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.

20 pages, 2 figures; final version

References in corpus (10)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Observation of one-way Einstein-Podolsky-Rosen steering
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Robust and versatile black-box certification of quantum devices
• Fine-grained EPR-steering inequalities
• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• Experimental investigation of partially entangled states for device-independent randomness generation and self-testing protocols
• Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
• Experimental demonstration of one-sided device-independent self-testing of any pure two-qubit entangled state

Cited by in corpus (12)

• Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario
• Distillation of genuine tripartite Einstein-Podolsky-Rosen steering
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Certifying sets of quantum observables with any full-rank state
• Distrustful quantum steering
• Certification of the maximally entangled state using non-projective measurements
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• Robust one-sided self-testing of two-qubit states via quantum steering
• Certifying Temporal Correlations
• Almost device-independent certification of GME states with minimal measurements
• Topologically noise robust network steering without inputs
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements