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arXiv:1806.00491 · PRX Quantum

Quantum Clocks are More Accurate Than Classical Ones

Mischa P. Woods, Ralph Silva, Gilles Pütz, Sandra Stupar, Renato Renner

Published Feb 3, 2022• 40 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/prxquantum.3.010319

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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.
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.
Even though our microscopic physical theories, such as classical or quantum mechanics, are time-reversal invariant, time appears to march forward irreversibly. It is widely believed that effective entropy increase due to the second law of thermodynamics is at the origin of this emergent arrow of time. Any system that is out of thermal equilibrium and produces entropy can thus be used as a clock, be it a melting ice cube or a sophisticated atomic clock. The understanding of entropy in physics has significantly advanced with the advent of information theory in the last century. It has also led to the insight that the amount of entropy a clock produces is linked to how precisely the clock works, and thereby, how much information the clock reveals about the passage of time. In this thesis, we ask: what fundamental limits does the underlying physical theory impose on the precision of clocks within that theory? To rigorously answer this question, we devise a minimal clock model within quantum theory. By consistently modeling all clock constituents as quantum systems, we can ensure we account for all the resources used by the clock. This includes, in particular, the readout. Classically, one can obtain this for free, but quantum mechanically, this has a resource cost associated with it. To this end, we consolidate existing frameworks that describe clocks in both classical and quantum theory. Revising fluctuation theorems from quantum thermodynamics, we demonstrate how such theorems impose limits on the attainable precision of clocks. These precision bounds turn out to be more stringent for classical systems than for quantum ones. Quantum clocks can harness coherence and correlations to suppress fluctuations, allowing them to exponentially surpass precision bounds that hold for classical clocks. We show this separation between classical and quantum clocks by constructing an explicit example that uses quantum dynamics to saturate the quantum precision bounds. Finally, we close the thesis by exploring implications of these timekeeping bounds beyond fundamental science in quantum technologies. We show how quantum clocks can be used to quantify the energetic cost of quantum computation by linking computational fidelity to thermodynamic entropy production.
Quantum mechanics imposes a fundamental trade-off between the accuracy of time measurements and the size of the systems used as clocks. When the measurements of different time intervals are combined, the errors due to the finite clock size accumulate, resulting in an overall inaccuracy that grows with the complexity of the set-up. Here, we introduce a method that, in principle, eludes the accumulation of errors by coherently transferring information from a quantum clock to a quantum memory of the smallest possible size. Our method could be used to measure the total duration of a sequence of events with enhanced accuracy, and to reduce the amount of quantum communication needed to stabilize clocks in a quantum network.
This paper explores the potential of quantum entanglement for constructing ultra-precise timekeeping devices, surpassing the limitations of classical clocks. The core concept involves leveraging the inherent correlations within entangled quantum states to achieve unprecedented temporal resolution. We detail a proposed architecture for a quantum entanglement clock, focusing on utilizing the phase-sensitive nature of entangled particles to perform time measurements. The theoretical framework demonstrates how entanglement can fundamentally alter time measurement, offering a pathway towards dramatically improved accuracy. This work highlights the significance of quantum mechanics in redefining the boundaries of precision measurement and opens new avenues for technological advancements in areas such as fundamental physics research, metrology, and navigation systems. This research presents a novel approach to timekeeping, moving beyond the constraints of classical mechanics and into the realm of quantum phenomena.
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.
Atomic clocks are our most accurate indicators of time. Their applications range from GPS systems to synchronization of electronics, astronomical observations, and tests of fundamental physics. Here we propose a protocol that combines an atomic clock with a quantum memory, realizing a stopwatch that can be paused and resumed on demand. Taking advantage of the quantum memory, the stopwatch can measure the total time elapsed in a sequence of time intervals with the ultimate precision allowed by quantum mechanics, outperforming stopwatches that use only classical memories. The working principle of the quantum stopwatch is a new type of information compression,tailored to store the state of the quantum clock into a quantum memory of exponentially smaller size. Our protocol can be used to generate quantum states with Heisenberg limited sensitivity and to efficiently synchronize clocks in quantum communication networks.