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arXiv:1905.09707

Accuracy enhancing protocols for quantum clocks

Yuxiang Yang, Lennart Baumgärtner, Ralph Silva, Renato Renner

Published May 23, 2019• 3 citations
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Abstract

The accuracy of the time information generated by clocks can be enhanced by allowing them to communicate with each other. Here we consider a basic scenario where a quantum clock receives a low-accuracy time signal as input and ask whether it can generate an output of higher accuracy. We propose protocols that use a quantum clock with a $d$-dimensional state space to achieve an accuracy enhancement by a factor of $d$, for large enough $d$. If no feedback to the input signal is allowed, this enhancement is temporary. With feedback the accuracy enhancement can be retained indefinitely. Our protocols are specific to quantum clocks, and may be used to synchronise them in a network, defining a time scale that is more accurate than what can be achieved by non-interacting or classical clocks.

DOI
10.48550/arxiv.1905.09707

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The accuracy of the time information generated by clocks can be enhanced by allowing them to communicate with each other. Here we consider a basic scenario where a quantum clock receives a low-accuracy time signal as input and ask whether it can generate an output of higher accuracy. We propose protocols that use a quantum clock with a ddd-dimensional state space to achieve an accuracy enhancement by a factor of ddd, for large enough ddd. If no feedback to the input signal is allowed, this enhancement is temporary. With feedback the accuracy enhancement can be retained indefinitely. Our protocols are specific to quantum clocks, and may be used to synchronise them in a network, defining a time scale that is more accurate than what can be achieved by non-interacting or classical clocks.
A clock is, from an information-theoretic perspective, a system that emits information about time.One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks.Here we show a quantum-over-classical advantage for clocks or, more precisely, the task of generating information about what time it is.The argument is based on information-theoretic considerations: we analyze how the accuracy of a clock scales with its size, measured in terms of the number of bits that could be stored in it.We find that a quantum clock can achieve a quadratically improved accuracy compared to a purely classical one of the same size.
It is essential to establish precise times in future communication networks. Any real-time task's function depends on the system's ability to synchronise time. Time synchronisation is critical in the current communication network and must be maintained to transmit data packets. The functionality of 6G, the Tactile Internet, Time-Sensitive Networking, and ultra-reliable low-latency communications is highly susceptible to time synchronisation. We investigated the idea of employing time synchronisation across different communication network nodes. The current state-of-the-art employs network protocols like Precision-Time Protocol for synchronising clocks across different nodes. These network protocols are not robust and can generate jitters in data transmission. In this paper, we suggested synchronising the time of the node clocks at three different places using quantum technology. Notably, the oscillation frequencies of each qubit (or oscillator) located at these nodes can be synchronised using the quantum synchronisation technique. This set of three oscillators will work as a single clock and will be the master clock of the network. We propose distributing precise time and frequency standards using quantum synchronisation on node clocks. We can synchronise the three qubits (each placed at one node) to oscillate at an identical frequency by applying an external field of a wavelength of 813.32813.32813.32 nm. We analysed our model for different coupling constants and dissipation rates to provide an analysis of the behaviour of the amount of synchronisation in different experimental configurations. The optimal accuracy for our system is 1.6×10151.6 \times 10^{15}1.6×1015 signals per second. Further, we used the Allan deviation to examine the stability of our system for various noise strengths.
Accurate timekeeping is essential for scientific and technological advancements, particularly in areas of communication, networking, navigation, and high precision measurements. While many methods of time resolution are already established using classical resources, they fail to combine high precision outcomes with large-scale implementations. Additionally, numerous quantum networking architectures using satellite-assisted methods have demonstrated quantum communication on scales exceeding ground-based methods. For these reasons, we propose the use of a time synchronization method by which pairs of highly time-correlated photons are exchanged between clocks on satellites and clocks on Earth, al- lowing users to reconstruct the time offsets between their clocks. This is known as Quantum Clock Synchronization (QCS). We analyze global time synchronization, via numerical simulation, using a network of satellites equipped with quantum resources, such as entangled photon sources (SPDC) and single photon detectors. We find that for satellites in low-earth orbits, a configuration of 50 evenly-space satellites provides constant visibility and sub-nanosecond time synchronization to any location on Earth. Due to practical constraints, clocks available for use on satellites are often of lesser quality than those available for ground use. However, by allowing the satellites in our network to synchronize among themselves, we overcome this limitation, forming a highly precise “master clock” capable of global, high precision time synchronization. We then examine the amount of quantum security provided by polarization-entangled photon sources as a potential way to protect an experimental implementation of QCS from attacks such as signal spoofing. To do this, we identify regions on Earth where Bell violations between exchanged entangled photons can ensure quantum security at various confidence vii levels. Combined with similar insights gained from determining the network scale of our QCS protocol at the single-link level, we demonstrate the potential for highly precise, global, and potentially quantum-secure clock synchronization. Finally, we modify our QCS protocol to support frequency, or tick-rate, offsets in addition to constant time offsets. We motivate this by presenting some relativistic effects that can introduce frequency differences between clocks in space and on Earth. Provided that relative velocities between clocks are corrected for, we identify constant and variable clock defects through numerical simulations.
Precise time synchronisation underpins critical infrastructure from telecommunications and financial markets to power grids and scientific metrology. Several families of quantum protocols have been proposed and demonstrated for clock synchronisation and time distribution, exploiting entangled photon pairs, quantum key distribution (QKD) correlations, Hong-Ou-Mandel interference, and entangled clock networks. We critically assess these approaches, reviewing the main quantum time synchronisation (QTS) protocol families, quantifying the gap between theory and experiment, and identifying practical bottlenecks in sources, detectors, and channels. We survey the classical timing landscape from Network Time Protocol (NTP) and GPS to laboratory-grade optical frequency transfer, and compare quantum and classical methods at equivalent maturity. We examine use cases including financial trading, power grids, telecommunications, scientific metrology, and military applications, evaluating whether quantum timing offers a realistic advantage. We show that time transfer, not clock performance, is now the bottleneck for distributed optical timekeeping: the best demonstrated synchronisation uncertainty (2.46~ps) falls two to three orders of magnitude short of what optical clocks with fractional frequency uncertainties of 10−1810^{-18}10−18--10−1910^{-19}10−19 require. Our assessment is that quantum time synchronisation will not replace classical methods for most applications in the near-to-medium future. Its near-term value lies in physical-layer security against timing manipulation and integration with quantum communication networks, while closing the synchronisation gap for scientific metrology remains the most critical open challenge.
The ability to measure, hold and distribute time with high precision and accuracy is a foundational capability for scientific exploration. Beyond fundamental science, time synchronization is an indispensable feature of public and private communication, navigation and ranging, and distributed sensing, amongst others technological applications. We propose the implementation of a quantum network of satellite- and ground-based clocks with the ability to implement Quantum Clock Synchronization to picosecond accuracy. Implementation of the proposed QCS network offers a double advantage: (1) a more accurate, robust, and secure time synchronization network for classical applications than currently possible, and (2) a resource to fulfill the much more stringent synchronization requirements of future quantum communication networks.
Atomic frequency standards have achieved steadily increasing precision over the past seventy years, enabled in part by feedback mechanisms that stabilise their output. In parallel, the timekeeping capabilities of quantum systems have been explored within the recently developed ticking-clock framework, which models clocks as dynamical systems producing a stochastic sequence of ticks. However, a theoretical description that unifies these perspectives and incorporates feedback into autonomous quantum clocks has been lacking. We introduce a framework for feedback-controlled clockworks in which classical information extracted from the tick sequence is used to influence the subsequent dynamics of the clock. We show that such feedback preserves the core structural features of self-timing and clockwork independence that characterise autonomous ticking clocks. We further identify the signal-to-noise ratio S\mathfrak{S}S as the fundamental figure of merit for assessing the performance of feedback-controlled clocks. Applying our framework to two representative architectures, we prove that classical clockworks cannot surpass the optimal signal-to-noise ratio achievable without feedback. In contrast, for quantum clockworks we present numerical evidence that feedback can provide a genuine and robust performance enhancement, improving the maximal attainable signal-to-noise ratio. We provide additional numerical evidence, suggesting that the magnitude of the improvement strongly depends on the amount and type of the stored, classical information. These results establish feedback as a potentially essential ingredient in pushing the fundamental limits of timekeeping in the quantum regime.