Quantum Clock Synchronization: Achieving Optimal Accuracy with Minimal Communication

Title: Quantum Clock Synchronization: Achieving Optimal Accuracy with Minimal Communication

Abstract: Quantum clock synchronization is a method used to determine the time difference between two spatially separated parties. In this research, we improved upon I. Chuang's quantum clock synchronization algorithm, showing that it is possible to achieve tonbits of accuracy while communicating only one qubit in one direction and using an O(2n) range of frequencies. We also proved a quantum lower bound of Ω(2n) for the product of the transmitted qubits and the range of frequencies, demonstrating that our algorithm is optimal.

Introduction: Quantum clock synchronization is a well-studied problem with many practical and scientific applications. Two standard methods for synchronizing remote clocks are Einstein Synchronization and Eddington's Slow Clock Transport. Recently, two quantum protocols were proposed: one using prior quantum bit entanglement and the other by I. Chuang, which we will focus on.

Methodology: Our computational model assumes that Alice sends a photon with a specific tick rate to Bob. The state of the received photon is eiωtZ|ψ/angbracketright, where t is the time the photon spent in transit and Z is the Pauli matrix. We define a black box quantum procedure, tqh, that takes as input a quantum register holding the tick rate k and a qubit |ψ/angbracketright. The output is a state with a phase that depends on T and k.

Optimal Quantum Algorithm: We describe a protocol for synchronizing two remote clocks by communicating one photon. Alice starts by preparing a register Ro. She then sends the qubit |ψ/angbracketright to Bob with ticking rate ( −2πkω0). Along a classical channel, she tells him her time tA at the moment of the quantum communication. Bob receives at time tB (according to his clock) a quantum state e−2πikω0ttrZ|ψ/angbracketright. He applies a phase change e2πikω0(tB−tA)Z, resulting in the final state e2πikω0(tB−tA−ttr)Z|ψ/angbracketright = e2πikω0TZ|ψ/angbracketright.

Results: We improved upon Chuang's result by presenting an algorithm that achieves tonbits of accuracy while communicating only one qubit in one direction and using an O(2n) range of frequencies. Furthermore, we proved a quantum lower bound of Ω(2n) for the product of the frequency range and the number of transmitted qubits, showing that our algorithm is optimal in this model.

Implications: This research has significant implications for the field of quantum communication. Our algorithm achieves optimal accuracy with minimal communication, which can lead to more efficient and effective methods for synchronizing remote clocks. This research also contributes to the ongoing efforts to develop quantum communication protocols that can outperform their classical counterparts.

Link to Article: https://arxiv.org/abs/0103021v3 Authors: arXiv ID: 0103021v3