Robust Semi-Device Independent Certification of All Pure Bipartite Maximally Entangled States via Quantum Steering

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.

arXiv comment20 pages, 2 figures; final version

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• Distrustful quantum steering
• Certifying sets of quantum observables with any full-rank state
• Certification of the maximally entangled state using non-projective measurements
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• "All-versus-nothing" proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario
• Certifying Temporal Correlations
• Almost device-independent certification of GME states with minimal measurements
• Robust one-sided self-testing of two-qubit states via quantum steering
• Topologically noise robust network steering without inputs
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements