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Applied Physics B

Quantum clock synchronization under decoherence effect

Bagher Noorbakhsh, Ali Soltanmanesh, Mehdi Aslinezhad

Published Feb 16, 2024• 2 citations
Publisher

Abstract

Abstract In this paper, we study a quantum clock synchronization for a three observer locating system, using entangled qubits and discuss the effect of the environmental noise on the phase of the system using decoherence theory. We will show that the error on the final result of the clock synchronization can be less than the current classical synchronizations, under suitable circumstances. Finally, with an appropriate modelling of the environment we can correct the error of the synchronization for a more accurate locating.

DOI
10.1007/s00340-024-08175-3

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Abstract In this paper, we study a quantum clock synchronization for a three observer locating system, using entangled qubits and discuss the effect of the environmental noise on the phase of the system using decoherence theory. We will show that the error on the final result of the clock synchronization can be less than the current classical synchronizations, under suitable circumstances. Finally, with an appropriate modelling of the environment we can correct the error of the synchronization for a more accurate locating.
In laboratory environment, the channel apparatus will generate particular dominant quantum noise. The noise then will give rise to some errors during synchronization. In this work, the accuracies of one qubit transport protocol and entangled states transport protocol in the presence of noise have been studied. With the help of three important and familiar noise models, the quantum noise will degrade the accuracy has been proved. Due to the influence of quantum noise, the accuracy of entangled qubits decrease faster than that of one qubit. The entangled states will improve the accuracy in noise-free channel, and will degrade the accuracy in noise channel.
Abstract A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of a common phase reference between the parties to be synchronized. In general, the definition of the quantum states between two parties do not have consistent phase definitions, which can lead to an unknown systematic error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which is a non-local approach to synchronize two clocks independent of the properties of the intervening medium. Starting with noisy Bell pairs, we show that the scheme produces a singlet state for any combination of (i) differing basis conventions for Alice and Bob; (ii) an overall time offset in the execution of the purification algorithm; and (iii) the presence of a noisy channel. Error estimates reveal that better performance than existing classical Einstein synchronization protocols should be achievable using current technology.
We propose a quantum analogue of the Huygens clock, where the phases of two spins synchronize through their interaction with a shared environment. This environment acts like the escapement mechanism in a mechanical clock, regulating the gear train and allowing discrete timing advances. In our model, the relative phases of the two spins synchronize via a mutually correlated environment. We demonstrate that several arguments can significantly reduce the cardinality of the allowed measurements for a system of qubits, thus simplifying the problem. We present a numerically efficient method to calculate the degree of quantumness in the correlations of the final density matrix, providing a tight upper bound for rank 3 and rank 4 density matrices. We suggest a potential realization of noise-induced synchronization between two nuclear spins coupled to a common ancilla undergoing dynamical decoupling.
An important requirement in implementing distributed computing and sensing application is the synchronization of clocks at various locations. The Internet relies on the Network Time Protocol (NTP), which synchronizes clocks with accuracy in the order of milliseconds. More recently an ensemble of atomic clocks is used for navigation based on GPS. These clocks are highly accurate and provide time with very low uncertainty. Even so, many physics experiments such as distributed LIGO-based systems may require more accurate clock synchronization that is achievable using quantum entanglement. This requires the deployment of a network of quantum clocks synchronized by exploiting entangled atomic clock qubits. In this paper, we carry out a simulation study of synchronizing a network of quantum clocks interconnected by a fiber plant that supports the ESnet; the latter is used to support the classical communication needed for teleportation. We consider an existing protocol for synchro-nizing the atomic clock qubits that relies on the GHZ states. To assess the performance of the protocol we developed a discrete-event simulation of the network using IBM Qiskit framework for underlying quantum gate operations and measurements. The simulation results shed light on the resources required in terms of the number entangled qubits and the time needed to achieve the synchronization of different number of nodes in ESnet.