Signal acquisition via polarization modulation in single photon sources

A simple model system is introduced for demonstrating how a single photon source might be used to transduce classical analog information. The theoretical scheme results in measurements of analog source samples that are (i) quantized in the sense of analog-to-digital conversion and (ii) corrupted by random noise that is solely due to the quantum uncertainty in detecting the polarization state of each photon. This noise is unavoidable if more than 1 bit per sample is to be transmitted and we show how it may be exploited in a manner inspired by suprathreshold stochastic resonance. The system is analyzed information theoretically, as it can be modeled as a noisy optical communication channel, although unlike classical Poisson channels, the detector’s photon statistics are binomial. Previous results on binomial channels are adapted to demonstrate numerically that the classical information capacity, and thus the accuracy of the transduction, increases logarithmically with the square root of the number of photons, $N$. Although the capacity is shown to be reduced when an additional detector nonideality is present, the logarithmic increase with $N$ remains.

Figure 1

Channel capacity, $C$, for a perfect detector $\left(a=0\right)$ as a function of increasing number of photons per source sample, $N$ ($N$ is defined only for integer values, but a solid line is used as an aid to visibility). Also shown is $C_{\infty }$, i.e., the lower bound to the channel capacity given by Eq. (9), which asymptotically approaches capacity as $N\to \infty$, a better lower bound to the channel capacity, $I_L$ (described in the text), and an upper bound, $I_U$.

Figure 2

Channel capacity for various $N$ as a function of the maximum angle, $a$, of a randomly varying (uniformly distributed $\Phi$) angle in the detector’s polarizer (i.e., increasing detector noise).