Quantum Reading of a Classical Digital Memory

We consider a basic model of digital memory where each cell is composed of a reflecting medium with two possible reflectivities. By fixing the mean number of photons irradiated over each memory cell, we show that a nonclassical source of light can retrieve more information than any classical source. This improvement is shown in the regime of few photons and high reflectivities, where the gain of information can be surprising. As a result, the use of quantum light can have nontrivial applications in the technology of digital memories, such as optical disks and barcodes.

Figure 1

Basic model of memory: Digital information is stored in a memory whose cells have different reflectivities: $r=r_0$ encoding bit value $u=0$, and $r=r_1$ encoding bit value $u=1$. Readout of the memory: In general, a digital reader consists of transmitter and receiver. The transmitter $T(M,L,\rho )$ is a bipartite bosonic system, composed by a signal system $S$ (with $M$ modes) and an idler system $I$ (with $L$ modes), which is given in some global state $\rho$. The signal $S$ emitted by this source has bandwidth $M$ and energy $N$ (mean number of photons). The signal is directly shined over the cell, and its reflection $R$ is detected together with the idler $I$ at the output receiver, where a suitable measurement retrieves the value of the bit up to an error probability $P_{\mathrm{err}}$.

Figure 2

Left panel: Minimum information gain $G$ over the memory plane $\{r_0,r_1\}$. For a few-photon signal ($N=30$), we compare a narrow band EPR transmitter ($M=30$) with all the classical transmitters. Inside the black region ($r_0\approx r_1$) our investigation is inconclusive. Outside the black region, we have $G>0$. Right panel: $G$ plotted over the plane $\{r_0,r_1\}$ in the presence of decoherence ($\epsilon =\overline{n}={10}^{-5}$). For a few-photon signal ($N=30$), we compare a narrow band EPR transmitter ($M=30$) with all the classical transmitters $T(M,L,{\rho }_c)$ having $M\le M^{*}=5\times {10}^6$.

Figure 3

Minimum information gain $G$ versus $r_0$ and $N$. Left picture refers to $M=1$, right picture to $M\to \infty$. (For arbitrary $M$ the scenario is intermediate.) Outside the inconclusive black region we have $G>0$. For $M\to \infty$ the black region is completely collapsed below $N_{\mathrm{th}}=1/2$.

Figure 4

Left panel: $G$ optimized over $M$ and $\phi$. $G$ can be higher than 0.6 bit per cell. Results are shown in the absence of decoherence ($\epsilon =\overline{n}=0$) considering $r_0=0.85$, $r_1=1$ and $N=35$. Right panel: $G$ optimized over $M$ and $\phi$. Results are shown in the presence of decoherence ($\overline{n}=\epsilon ={10}^{-5}$) considering $r_0=0.85$, $r_1=0.95$, $N=100$, and $M^{*}={10}^6$.