Quantum reading capacity under thermal and correlated noise

Quantum communication theory sets the maximum rates at which information can be encoded and decoded reliably given the physical properties of the information carriers. Here we consider the problem of readout of a digital optical memory, where information is stored by means of the optical properties of the memory cells that are in turn probed by shining a laser beam on them. Interesting features arise in the regime in which the probing light has to be treated quantum mechanically. The maximum rate of reliable readout defines the quantum reading capacity, which is proven to overcome the classical reading capacity—obtained by probing with classical light—in several relevant settings. We consider a model of optical memory in which information is encoded in the (complex-valued) attenuation factor and study the effects on the reading rates of thermal and correlated noise. The latter type of noise arises when the effects of wave diffraction on the probing light beam are taken into account. We discuss the advantages of quantum reading over the classical one and show that the former is substantially more robust than the latter under thermal noise in the regime of low power per pulse.

Figure 1

Density plots of the absolute information gain $G_a$ (left) and of the relative information gain $G_r$ (right) comparing the EPR transmitter with the coherent state transmitter, as a function of $z_0$, $z_1$, for positive values of the attenuating factors ($0\le z_1\le z_0\le 1$). The top plots are for $n=0.1$, $n_{\mathrm{th}}=1$; those on the bottom are for $n=1$, $n_{\mathrm{th}}=1$.

Figure 2

Density plot of the information gain $G_a$ (left) and of the relative information gain $G_r$ (right) as a function of $n$ and $n_{\mathrm{th}}$ for amplitude encoding $z_0=0$, $z_1=1$ (top) and phase encoding $z_0=1$, $z_1=-1$ (bottom).

Figure 3

The plot shows as a function of the ratio $\ell /x_{\mathsf{R}}$: (a) the attenuating factors ${\tau }_{\min }$ and ${\tau }_{\max }$; (b), (c), (d) the lower and upper bounds on the reading rates for $p_0=p_1=1/2$ with the EPR transmitter (solid lines) and the coherent-state transmitter (dashed lines). In (b) $z_0=0$, $z=1$, $n=1$, $n_{\mathrm{th}}=1$; in (c) $z_0=0$, $z_1=1$, $n=0.1$, $n_{\mathrm{th}}=1$; in (d) $z_0=1$, $z_1=-1$, $n=0.1$, $n_{\mathrm{th}}=1$.