Maximal qubit violations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-locality in star and chain networks
Brian Doolittle, Eric Chitambar
Abstract
The nonlocal correlations of noisy quantum systems are important for both understanding nature and developing quantum technology. We consider the correlations of star and chain quantum networks in which noisy entanglement sources are measured by nonsignaling parties. We derive the necessary and sufficient conditions for when a broad family of star and chain $n$-locality inequalities achieve their maximal quantum violation assuming that each party's dichotomic observables are separable across qudit systems. When pairs of local dichotomic observables are considered on qubit systems, we derive maximal $n$-local violations that are larger and more robust to noise than the maximal $n$-locality violations reported previously. To obtain these larger values, we consider observables that we have not found in previous studies. Thus, we gain insights into self-testing entanglement sources and measurements in star and chain networks.