A coherent receiver configured to assign a first transmission signal to first transmission polarization, assign a second transmission signal to second transmission polarization, and receive a quadrature multiplexed signal formed by applying quadrature multiplexing to the first transmission polarization and the second transmission polarization, the receiver comprising: detection means for detecting the first transmission polarization and the second transmission polarization according to prescribed first reception polarization and second reception polarization and obtaining a first detected signal and a second detected signal; quantization means for quantizing the first detected signal and the second detected signal and obtaining a first quantized signal and a second quantized signal; and signal processing means for, when filtering the first quantized signal and the second quantized signal using a prescribed filtering control algorithm to form a first demodulated signal and a second demodulated signal respectively, adjusting filter coefficients of the filtering control algorithm according to the first quantized signal and the second quantized signal and the first demodulated signal and the second demodulated signal, and outputting the first demodulated signal and the second demodulated signal to a first output terminal and a second output terminal, respectively, wherein the filtering control algorithm is an algorithm for filtering with a matrix in which double-row double-column elements are used as the filter coefficients, and the signal processing means is configured to adjust the filter coefficients by performing reordering the elements of the matrix in accordance with an identification result which identifies whether or not at least one of the first demodulated signal and the second demodulated signal has a prescribed data series. detection means for detecting the first transmission polarization and the second transmission polarization according to prescribed first reception polarization and second reception polarization and obtaining a first detected signal and a second detected signal; quantization means for quantizing the first detected signal and the second detected signal and obtaining a first quantized signal and a second quantized signal; and signal processing means for, when filtering the first quantized signal and the second quantized signal using a prescribed filtering control algorithm to form a first demodulated signal and a second demodulated signal respectively, adjusting filter coefficients of the filtering control algorithm according to the first quantized signal and the second quantized signal and the first demodulated signal and the second demodulated signal, and outputting the first demodulated signal and the second demodulated signal to a first output terminal and a second output terminal, respectively, wherein the filtering control algorithm is an algorithm for filtering with a matrix in which double-row double-column elements are used as the filter coefficients, and the signal processing means is configured to adjust the filter coefficients by performing reordering the elements of the matrix in accordance with an identification result which identifies whether or not at least one of the first demodulated signal and the second demodulated signal has a prescribed data series.