Practical Quantum Clock Synchronization Using Weak Coherent Pulses

TL;DR

The paper addresses precise, authenticated clock synchronization for quantum networks by introducing a bidirectional scheme that uses attenuated weak coherent pulses and Hong-Ou-Mandel interference. By exploiting channel reciprocity and post-selection on BB84 polarization states, it derives a two-way timing protocol that cancels unknown propagation delays and yields sub-nanosecond offset estimates. Numerical simulations under realistic telecom parameters demonstrate sub-100 ps accuracy in metro-scale links and reveal clear security signatures against intercept-resend and photon-number splitting attacks, with decoy-state methods proposed for further robustness. The approach highlights practical advantages of WCPs—namely high repetition rates and adjustable mean photon numbers—to extend distance and improve synchronization throughput, positioning this method as a feasible, authenticated timing backbone for quantum repeater networks.

Abstract

Establishing and maintaining a common time reference across spatially separated devices is a prerequisite for networked quantum experiments and secure communications. Classical two-way timing protocols such as Network Time Protocol (NTP) or Precision Time Protocol (PTP) are vulnerable to asymmetric channel delays and cannot provide the picosecond-level precision demanded by quantum repeater networks. We propose and numerically evaluate a quantum-enhanced clock synchronization protocol based on attenuated weak coherent pulses (WCPs) and bidirectional Hong--Ou--Mandel (HOM) interferometry. Our simulations assume telecom-band photons ($1550\,\mathrm{nm}$) with a temporal width of $10.0\,\mathrm{ns}$, a repetition rate of $f = 10\,\mathrm{MHz}$, effective mean photon number $μ= 1.0$, detector efficiency $η= 85\%$, detector timing jitter of $150\,\mathrm{ps}$, and channel loss of $0.2\,\mathrm{dB/km}$. We simulate that sub-nanosecond clock-offset accuracy and precision can be achieved under these operating conditions. This work demonstrates that high-repetition-rate WCPs combined with HOM interference can provide flexible and secure quantum clock synchronization at sub-nanosecond precision.

Figures (9)

• Figure 1: Simulated coincidence probability (\ref{['eq:coh_coin']}) as a function of relative time delay, $\tau$, for interfering WCPs. The plots show the effect of varying the mean photon number per pulse ($\mu$) and the polarization mismatch angle ($\Phi$) while holding the temporal width constant at $\sigma_{t}=10.0$ ns. As $\mu$ increases, the dip is more apparent, though relative depth is reduced, and as $\Phi$ increases from $0$ to $\pi$/2, the interference visibility is reduced, causing the dip to become shallower.
• Figure 2: Simulated coincidence probability versus relative time delay, $\tau$, for different spectral bandwidths, represented by the temporal width, $\sigma_t$. The mean photon number is fixed at $\mu=1.0$ and the polarization is perfectly matched. A smaller temporal width results in a narrower interference dip, demonstrating the inverse relationship between the temporal coherence of the photons and the width of the Hong-Ou-Mandel dip.
• Figure 3: Spacetime diagram of the two-way timing exchange between Alice (left world line) and Bob (right world line). The protocol aims to determine the unknown clock offset, $\delta$, between their local clocks. Alice sends a signal at her local time $t_0^A$ (red line), and Bob sends a signal at his local time $t_0^B$ (blue line). By using the locally measured time intervals $\Delta t_{AA}$ and $\Delta t_{BB}$, the offset can be determined while canceling the unknown propagation delay of the channel.
• Figure 4: Schematic for Alice and Bob's synchronization signals. Both prepare pulses with randomly selected BB84 polarization state separated in time by a period $T_{\mathrm{rep}}$. Each pulse has a temporal width $\sigma_t$. The disparity in the start time is the offset $\delta$. The color of each pulse indicates the prepared BB84 polarization state.
• Figure 5: Schematic of the experimental protocol. Alice and Bob employ symmetric setups. The Source module consists of a classical communication-band laser equipped with intensity and polarization modulators to generate bright pulses with controllable polarization states. At Alice’s side, beam splitter 1, BS1, divides the pulses: one copy remains local, while the other is transmitted to the network. Variable optical attenuators, ATT1 and ATT2, reduce the pulse intensity to the desired photon level ($\mu$). The pulse attenuated by ATT2 is sent through the quantum channel, QC1, to Bob. At BS2, Alice’s locally attenuated pulses interfere with those arriving from Bob’s side via the network. Single-photon detectors, D1 and D2, register detection events following the interference. A variable delay line, VDL, compensates for the relative phase difference between the paths. Detection events are time-tagged and correlated using a time-to-digital converter, TDC. A precision atomic clock, AC, provides timing discipline for the modulators and the TDC, minimizing drift among the high-speed electronic components.