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Bell state measurement (BSM) plays a vital role in quantum information. Thereare many researches on BSM of qubit Bell state, however, there is no definitesolution of how to realize high-dimensional Bell state measurement (HDBSM). Inthis paper, We present a scheme for realizing arbitrary high-dimensionaltwo-particle Bell state measurement by auxiliary entanglement. In our scheme,the maximal entangled states with different degrees of freedom (DOF) are usedas auxiliary states, and then the HDBSM can be achieved by implementing Bellmeasurement with different degrees of freedom. We present the detailed HDBSMscheme for three and four-dimensional Bell state, and the general formula forarbitrary high-dimensional Bell state. Furthermore, We have designed theexperimental scheme for three-dimensional BSM, and given the method ofarbitrary dimension. This method can promote the high-dimensional quantuminformation task.

An arbitrary two-particle high-dimensional Bell state measurement by auxiliary entanglement