arXiv:2306.06897 · Entropy

Fisher Information as General Metrics of Quantum Synchronization

Yuan Shen, Hong Yi Soh, L. C. Kwek, W. J. Fan

Published Jul 26, 2023• 9 citations

Abstract

Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization.

DOI: 10.3390/e25081116

Related papers

Quantum synchronization and dissipative quantum sensing

Gaurav M. Vaidya, Simon B. Jäger, Athreya Shankar

We study the phenomenon of quantum synchronization from the viewpoint of quantum metrology. By interpreting quantum self-sustained oscillators as dissipative quantum sensors, we develop a framework to characterize several aspects of quantum synchronization. We show that the quantum Fisher information (QFI) serves as a system-agnostic measure of quantum synchronization that also carries a clear operational meaning, viz., it quantifies the precision with which the amplitude of a weak synchronizing drive can be measured. We extend our analysis to study many-body oscillators subjected to multiple drives. We show how the QFI matrix can be used to determine the optimal drive that maximizes quantum synchronization, and also to quantitatively differentiate the synchronization responses induced by different drives. Our work highlights multiple connections between quantum synchronization and quantum metrology, paving a route toward finding quantum technological applications of quantum synchronization.

arXiv:2405.10643Physical Review AJan 6, 202515 citations

Quantum synchronization: A tutorial guide

Sourabh Lahiri, Shamik Gupta

Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.

quant-pharXiv:2609.14375Sep 15, 20260 citations

Synchronization along quantum trajectories

Najmeh Eshaqi-Sani, Gonzalo Manzano, Roberta Zambrini +1 more

We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol oscillators interacting through dissipative coupling. \nWe show the deep impact of synchronization on the statistics of phase-locking indicators and other correlation measures defined for single trajectories, spotting a link between the presence of synchronization and the emergence of large tails in the probability distribution for the entanglement along trajectories. Our results shed new light on fundamental issues regarding quantum synchronization providing new methods for its precise quantification.

Jan 1, 202037 citations

Measurement Noise Susceptibility in Quantum Estimation

Stanisław Kurdziałek, Rafał Demkowicz-Dobrzański

Fisher information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of the maximal achievable precision of the estimation of the parameters encoded in quantum states using the most general quantum measurement. It fails, however, to quantify the robustness of quantum estimation schemes against measurement imperfections, which are always present in any practical implementations. Here, we introduce a new concept of Fisher information measurement noise susceptibility that quantifies the potential loss of Fisher information due to small measurement disturbance. We derive an explicit formula for the quantity, and demonstrate its usefulness in the analysis of paradigmatic quantum estimation schemes, including interferometry and superresolution optical imaging.

arXiv:2206.12430Physical Review LettersApr 21, 202325 citations

Properties and relative measure for quantifying quantum synchronization

Wenlin Li, Wen-Zhao Zhang, Chong Li +1 more

Although quantum synchronization phenomena and corresponding measures have been widely discussed recently, it is still an open question how to characterize directly the influence of nonlocal correlation, which is the key distinction for identifying classical and quantum synchronizations. In this paper, we present basic postulates for quantifying quantum synchronization based on the related theory in Mari's work [Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605], and we give a general formula of a quantum synchronization measure with clear physical interpretations. By introducing Pearson's parameter, we show that the obvious characteristics of our measure are the relativity and monotonicity. As an example, the measure is applied to describe synchronization among quantum optomechanical systems under a Markovian bath. We also show the potential by quantifying generalized synchronization and discrete variable synchronization with this measure.

Physical review. EJul 14, 201749 citations

A Proposal for Quantum Fisher Information Optimization and its Relation with Entanglement Measures

Volkan Erol

Studies about Quantum Information Theory continue actively in many research institutions. Very recently, pratical setups of large scale quantum computers are widely studied e.g. quantum repeaters, memories and processors. Entanglement provides us a computational advantage in realization of quantum algorithms. Some ways to quantifiying entanglement were defined. The best formal way to quantify it, is the methods that we call Entanglement Measures or Entanglement Monotones. In this research area, State Ordering Problem is defined and still an open problem especially for multiparticle entangled states. Fisher Information provides a good background for the solution of some actual Information Theory problems. Quantum Fisher Information (QFI) is a value that could be used in situations where phase sensitivity is important and this concept is expected to be the quantum version of the mentioned inftrastructure for Quantum Systems. QFI cannot be defined as an Entaglement Measure or Monotone. In the scope of this thesis, a new optimization technique is proposed for optimizing QFI and thanks to this optimization method, the ordering relation between QFI and entanglement measures is studied. Based on the studies made in the area of quantum state ordering, new and interesting analysis results are found and reported. The main important and interesting result achieved is that for two qubit quantum states, QFI maximized under Local Operation and Classical Communication has an interesting ordering relation with entanglement measures especially with Relative Entropy of Entanglement. Our study is extended for the qubit-qutrit systems and ordering relations and classification results are presented. For some quantum systems, the changes in QFI under decoherence channels are also considered.

arXiv:1705.04682May 12, 20178 citations