In this reply we clarify the main points of our manuscript and respond to the critique in the Comment arXiv:2002.11514. In particular, we emphasize that our conclusion "squeezing loses effectiveness in the deep quantum regime" does not contradict the previous work arXiv:1801.10383, but instead adds to it, and raises fundamental questions on classifying parameter regimes for quantum synchronization. Moreover, we address the concern brought up on the validity of the master equation in the deep quantum regime, and show that our noise-enhanced synchronization differs from previous literature. Through numerical examples, we also demonstrate that the choice of ansatz, while appearing inconsistent, does not lead to erroneous conclusions. Lastly, we expound on the physics of noise-boosted synchronization, and show that it is indeed a genuine feature unique to the deep quantum regime. However, we note that single photon dissipation is a more accurate term, and will move to using that.
Recently a protocol for Quantum Clock Synchronization (QCS) of remote clocks using quantum entanglement was proposed by Jozsa et al. This method has the goal of eliminating the random noise present in classical synchronization techniques. However, as stated QCS depends on the two members of each entangled pair undergoing the same unitary evolution even while being transported to different locations. This is essentially equivalent to a perfect Eddington Slow Clock Transfer protocol and thus, not an improvement over classical techniques. We will discuss this and suggest ways in which QCS may sti…
We consider a star network consisting of N oscillators coupled to a central one which in turn is coupled to an infinite set of oscillators (reservoir), which makes it leaking. Two of the N + 1 normal modes are dissipating, while the remaining N - 1 lie in a frequency range which is more and more squeezed as the coupling strengths increase, which realizes synchronization of the single parts of the system.
Reply to Comment on "Properties and dynamics of generalized squeezed states"
Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT)（先进ICT研究所，国家信息通信技术研究所）；Research Institute for Science and Technology, Tokyo University of Science（理研，东京科学大学）；Institute for Quantum Computing, University of Waterloo（量子计算研究所，滑铁卢大学）；Red Blue Quantum Inc.（红蓝量子公司）
It is desirable to observe synchronization of quantum systems in the quantum regime, defined by low number of excitations and a highly non-classical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelms synchronization in this regime. Here we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible f…
Synchronization occurs ubiquitously in nature. The van der Pol oscillator has been a favorite model to investigate synchronization. Here we study the oscillator in the deep quantum regime, where nonclassical effects dominate the dynamics. Our results show: (i) squeezed driving loses its effect, (ii) noise boosts synchronization, (iii) synchronization is bounded, and (iv) the limit-cycle is insensitive to strong driving. We propose a synchronization measure and analytically calculate it. These results reflect intrinsic differences between synchronization in the quantum and deep quantum regimes.
A recent manuscript ( arXiv:2002.07488 (2020) ) compares the effect of linear dissipators and squeezing drive on quantum synchronisation. We point at serious mistakes in the validity of the equations they use, the consistency of the ansatz employed, the unregulated fashion in which parameters are varied and the misleading scientific statements made in their manuscript.
A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to overcome the classical power/bandwidth limits on these procedures, enhancing their accuracy. Frequency entangled pulses could be used to construct quantum positioning systems (QPS), to perform clock synchronization, or to do ranging (quantum radar): all of these techniques exhibit a similar enhancement compared with analogous protocols that use classical light. Q…
Large-scale array of squeezed light and synchronization using atomic vapor
Fudan University（复旦大学）；Shanghai Institute of Technical Physics, Chinese Academy of Sciences（中国科学院上海技术物理研究所）；Weizmann Institute of Science（魏茨曼科学研究所）；Shanxi University（山西大学）
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a simple, one-dimensional classical stochastic differential equation approximately describing the phase dynamics of the system under the semiclassical approximation. The density matrix and power spectrum of the original quantum system can be approximately reconstructed from the reduced phase equation. The developed framework enables us to analyze synchronizatio…
We introduce and characterize two different measures which quantify the level of synchronization of interacting continuous variable quantum systems. The two measures allow to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is in principle unbounded, however in the absence of quantum resources (e.g. squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronizat…
Exceptional point induced quantum phase synchronization and entanglement dynamics in mechanically coupled gain-loss oscillators
School of Nanoscience and Technology, IIT Kharagpur（IIT 哈格普尔理工学院纳米科学与技术学院）；Electronics and Electrical Communication Engineering Department, IIT Kharagpur（IIT 哈格普尔理工学院电子与电气通信工程系）；School of Natural and Computing Sciences, University of Aberdeen（阿伯丁大学自然与计算科学学院）
Dual Role of Squeezed-Reservoir in Quantum Phase Synchronization: Boosting and Blockade
School of Physics and Electronic Information, Gannan Normal University（赣南师范大学物理与电子信息学院）；School of Information Engineering, Jiangxi University of Science and Technology（江西理工大学信息工程学院）；Jiangxi Provincial Key Laboratory of Multidimensional Intelligent Perception and Control, Jiangxi University of Science and Technology（江西理工大学多维智能感知与控制江西省重点实验室）
We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when the information source and sink are frame-wise asynchronous. This eliminates the need of frame synchronization at the hardware level and allows for parsing qubit sequences during quantum information processing. Our framework exploits binary constant-weight codes that are self-synchronizing. Possible applications may include asynchronous quantum communication…
