A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement

Fidelity plays an important role in quantum information processing,which provides a basic scale for comparing two quantum states.At present,one of the most commonly used fidelities is Uhlmann-Jozsa(U-J)fidelity.However,U-J fidelity needs to calculate the square root of the matrix,which is not trivial in the case of large or infinite density matrices.Moreover,U-J fidelity is a measure of overlap,which has limitations in some cases and cannot reflect the similarity between quantum states well.Therefore,a novel quantum fidelity measure called quantum Tanimoto coefficient(QTC)fidelity is proposed in this paper.Unlike other existing fidelities,QTC fidelity not only considers the overlap between quantum states,but also takes into account the separation between quantum states for the first time,which leads to a better performance of measure.Specifically,we discuss the properties of the proposed QTC fidelity.QTC fidelity is compared with some existing fidelities through specific examples,which reflects the effectiveness and advantages of QTC fidelity.In addition,based on the QTC fidelity,three discrimination coefficients d_(1)^(QTC),d_(2)^(QTC),and d_^(3)^(QTC)are defined to measure the difference between quantum states.It is proved that the discrimination coefficient d_(3)^(QTC)is a true metric.Finally,we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.

An information-volume-based distance measure for decision-making

D-S evidence theory,as a general framework for reasoning with uncertainty,allows combining pieces of evidence from different information sources to derive a degree of belief function that is a type of fuzzy measure.However,the mass assignments given by unknown information sources are disordered.How to measure the difference between the mass assignments has aroused people’s interest.In this paper,inspired by the information volume,a novel distance-based measure is proposed to measure the difference between mass assignments.The method can refine the uncertain information given by experts and compare the refined information to obtain the difference between mass assignments.At the same time,it is verified that the measure not only meets the properties of distance,but also proves the superiority of the proposed Information Volume Distance(IVD)through simulation experiments.Meanwhile,in the process of information fusion,the reliability of each source could be quantified through IVD.Therefore,based on IVD,a new multi-source information algorithm is proposed to solve the problem of multi-source information fusion.Moreover,algorithm is applied to decision-making problem and compare with other methods to verify the effectiveness.