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Optics & Laser Technology

High-dimensional entanglement purification with Hermitian generalized-XOR gate of hybrid system

Wei Zi-hao, JI QI, Zi-Yi Guo, Zhe Yang, Rui‐Yang Yuan, Bao‐Cang Ren

Published Jun 23, 2026• 0 citations
Publisher
DOI
10.1016/j.optlastec.2026.115744

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A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of nonlinear quantum maps is generated in a natural way by a Hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other known purification schemes.
High-dimensional quantum entanglement offers significant advantages over its two-dimensional counterparts in various quantum information processing tasks. We propose a scalable method for implementing an arbitrary high-dimensional entanglement purification protocol (HDEPP) using path superposition. By selecting appropriate single-qudit gates, qudit-flip errors and phase-flip errors can be purified. Counterintuitively, the HDEPP becomes more robust for higher-dimensional systems and exhibits enhanced purification fidelity as the dimension increases. Our HDEPP not only requires fewer operational resources but also in principle can achieve unity fidelity through multiple rounds of iteration. Furthermore, we develop feasible optical schemes to purify the frequency degree of freedom of photons suffering from qudit-flip and phase-flip errors using hyperentanglement. This work paves the way toward high-dimensional quantum communication and quantum networks.
High-fidelity entanglement plays an important role in quantum networks for guaranteeing the integrity of quantum information processing. We present an error identification entanglement purification protocol (EIEPP) for maintaining high-fidelity entanglement of stationary systems. In EIEPP, the hybrid controlled-x gate for stationary systems and high-dimensional spatial-mode state of photons has been constructed using a stationary-whispering gallery mode resonator-waveguides system, and it is used to construct an error number gate (ENG) and error position gate (EPG) for noisy entangled stationary systems. Using ENG and EPG, the stationary systems with errors are discarded according to the measurement results of high-dimensional entangled photon states, and typically high-fidelity entangled states of stationary systems can be achieved with high yield in both ideal and practical situations. This EIEPP has superior performance for stationary systems with amplitude damping noise, and it is also applicable for stationary systems with other types of noise.