[Paper Review] Accuracy enhancing protocols for quantum clocks

Yuxiang Yang, Lennart Baumgärtner+2 more|arXiv (Cornell University)|May 23, 2019

Quantum Computing Algorithms and Architecture3 references4 citations

TL;DR

This paper proposes quantum protocols that enable a quantum clock (the Enhancing Clock, EC) to boost the accuracy of an input time signal by a factor of d, where d is the dimension of the EC's state space. By leveraging quantum dynamics and adaptive control, the EC achieves quadratic accuracy improvement over classical methods, with feedback allowing indefinite retention of enhanced accuracy.

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.

Motivation & Objective

• To develop protocols that allow a quantum clock to improve the accuracy of an input time signal beyond classical limits.
• To investigate how quantum coherence and control in a d-dimensional system can enhance timekeeping precision.
• To explore the role of feedback in maintaining long-term accuracy enhancement in quantum clock networks.
• To establish a foundation for quantum signal processing tailored to time-keeping systems without external time references.
• To enable more accurate, shared time references in distributed quantum networks using minimal entanglement.

Proposed method

• Design a quantum Enhancing Clock (EC) with a d-dimensional Hilbert space to process an input time signal.
• Implement a dynamics-switching protocol where the EC's internal Hamiltonian is adaptively controlled based on incoming ticks.
• Use quantum state preparation and unitary evolution to encode time information with higher resolution than classical counterparts.
• Introduce feedback mechanisms allowing the EC to adjust the input clock’s signal, preserving accuracy over time.
• Compare performance against classical protocols like tick-bunching and fixed-dynamics processing.
• Employ confidence interval analysis to quantify accuracy improvement, measuring reduction in inaccuracy by a factor of d.

Experimental results

Research questions

• RQ1 Can a quantum clock enhance the accuracy of an input time signal by a factor scaling with its Hilbert space dimension d?
• RQ2 How does quantum dynamics in a d-dimensional system outperform classical signal processing in time-keeping tasks?
• RQ3 What is the role of feedback in maintaining long-term accuracy enhancement in quantum clock protocols?
• RQ4 Can quantum protocols achieve accuracy improvements beyond classical bounds without requiring entanglement between nodes?
• RQ5 How can such protocols be used to establish a shared, high-accuracy time reference in a distributed network?

Key findings

• The proposed quantum protocols achieve an accuracy enhancement by a factor of d for large enough d, significantly outperforming classical methods.
• The dynamics-switching protocol (Protocol 1) reduces inaccuracy by a factor of d, with numerical simulations confirming its superiority over tick-bunching and fixed-dynamics protocols.
• Without feedback, the accuracy gain is temporary; with feedback, the enhanced accuracy can be maintained indefinitely.
• The protocols rely fundamentally on quantum dynamics and adaptive control—classical analogues cannot achieve the same scaling in accuracy.
• The protocols do not require shared entanglement among nodes, making them complementary to existing entanglement-based synchronization schemes.
• When applied to networked clocks, the protocols can reduce the overall inaccuracy to the product of individual errors from standard synchronization methods.