Restoring Quantum Superiority of Noisy Quantum Illumination

TL;DR

This work tackles the challenge of preserving the quantum superiority of quantum illumination in realistic noisy environments. By moving beyond the Born–Markov approximation and analyzing non-Markovian decoherence, the authors show that the formation of a bound state in the single-excitation energy spectrum of each light mode plus its local bath can restore the ideal, entanglement-enhanced resolution. The long-time performance, quantified by the fidelity-based lower bound $F^-$, becomes sensitive to the bound-state parameter $Z$ and the squeezing $r$, with $F^-(\infty) < 1/2$ when a bound state exists and improving with larger $r$; the bound-state condition is $\omega_0 < \eta \omega_c \Gamma(s)$. This provides a physical principle and a reservoir-engineering path to realize high-resolution quantum illumination and quantum radar in the noisy intermediate-scale quantum era, broadening practical applicability of quantum sensing under realistic decoherence.

Abstract

Quantum illumination uses quantum entanglement as a resource to enable higher-resolution detection of low-reflectivity targets than is possible with classical techniques. This revolutionary technology could transform modern radar. However, it is widely believed that the decoherence induced by the ubiquitous quantum noise destroys the superiority of quantum illumination, severely constraining its performance and application in our present noisy intermediate-scale quantum era. Here, we propose a method to restore the quantum superiority of the quantum illumination in the presence of quantum noises. Going beyond the widely used Born-Markov approximation, we discover that the resolution of noisy quantum illumination is highly sensitive to the energy spectrum of the composite system formed by each of the two light modes and its local quantum noise. When a bound state is present in the energy spectrum, the resolution asymptotically approaches its ideal form. Our result establishes a physical principle to preserve the quantum superiority and paves the way for the realization of high-resolution quantum illumination in noisy situations.

Figures (3)

• Figure 1: (a) Diagrammatic sketch of the quantum illumination scheme. (b) Evolution of the resolution characterized by the lower bound $F^-(t)$ of the minimum error probability $P(t)$ in different values of squeezing parameter $r$ under the Born-Markovian decoherence. The blue line is the ideal result. We use $\omega_{c}=10\omega_{0}$, $\eta=0.05$, $\xi=10^{-3}$, $s=0.8$, and $\beta=\omega_{0}^{-1}$.
• Figure 2: (a) Energy spectrum (blue dots) via solving Eq. \ref{['eq:eq19']}, $|u(t=400\omega_{0}^{-1})|$ (red rectangles) via solving Eq. \ref{['uead']}, and $Z$ (red lines) via evaluating the the residue contributed by the bound state as a function of $\eta$ when $s=0.8$ and $\omega_{c}=10\omega_{0}$ in (a) and $s$ when $\eta=0.2$ and $\omega_{c}=5\omega_0$ in (c). Evolution of the corresponding $F^{-}(t)$ in different values of (b) $\eta$ and (d) $s$. The analytical results predicted by Eq. (\ref{['eq:eq21']}) in the presence of the bound state are presented by the blue lines. Other parameters are $\xi=10^{-3}$ and $\beta=2\omega_{0}^{-1}$.
• Figure 3: Steady-state $F^-$ at $t=400\omega_0^{-1}$ in different values of the squeezing parameter $r$ as the functions of (a) $\eta$ and (b) $s$. The blue lines denote the analytical results predicted by Eq. (\ref{['eq:eq21']}). Other parameters are the same as Fig. \ref{['fig:fig2']}.