Deterministic high-dimensional entangled states analysis and quantum teleportation

Entanglement in high-dimensional systems plays a vital role in quantum information processing (QIP), as it extends the available Hilbert space, supports the manipulation of more intricate information, and broadens the scope of implementable quantum operations. In the paper, we present a deterministic scheme for the four-dimensional two-qudit Bell entangled state analysis for the four-photon system in the polarization degree of freedom, resorting to the weak cross-Kerr nonlinearity and some linear optical components. In our scheme, the analysis of four-dimensional Bell entangled state is constructed by three-photon Toffoli gate and quantum nondemolition detectors (QND1 and QND2). By phase shifts of the coherent beams, the 16 orthogonal four-dimensional two-qudit Bell states can be completely distinguished from each other. The proposal can be extended to the four-dimensional three-qudit entangled state analysis and n-qudit entangled state analysis. In addition, our deterministic scheme for high-dimensional entangled state analysis can be applied to high-dimensional quantum teleportation, including both uncontrolled and controlled quantum teleportation protocols. Moreover, our scheme can achieve high fidelity and efficiency, further broadening its applicability in high-dimensional QIP.