  Entanglement of quasiclassical (coherent) states of two harmonic oscillators
leads to striking quantum effects and is useful for quantum technologies. These
effects and applications are closely related to nonlocal correlations inherent
in these states, manifested by the violation of Bell inequalities. With
previous frameworks, this violation is limited by the size of the system, which
does not approach the maximum even when the amount of entanglement approaches
its maximum. Here we propose a new version of Bell correlation operators, with
which a nearly maximal violation can be obtained as long as the associated
entanglement approximates to the maximum. Consequently, the revealed
nonlocality is significantly stronger than those with previous frameworks for a
wide range of the system size. We present a new scheme for realizing the gate
necessary for measurement of the nonlocal correlations. In addition to the use
in test of quantum nonlocality, this gate is useful for quantum information
processing with coherent states
