Empty-Signal Detection: Overcoming the Fundamental QBER Limit in Repeaterless Quantum Communication in Principle

TL;DR

This work identifies the fundamental QBER barrier in repeaterless quantum communication and introduces empty-signal detection (ESD) as a rigorous, principle-based framework to overcome it. By encoding particle-existence information into auxiliary degrees of freedom and using controlled operations with multi-copy analysis, ESD reliably discerns vacuum events without perturbing the transmitted quantum state, stabilizing NESR against distance. The key theoretical result shows that, if pP_s > Q_s, NESR can asymptotically reach (pP_s - Q_s)/(P_s - Q_s), effectively decoupling NESR from channel transmission rate and enabling arbitrarily long PRQC in principle. The approach also discusses practical device requirements, security, efficiency trade-offs, and circuit-optimization strategies, highlighting that the ultimate limit shifts from fundamental feasibility to efficiency considerations while broadening potential applications beyond PRQC.

Abstract

The distance of practical repeaterless quantum communication (PRQC) has long been theoretically limited by the fundamental quantum bit error rate (QBER) induced by vacuum signals and single-photon detector (SPD) dark counts. As the communication distance increases, the channel transmission rate decays exponentially, causing vacuum-induced dark counts to dominate detection events and drive the QBER toward 50%, thereby rendering PRQC infeasible. To address this fundamental limitation, we introduce an empty-signal detection (ESD) paradigm that provides a rigorous theoretical framework for overcoming the fundamental distance limit of PRQC. By encoding particle-existence information (PEI) onto auxiliary degrees of freedom (DOF) and employing controlled operations together with multi-copy analysis, the ESD module enables vacuum events to be reliably identified and discarded without disturbing the transmitted quantum state. This stabilizes the non-empty signal rate (NESR) at a high, distance-independent value and suppresses the fundamental QBER to a sufficiently low level, irrespective of the channel transmission rate. Consequently, PRQC can, in principle, be extended to arbitrarily long distances, limited only by efficiency considerations rather than by intrinsic feasibility constraints imposed by fundamental QBER. Despite ESD requiring further integration of quantum technologies and PRQC remaining speed-limited in practice, this work establishes the first rigorous theoretical framework that, in principle, overcomes the fundamental QBER limitation in PRQC, thereby clarifying its ultimate feasibility over arbitrarily long distances.

Figures (6)

• Figure 1: Architecture of the ESD module (left) and receiver scheme (right). Each incoming signal first passes through the ESD module, where the auxiliary DOF $L$ of the input particle is coupled to $n$ auxiliary systems $L_{i}$ via controlled operations. The side outputs are then measured projectively, and the number of effective detections in state $|1\rangle$ determines whether the received signal is identified as empty or not.
• Figure 2: NESR as a function of channel transmission rate $t$ for different controlled-gates. The case $n=0,k=0$ corresponds to standard PRQC without ESD. Introducing ESD modules significantly enhances the NESR, particularly at low transmission rates. For instance, with $(n,k)=(7,3)$, the NESR increases by about seven orders of magnitude at $t=10^{-12}$ when $P=0.99$ (high-performance C-NOT), and by roughly five orders of magnitude even for a low-fidelity gate with $P=0.1$ (C-NOT with fidelity lower than 10%). These results highlight that ESD effectively improves NESR against channel loss.
• Figure 3: Fundamental QBER as a function of transmission rate $t$ under different ESD configurations. Applying ESD enables stable, low QBER even when the transmission rate drops by several orders of magnitude. For $(n,k)=(9,4)$, the QBER remains below 3% at $t=10^{-12}$ for both $P=0.99$ and $P=0.1$, whereas without ESD, communication fails once $t\lesssim10^{-6}$. These results confirm that the ESD framework robustly suppresses the fundamental QBER across a wide range of gate fidelities.
• Figure 4: NESR (\ref{['FigNESR-7']}, \ref{['FigNESR-9']}) and QBER (\ref{['FigQBER-7']}, \ref{['FigQBER-9']}) as functions of $n,k$ at fixed transmission rates. For $t=10^{-7}$, choosing $k\geq 2$ yields a high NESR, with QBER suppressed whenever $k>0$. For $t=10^{-9}$, $k\geq 3$ ensures reliable NESR, while QBER control requires $k>1$. Here $0\leq k\leq n\leq 9$ and $P=0.99$. These trends illustrate that even modest usage of ESD can significantly enhance NESR and suppress QBER.
• Figure 5: State preparation for the polarization DOF. A PBS separates the input signal by polarization; one path passes through an HWP that flips the polarization, and the two paths are recombined at a BS, yielding an output with fixed polarization.

Theorems & Definitions (4)

• Proposition 1
• Proposition 1
• Theorem 2
• Corollary 3