Genuine Einstein-Podolsky-Rosen steering of generalized three-qubit states via unsharp measurements

We aim to explore all possible scenarios of(1→2)(where one wing is untrusted and the others two wings are trusted)and(2→1)(where two wings are untrusted,and one wing is trusted)genuine tripartite Einstein-Podolsky-Rosen(EPR)steering.The generalized Greenberger-Horne-Zeilinger(GHZ)state is shared between three spatially separated parties,Alice,Bob and Charlie.In both(1→2)and(2→1),we discuss the untrusted party and trusted party performing a sequence of unsharp measurements,respectively.For each scenario,we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality.The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters.Moreover,both the sharpness parameters range and the state parameters range in the scenario of(1→2)steering are larger than those in the scenario of(2→1)steering.

Robustness self-testing of states and measurements in the prepare-and-measure scenario with 3 → 1 random access code

Recently, Tavakoli et al.proposed a self-testing scheme in the prepare-and-measure scenario, showing that self-testing is not necessarily based on entanglement and violation of a Bell inequality [Phys.Rev.A 98 062307(2018)].They realized the self-testing of preparations and measurements in an N → 1(N ≥ 2) random access code(RAC), and provided robustness bounds in a 2 → 1 RAC.Since all N → 1 RACs with shared randomness are combinations of 2 → 1 and 3 → 1 RACs, the3 → 1 RAC is just as important as the 2 → 1 RAC.In this paper, we find a set of preparations and measurements in the3 → 1 RAC, and use them to complete the robustness self-testing analysis in the prepare-and-measure scenario.The method is robust to small but inevitable experimental errors.