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A Note On Clauser-Horne-Shimony-Holt Inequality

Clauser-Horne-Shimony-Holt inequality, an extension of Bell’s inequality, is of great importance to modern quantum computation and quantum cryptography. So far, all experimental demonstrations of entanglement are designed to check Bell’s inequality or Clauser-Horne-Shimony-Holt inequality. In this note, we specify the math assumptions needed in the argument for Clauser-Horne-Shimony-Holt inequality. We then show the math argument for this inequality is totally indispensable of any physical interpretation, including the hidden variable interperation for EPR thought experiment and the Copenhagen interpretation for quantum mechanics.