Robust-fidelity high-dimensional qudit-dependent entanglement creation for photon systems with balanced state-selective reflection

Qudit-dependent quantum entanglement systems show high-dimensional state spaces and enhance loss tolerance in quantum information technology. In this paper, we first present the creation of arbitrary four-dimensional two-qudit maximally entangled states (CFDTQMESs) for two-photon system by virtue of linear-optics four-dimensional single-qudit quantum gates, and then extend this to the creation of arbitrary four-dimensional n -qudit ( n ≥ 3 ) maximally entangled states for n -photon system with the n − 1 creation process of two-qudit entangled states. As the hybrid polarization-spatial states of the single photon are used to encode the four-dimensional qudits, the proposed protocols for high-dimensional entanglement have an edge in terms of saving resources and restraining noise. Moreover, based on balanced state-selective reflection of nitrogen-vacancy center-cavity system, imperfect scattering process does not affect the fidelities of our protocols, resulting in near unit of fidelity for each protocol. Furthermore, we can extend the CFDTQMES to the creation of the d -dimensional m -qudit ( d ≥ 2 x + 1 , x , m = 2 , 3 , … ) entangled states.