Cryptography. The Epr Argument. Bell's Inequality

Philip L. Bowers

Zhengjun Cao, Lihua Liu

Quantum entanglement is of great importance to quantum cryptography and computation. So far, all experimental demonstrations of entanglement are designed to check Bell's inequality which is based on Bell's formulation for EPR paradox. In this note, we specify the assumptions needed in Bell's mathematical argument. We then show the contradictions among these assumptions. As a result, it becomes very easy to see that Bell's inequality is trivial.

Jean-Louis Basdevant, Jean Dalibard

Andrei Yu. Khrennikov

This paper is devoted to analysis of the role of projection postulate in Einstein, Podolsky, and Rosen-EPR [1] argument against completeness of QM. It will be shown that the EPR considerations do not match with von Neumann’s quantum measurement theory (QMT). The root of EPR’s conclusion on incompleteness of QM is the misuse of von Neumann’s projection postulate. EPR applied this postulate to observables with degenerate spectra (which is totally forbidden by von Neumann’s axiomatics of QM). Consequences for Bell’s inequality and quantum information theory are analyzed. This paper might stimulate discussion on the role of projection postulate in quantum information theory, especially quantum cryptography and teleportation.

WU Xin-zhong

This paper examines the history from EPR argument to Bell’s inequality and the influence of Bell’s inequality on the frontier exploration of quantum mechanics. It is found that Bell’s inequality has some hidden assumptions different from EPR argument: Following Schrodinger's assumption that the measurement process of EPR experiment undergos time, Karl Hess regards time as an implicit variable of time series, and Joy Christian obtains a local implicit variable inequality different from Bell's inequality. They extended the relativistic space-time geometric analysis method to the localized geometric morphological analysis of quantum states, and considered that the Bell’s inequality reasoning did not meet the requirements of the completeness of EPR argument. Quantum statistics given by identical particles is different from classical statistics. Innovative ensemble interpretation can also solve Bell's inequality and give a demonstration of quantum non-locality. The main research progress of quantum gravity is great, but there are many divergences. According to Einstein's local realism, the new explanation and expression of quantum mechanics may open up new ideas for the study of quantum gravity.