Described herein are systems and methods that manage polarization in coherent optical receivers by using analog signal processing that eliminates the need for ultra-fast, power-hungry ADCs and DSPs and that would require digitization of the full-bandwidth signal path and result in bulky and expensive circuit designs. Various embodiments of the invention provide polarization correction by using an analog polarization correction circuit that implements the equivalent of two matrix operations. This is accomplished by using analog electronics that comprises a combination of variable and unity gain amplifiers to align polarizations of input signals to generate a polarization-corrected output signal that is further aligned with the polarization frame of reference of the receiver.