We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (“position” and “momentum”) measurements. A contradiction is shown possible for two quantum states: a pair-coherent state, and a superpositions of two coherent states, where the superposition state has been squeezed by the action of a two-mode squeezing operator. In one case a contradiction is still possible for states of increasing photon number, though the effect becomes smaller and more difficult to observe. The high efficiency of the homodyne method of measurement of quadrature phase amplitudes may open a way for a loophole-free test of local hidden variable theories, and the effect of detection loss on the contradiction with local hidden variables is calculated.

• Received 22 September 1998

DOI:https://doi.org/10.1103/PhysRevA.60.4259