state. We have further used this inequality to self-test any bipartite pure entangled state by certifying two-dimensional sub-spaces of the qudit state by observing the structure of the assemblage obtained on Bob's side after Alice's measurement.
The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Here, we have shown that any bipartite pure entangled state can be self-tested through Quantum Steering. Analogous to the tilted CHSH inequality, we have established a new steering inequality called Tilted Steering Inequality for self-testing any pure two-qubit entangled state. We have further used this inequality to self-test any bipartite pure entangled state by certifying two-dimensional sub-spaces of the qudit state by observing the structure of the assemblage obtained on Bob's side after Alice's measurement.
The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Recently it was shown [A. Coladangelo, K. T. Goh, and V. Scarani, Nat. Commun. 8, 15485 (2017)] that all pure bipartite entangled states can be self-tested in the device-independent scenario by employing subspace methods introduced by Yang and Navascu\'es [Phys. Rev. A 87, 050102(R) (2013)]. Here, we have adapted their method to show that any bipartite pure entangled state can be certified in the semi-device-independent scenario through quantum steering. Analogous to the tilted Clauser-Horne-Shimony-Holt inequality, we use a steering inequality called the tilted steering inequality for certifying any pure two-qubit entangled state. Furthermore, we use this inequality to certify any bipartite pure entangled state by certifying two-dimensional subspaces of the qudit state by observing the structure of the set of assemblages obtained on the trusted side after measurements are made on the untrusted side. As a feature of quantum state certification via steering, we use the notion of assemblage-based robust state certification to provide robustness bounds for the certification result in the case of pure maximally entangled states of any local dimension.
We consider the problem of one-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the 2-2-2 steering scenario (involving two parties, two measurement settings per party, and two outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of the analogous Clauser-Horne-Shimony-Holt inequality of steering or the nonvanishing value of a quantity constructed using a correlation function called mutual predictability, together with the maximal violation of the fine-grained steering inequality, can be used to self-test any pure entangled two-qubit state in a one-sided device-independent way.
We demonstrate one-sided device-independent self-testing of any pure two-qubit entangled state based on a fine-grained steering inequality. The maximum violation of a fine-grained steering inequality can be used to witness certain steerable correlations, which certify all pure two-qubit entangled states. Our experimental results identify which particular pure two-qubit entangled state has been self-tested and which measurement operators are used on the untrusted side. Furthermore, we analytically derive the robustness bound of our protocol, enabling our subsequent experimental verification of robustness through state tomography. Finally, we ensure that the requisite no-signaling constraints are maintained in the experiment.
Entangled two-qubit states are the core building blocks for constructing quantum communication networks. Their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. In this work we study the self-testing of two-qubit entangled states via steering inequalities, with robustness analysis against noise. More precisely, steering inequalities are constructed from the tilted Clauser-Horne-Shimony-Holt inequality and its general form, to verify the general two-qubit entangled states. The study provides a good robustness bound, using both local extraction map and numerical semidefinite-programming methods. In particular, optimal local extraction maps are constructed in the analytical method, which yields the theoretical optimal robustness bound. To further improve the robustness of one-sided self-testing, we propose a family of three measurement settings steering inequalities. The result shows that three-setting steering inequality demonstrates an advantage over two-setting steering inequality on robust self-testing with noise. Moreover, to construct a practical verification protocol, we clarify the sample efficiency of our protocols in the one-sided device-independent scenario.
Certification of quantum systems and their properties has become a field of intensive study. Here, taking advantage of the one-sided device-independent (1SDI) scenario (also known as the quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including nonprojective d2-outcome measurements, which in turn can be used for certification of the maximal amount of randomness, that is, 2log2d bits. Finally, in the particular case of d=3, we propose an extended Bell scenario that transforms a 1SDI scheme to ``almost device independent.''
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.