Generating entangled states of two ququarts using linear optical elements

Recently, quantum systems with D-dimensional bases states (D > 2) or quDits have attracted much attention in the context of fundamental tests of quantum theory and potential applications in quantum information. In this paper, we discuss several schemes for generating entangled states of two ququarts (four-dimensional quantum systems). The ququart in our scheme is based on frequency-nondegenerate biphoton states of spontaneous parametric down-conversion and we show how the entangled states between two ququarts can be generated with simple linear optical elements, such as an ordinary 50/50 beamsplitter, a polarizing beamsplitter, or a dichroic beamsplitter. We also show that our scheme is capable of generating postselection-free two-ququart entangled states efficiently.