  We present a detailed investigation of minimum detection efficiencies, below
which locality cannot be violated by any quantum system of any dimension in
bipartite Bell experiments. Lower bounds on these minimum detection
efficiencies are determined with the help of linear programming techniques. Our
approach is based on the observation that any possible bipartite quantum
correlation originating from a quantum state in an arbitrary dimensional
Hilbert space is sandwiched between two probability polytopes, namely the local
(Bell) polytope and a corresponding nonlocal no-signaling polytope. Numerical
results are presented demonstrating the dependence of these lower bounds on the
numbers of inputs and outputs of the bipartite physical system.
