A weak form of selftesting
Abstract
The concept of selftesting (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally violated by multiple inequivalent quantum realisations. We completely characterise the quantum realisations achieving the maximal violation and we show that each of them requires a maximally entangled state of two qubits. This implies the existence of a new, weak form of selftesting in which the maximal violation allows us to identify the state, but does not fully determine the measurements. From the geometric point of view the set of probability points that saturate the quantum bound is a line segment. We then focus on a particular member of the family and show that the selftesting statement is robust, i.e. that observing a nonmaximal violation allows us to make a quantitative statement about the unknown state. To achieve this we present a new construction of extraction channels and analyse their performance. For completeness we provide two independent approaches: analytical and numerical. The noise robustness, i.e. the amount of white noise at which the bound becomes trivial, of the analytical bound is rather small (~0.06%), but the numerical method takes us into an experimentallyrelevant regime (~5%). We conclude by investigating the amount of randomness that can be certified using these Bell violations. Perhaps surprisingly, we find that the qualitative behaviour resembles the behaviour of rigid inequalities like the ClauserHorneShimonyHolt inequality. This shows that at least for some deviceindependent applications rigidity is not a necessary ingredient.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 DOI:
 10.48550/arXiv.1910.00706
 arXiv:
 arXiv:1910.00706
 Bibcode:
 2019arXiv191000706K
 Keywords:

 Quantum Physics
 EPrint:
 5 + 10 pages, 3 figures, comments welcome