Quantum-Enhanced Change Detection and Joint Communication-Detection

Abstract

Quick detection of transmittance changes in optical channel is crucial for secure communication. We demonstrate that pre-shared entanglement using two-mode squeezed vacuum states significantly reduces detection latency compared to classical and entanglement-augmented coherent-state probes. The change detection latency is inversely proportional to the quantum relative entropy (QRE), which goes to infinity in the absence of thermal noise, suggesting idealized instantaneous detection. However, in realistic scenarios, we show that QRE scales logarithmically with the inverse of the thermal noise mean photon number. We propose a receiver that achieves this scaling and quantify its performance gains over existing methods. Additionally, we explore the fundamental trade-off between communication capacity and change detection latency, highlighting how pre-shared entanglement enhances both.

Figures (5)

• Figure 1: In a lossy thermal noise bosonic channel $\mathcal{E}^{\bar{n}_{\rm B}, \eta_s}$, detecting abrupt transmittance changes from $\eta_0$ to $\eta_1$ at an unknown time $\tau_c$ is important. A quantum state $\hat{\rho}$ is continuously sent through the channel, with the potential to utilize pre-established entanglement with the receiver. The output state $\hat{\sigma}_s$ is then subject to measurement, and the collected data are processed using a CUSUM test. The receiver setup, indicated by a red square in the measurement block, includes a two-mode squeezing (TMS) operation followed by one or two photon-number-resolving (PNR) detector or other appropriate measurement configurations when the input state $\hat{\rho}$ is a TMSV state.
• Figure 2: Relative entropy vs mean photon number of the thermal noise level for various transceivers. The dashed curves are for the TMSV input state, and the solid curves are for the coherent input state. The number following "PNR" represents the maximum resolvable photon number of the detector, while the absence of a number indicates a ideal PNR detector. (a) $\bar{n} = 5$, $\eta_0 = 0.9$, $\eta_1 = 0.8$ (b) $\bar{n} = 400$, $\eta_0 = 0.9$, $\eta_1 = 0.8$.
• Figure 3: Proportion of energy in squeezing versus min-max normalized QRE. The solid curves are for $\eta_0 = 0.9$ and $\eta_1 = 0.8$, and the dashed curves are for $\eta_0 = 0.1$ and $\eta_1 = 0.05$. The blue curves are for $\bar{n}_{\rm B} = 10$, and the red curves are for $\bar{n}_{\rm B} = 10^{-6}$. The curves with crosses are for $\bar{n} = 0.1$, while the unmarked curves correspond to $\bar{n} = 100$.
• Figure 4: Relative entropy versus channel capacity in joint communication and change detection problem. $\bar{n} = 0.001$, $\bar{n}_{\rm B} = 10$, $\eta_0 = 0.9$, and $\eta_1 = 0.8$. Alice sends a codeword to Bob, who employs CUSUM test for change detection of transmittance and decode the codeword for communication.
• Figure 5: We numerically simulate the performance of the CUSUM test to evaluate change detection latency. Recall that the expected change-detection latency scales as $\frac{\ln(\gamma)}{S(p_1||p_0)}$, where $\gamma$ is the threshold parameter controlling the false alarm rate and $S(p_1||p_0)$ is the relative entropy. We adopt the same parameter settings as in Figure \ref{['fig:RE vs Capacity']}: $\bar{n} = 0.001$, $\bar{n}_{\rm B} = 10$, $\eta_0 = 0.9$, and $\eta_1 = 0.8$. Each plotted curve represents the average latency over 20000 independent Monte Carlo runs.

Theorems & Definitions (1)

• Conjecture 1