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Abstract
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 by Coladangelo et. al. (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 et. al. (Phys. Rev. A 87, 050102(R)). 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 CHSH inequality, we use a steering inequality called Tilted Steering Inequality for certifying any pure two-qubit entangled state. Further, we use this inequality to certify any bipartite pure entangled state by certifying two-dimensional sub-spaces of the qudit state by observing the structure of the set of assemblages obtained on the trusted side after measurements are made on the un-trusted 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.
Highlights
Quantum certification and benchmarking become tasks of paramount importance as we advance towards the second quantum revolution [1]
We have shown SDI certification of any pure bipartite entangled state by certifying two-dimensional subspace projections of the qudit state using a tilted steering inequality adapting the subspace methods previously employed in [6,17]
More importantly we derived robustness bounds for this certification in the case of the maximally entangled pure qudit state of dimension d; such explicit robust bounds are not known in the device-independent scenario
Summary
Quantum certification and benchmarking become tasks of paramount importance as we advance towards the second quantum revolution [1]. The authors of [46,47] obtained robust self-testing results using correlations for different subsets of maximally entangled states; the correlations-based approach is nonconstructive in nature while in the steering case we have shown explicit bounds. One-sided device-independent certification of any two-qubit pure entangled state was shown in [27], where the authors used two steering inequalities, the fine-grained inequality (FGI) [49] and analog CHSH [50] inequalities, for self-testing. We provide O( ) robustness bounds for our steering-based state certification result for maximally entangled pure qudit states which are not known in the device-independent scenario. The weight of the steerable part ps minimized over all possible decompositions of {σa|x}a,x gives the steerable weight SW({σa|x}a,x ) of that assemblage set
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