Discrimination Between Quantum Causality And Quantum Correlations

The motto "Correlation does not imply causation" has been coined since the age of David Hume and has been widely accepted as a commonsense that indicates the intrinsic difficulty for discriminating correlations and causations in classic cases.Actually,the classic discriminating rule(Reichenbach principle)per se is somewhat unprincipled since the discriminative results essentially depend on ad hoc selection of conditional variables.In some special quantum cases,Reid et al.presented a discriminating statistic C,which does not depend on any information of conditional variables,and hence can effectively discriminate quantum correlations(a.k.a quantum common causes)and quantum causations(a.k.a quantum direct causes)over two quantum random variables(?cv.e.,qubits).In this paper,we have formalized general quantum correlations and general quantum causations and investigated their decidability via the statistic C in general cases.We have demonstrated that(i)C ?[-1,1/27]if two qubits are influenced by quantum correlations;(?)C ?[-1/27,1]if the relation between two qubits are quantum causations.Our results shows that quantum correlations and quantum causations can be effectively discriminated,at least in a considerable scope.In addition,we have also given a geometric picture to illuminate the geometric interpretation of the probabilistic mixture of quantum correlations and quantum causations.The geometric picture also visually show that quantum common causes and quantum causality can be represented as two regular tetrahedrons respectively,which provides another way to discriminate between quantum common causes and quantum causality,and also to provides a basic heuristic to develop more complete methods for discriminating the cases corresponding to the overlapped area of C ?[-1/27,1/27].