We have carried out the spin-correlation measurement of two protons in a spin singlet state aiming to test the EPR paradox presented by Einstein, Podolsky and Rosen in 1935. The EPR proposed a thought experiment in which they showed according to quantum mechanics that the result of a measurement of an entangled quantum system performed on earth, for example, can instantaneously influence the result of a measurement performed on the far distant Galaxy regardless of the distance. This of course contradicts with the theory of special relativity by Einstein, no information can be transmitted faster than the speed of light. Therefore, EPR argued that quantum mechanics must be incomplete.

In 1964, Bell found an extremely important inequality which is the embodiment of the EPR arguments. The prediction of the spin-correlation by the Bell's inequality is different from that by the quantum mechanics so that we can test experimentally which assertion is right by the measurement.

After a short introduction of the EPR paradox, I try to explain how we realized an almost pure spin singlet state of two protons experimentally, and how we measured the spin polarizations of two protons.