Quantum Theory of Noise in Stokes Vector Receivers and Application to Bit Error Rate Analysis

Polarization-modulated optical signals can be demodulated via direct detection of Stokes vectors. In this article, we develop a quantum theory of noise in the Stokes vector receiver. Examining the conditions that enable simultaneous measurement of three elements of the Stokes vector, we demonstrate that an optical pre-amplifier in front of the Stokes vector receiver can reduce the power penalty associated with simultaneous measurements, down to the quantum limit of 3 dB. Then, the 3-D Gaussian noise model for the shot noise and optical pre-amplifier noise is discussed. Subsequently, based on the noise analyses, we derive bit error rate formulae for the cubic-lattice polarization modulation format and evaluate the sensitivity of the Stokes vector receiver.