Quantum Inf Process (2017) 16:105
Construction of Bell inequalities based on the CHSH
· Jing Wang
· Ming Li
· Dongmeng Chen
Received: 17 September 2016 / Accepted: 28 February 2017 / Published online: 9 March 2017
© Springer Science+Business Media New York 2017
Abstract It is a computationally hard task to ﬁnd all Bell inequalities for a given
number of parties, measurement settings, and measurement outcomes. We investigate
the construction of the Clauser-Horne-Shimony-Holt Bell inequalities, based on which
we present a set of new Bell inequalities. The maximal violations of the constructed
Bell inequalities are analysed, and computable formulas are derived.
Keywords Nonlocality · CHSH · Bell inequalities · Quantum entanglement
If there exists a Local Hidden Variable (LHV) model to describe a quantum system,
then we say the system is local. However, not all quantum systems can be associated
with an LHV model, highlighting what is now known as quantum nonlocality .
Actually, quantum nonlocality, as one of the most striking characteristics of quantum
mechanics, has been recognized as an essential resource for quantum information
tasks , such as quantum key distribution [3–5], communication complexity , and
randomness generation [7,8].
To check whether there exists quantum nonlocality or not, one method is to construct
the LHV model for a given quantum system. In 1989, Werner explicitly constructed
LHV models for bipartite entangled Werner states . The authors in [10,11]have
presented LHV models with all measurements and with projective measurements for
more entangled Werner states.
College of the Science, China University of Petroleum, Qingdao 266580, China
Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany