## 1 Introduction  
Quantum key distribution (QKD) [1] allows two authenticated distant participants [PERSON] and [PERSON] to securely share a long random string often called cryptographic keys even in the presence of an eavesdropper [PERSON]. The keys can be used to carry out perfectly secure communication via one-time-pad and perfectly secure authentication via Wigman-Carter authentication scheme [2]. The first and the best-known QKD protocol is BB84 proposed by [PERSON] and [PERSON] in 1984 [3]. Since then, QKD technologies have made significant progresses. The unconditional security of QKD has been proved through a series of outstanding works [4; 5; 6]. Practical security of QKD has also been fully studied, such as the decoy state method [7; 8; 9] for beating the photon-number-splitting attack, and the measurement-device-independent QKD for removing detector side channel attacks [10]. Up to now, the transmission distance reaches 421 km in optical fiber [11], and 1200 km in free space from the Micius satellite to the Xinglong ground station [12]. Several QKD network testbeds have been built and demonstrated in metro areas [13; 14; 15; 16]. Scientists hope to build a global quantum network through quantum satellites connecting terrestrial quantum networks over commercial optical fiber in the future. To build terrestrial QKD networks over commercial optical fiber, the stability of QKD systems or exactly anti-quantum-channel disturbance is especially crucial and has received extensive attention from both scientific researchers and engineers. Polarization encoding QKD systems rely on complicated feedback compensation because polarization states of photons are randomly disturbed in optical fiber quantum channels due to environmental vibration and/or temperature variation, and it is not suitable for strong environmental disturbance. Owing to the fact that phase information encoded in quantum states can be maintained in environmental disturbance, phase encoding or time-bin phase encoding QKD systems are more competitive in such situations as overhead and tube optical cables along roads or bridges. However, decoding the phase information with unbalanced-arm Mach-Zehnder or Michelson interferometers also suffers from polarization disturbance in transmission fiber that results in the fringe visibility of the interferometers varying fast [17]. To solve the problem, [PERSON] et al. proposed the \"plug and play\" bidirectional QKD system which can automatically compensate the polarization disturbance besides the phase drifting in the channel [18], and has been applied in QKD products by ID Quantique, Inc., a well-known quantum company (located in Geneva, Switzerland). Moreover, [PERSON] et al. proposed the Faraday-Michelson (F-M) unidirectional QKD system [19], which has been applied in the phase encoding QKD products by Anhui Asky Quantum Technology Co., Ltd. (Anhui, China), and designed in the latest time-bin phase QKD scheme in a patent proposed by the University of Science and Technology of China [20]. According to Ref. [17], for phase encoding QKD systems, the disturbances of quantum channel are collected in the system if there is polarization-induced fading at the receiver's interferometer. Thus, it is crucial to construct an unbalanced-arm interferometer that can self-compensate quantum channel disturbance. Up to now, the effective and widely used solutions are mainly based on the two schemes mentioned above or their variants. Both of the schemes are based on the Faraday magneto-optic devices, which is not conducive to photonic integration and applications in magnetic environments. In this article, we propose a new decoder based on a quarter-wave plate reflector-Michelson (Q-M) interferometer, which is free of polarization disturbance caused by quantum channel and optical devices in QKD systems. The theoretical analysis is given to reveal how the Q-M interferometer works to eliminate the polarization-induced signal fading automatically. We also build a time-bin phase encoding QKD system based on the Q-M interferometer.