Quantum-enhanced quickest change detection of transmission loss

Abstract

Augmenting a train of bright phase-modulated laser-light pulses of a coherent communications system with infinitesimally small quantum photons per pulse -- entangled across several time bins -- prepared by splitting squeezed light in a temporal-mode interferometer can dramatically enhance a homodyne receiver's ability to detect a sudden change in the channel loss, by up to a factor that is the inverse of the pre-change loss, without affecting the communications rate. We discuss the quantum limit of quickest change detection, and the problem of joint communications and change detection that our study opens up.

Figures (12)

• Figure 1: (a) Identical laser-light pulses of amplitude $\alpha$, $\alpha \in {\mathbb R}$ (i.e., tensor product of coherent states $|\alpha\rangle^{\otimes k}$), each of mean photon number $|\alpha|^2 \equiv N+N_a$, $N_a \ll N$. (b) Identical squeezing-augmented laser-light pulses, a.k.a. displaced squeezed states of light, $|\alpha; r\rangle^{\otimes k}$, where $|\alpha|^2 \equiv N \gg N_a \equiv {\rm sinh}^2(r)$, i.e., the energy attributable to squeezing ($N_a$) is much less compared to the photon energy in the coherent amplitude ($N$). (c) Blocks of $n$ laser-light pulses $|\alpha\rangle^{\otimes n}$, each with mean photon number $N = |\alpha|^2$ are augmented by a continuous variable (CV) entangled state, generated by splitting a squeezed-vacuum pulse of mean photon number $nN_a$ in an $n$-mode equal splitter, such that the photon energy attributable to quantum augmentation, per pulse, is $N_a \ll N$.
• Figure 2: Relative entropy $S(P_2||P_1)$ between the post-change and pre-change distributions at the homodyne-detection receiver's output, per detected pulse, as a function of $N_a \in [0, 5]$ photons, for $N = 100$ photons, $\eta_1 = 0.9$ and $\eta_2 = 0.85$, for the: (a) classical baseline (red-dashed), (b) squeezing-augmented (red solid), and (c) entanglement-augmented (blue dash-dotted plots, $n = 2, 4, \ldots, 256$) transmitters.
• Figure 3: Monte-Carlo plot of factor-of-improvement of detection latencies, $\tau^{(0)}/\tau^{(1)}$, as a function of $S^{(1)}/S^{(0)}$ (for ARL, $\gamma = 2$ million held constant for both) shows a $1:1$ correlation, as expected Page1957. The parameters chosen for the simulation: $N=100$, $N_a \in (0.01, 1]$, $\eta_1 = 0.9$, $\eta_2 = 0.85$, $n_c = 1000$, and all the simulations are run until $k = 5000$.
• Figure 4: The plot of $S(P_2||P_1)$ with respect to $10\log_{10}(e^{2s})$, the dB-squeezing of the seed squeezed-light source, used to generate the $n$-mode entanglement state. With $s$ held fixed, the $n=2$ case is seen to outperform all others.
• Figure 5: CRE as a function of the pre-change channel loss in dB. An ideal Kennedy receiver achieves CRE$=\infty$, but its CRE is very sensitive to amplitude and phase noise in the LO. An imperfect LO pulse is a coherent state $|\alpha_{\rm{LO}}(1+\epsilon)e^{i\theta}\rangle$, where $0 < \epsilon \ll 1$ is the amplitude error and $\theta \sim {\mathcal{N}}(0, \sigma^2)$, a Normal distributed random variable with variance $\sigma^2 \ll 1$ (mildly truncated to $[-\pi, \pi]$) is the phase error. Homodyne detection on the other hand is very robust to LO noise.