We present two schemes for error-correction of polarization entanglement with time-bin entanglement and frequency entanglement in hyper-entangled state. In these two protocols, by performing the polarization parity-check operation, the bit-flip and phase-flip errors on the polarization part can be corrected and eliminated in one step. The parties in quantum communication can obtain maximally hyper-entangled states in two degrees of freedom in a deterministic way. Our protocols for purification are useful in practical applications for long-distance quantum communication.

中文翻译：

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超纠缠态偏振纠缠的纠错

我们提出了两种在超纠缠态下纠错偏振纠缠方案的方法，其中包括时频纠缠和频率纠缠。在这两种协议中，通过执行极化奇偶校验操作，可以一步一步地纠正和消除极化部分的位翻转和相位翻转错误。量子通信中的当事方可以确定性的方式获得两个自由度的最大超纠缠态。我们的纯化协议可用于长距离量子通信的实际应用。