In this paper, we study the decoherence property of synchronization master equation for networks of qubits interconnected by swapping operators. The network Hamiltonian is assumed to be diagonal with different entries so that it might not be commutative with the swapping operators. We prove a theorem establishing a general condition under which almost complete decohernece is achieved, i.e., all but two of the off-diagonal entries of the network density operator asymptotically tend to zero. This result explicitly shows that quantum dissipation networks tend to forget the information initially encoded when the internal (induced by network Hamiltonian) and external (induced by swapping operators) qubit interactions do not comply with each other.
We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the quantum synchronization effects between optomechanical systems and find that the error between the systems and the fluctuation of error are sensitive to coupling intensity by calculating the largest Lyapunov exponent of the model and quantum fluctuation, respectively. Through taking the appropriate coupling intensity, we can control quantum synchronization ev…
Based on the concepts of quantum synchronization and quantum phase synchronization proposed by A. Mari \textit{et al.} in Phys. Rev. Lett. 111, 103605 (2013), we introduce and characterize the measure of a more generalized quantum synchronization called quantum $φ$-synchronization under which the pairs of variables have the same amplitude and possess the same $φ$ phase shift. Naturally, quantum synchronization and quantum anti-synchronization become special cases of quantum $φ$-synchronization. Their relations and differences are also discussed. To illustrate these theories, we investigate the…
We extend the concepts of quantum complete synchronization and phase synchronization, which are proposed firstly in [Phys. Rev. Lett, 111 103605 (2013)], to more widespread quantum generalized synchronization. The generalized synchronization can be considered as a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measurement are further proposed and analyzed in this paper. As an example, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling sy…
I consider quantum protocols for clock synchronization, and investigate in particular whether entanglement distillation or quantum error-correcting codes can improve the robustness of these protocols. I also draw attention to some unanswered questions about the relativistic theory of quantum measurement. This paper is based on a talk given at the NASA-DoD Workshop on Quantum Information and Clock Synchronization for Space Applications (QuICSSA), September 25-26, 2000.
Synchronization phenomena have been recently reported in the quantum realm at atomic level due to collective dissipation. In this work we propose a dimer lattice of trapped atoms realizing a dissipative spin model where quantum synchronization occurs instead in presence of local dissipation. Atoms synchronization is enabled by the inhomogeneity of staggered local losses in the lattice and is favored by an increase of spins detuning. A comprehensive approach to quantum synchronization based on different measures considered in the literature allows to identify the main features of different sync…
In this article, we investigate the problem of engineering synchronization in non-Markovian quantum systems. First, a time-convoluted linear quantum stochastic differential equation is derived which describes the Heisenberg evolution of a localized quantum system driven by multiple colored noise inputs. Then, we define quantum expectation synchronization in an augmented system consisting of two subsystems. We prove that, for two homogenous subsystems, synchronization can always be synthesized without designing direct Hamiltonian coupling given that the degree of non-Markovianity is below a cer…
We investigate quantum synchronization phenomenon within the complex network constituted by coupled optomechanical systems and prove the unknown identical quantum states can be shared or distributed in the quantum network even though the topology is varying. Considering a channel constructed by quantum correlation, we show that quantum synchronization can sustain and maintain high levels in Markovian dissipation for a long time. We analyze state sharing process between two typical complex networks, that is, a small-world network corresponding to linear motif state sharing and a scale-free netw…
Phase synchronization was proved to be unbounded in quantum level, but the witness of phase synchronization is always expensive in terms of the quantum resource and non-local measurements involved. Based on the quantum uncertainty relation, we construct two local criterions for the phase synchronization in this paper. The local criterions indicate that the phase synchronization in the quantum level can be witnessed only by the local measurements, and the deduction has been verified in the optomechanics system in numerical way. Besides, by analyzing the physical essence of the phase synchroniza…
Measure synchronization is a well-known phenomenon in coupled classical Hamiltonian systems over last two decades. In this paper, synchronization for coupled Harper system is investigated in both classical and quantum contexts. The concept of measure synchronization involves with the phase space and it seems that the measure synchronization is restricted in classical limit. But, on the contrary, here, we have extended the aforesaid synchronization in quantum domain. In quantum context, the coupling occurs between two many body systems via a time and site dependent potential. The coupling leads…
We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information.
The ability to measure, hold and distribute time with high precision and accuracy is a foundational capability for scientific exploration. Beyond fundamental science, time synchronization is an indispensable feature of public and private communication, navigation and ranging, and distributed sensing, amongst others technological applications. We propose the implementation of a quantum network of satellite- and ground-based clocks with the ability to implement Quantum Clock Synchronization to picosecond accuracy. Implementation of the proposed QCS network offers a double advantage: (1) a more a…
High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, t…
Measuring velocities requires the synchronization of spatially-separated clocks. Because this synchronization must precede the determination of velocities, no system of clock synchronization--such as that based on Einstein's presumption of light-speed isotropy--can ever be founded on an experimentally-validated velocity. I argue that this very old observation, which lingers in the philosophical literature under the heading ``Conventionality of Synchronization,'' suggests an explanation of why ``spooky'' quantum correlations can transfer no information at any speed, superluminal or otherwise. T…
We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually through an optical fiber or a phonon tunneling. The cavities are filled with Kerr-type nonlinear medium. It is found that, no matter which the coupling and periodically modulation we choose, both of the quantum synchronization of nonlinear optomechanical system are more appealing than the linear optomechanical system. It is easier to observe greatly enhanced qua…
Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently this effect has been analyzed and observed in a number of physical systems close to the quantum mechanical regime. In this work we propose the mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semi-classical to intrinsically quantum mechanical systems. Specifically we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later w…
We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional Hilbert space. The analysis of the simplest two qubit version of the quantum model shows that all its stationary states are nonseparable.
We study the quantum synchronization of a single spin driven by an external semiclassical signal for spin numbers larger than $S = 1$, the smallest system to host a quantum self-sustained oscillator. The occurrence of interference-based quantum synchronization blockade is found to be qualitatively different for integer vs. half-integer spin number $S$. We explain this phenomenon as the interplay between the external signal and the structure of the limit cycle in the generation of coherence in the system. Moreover, we show that the same dissipative limit-cycle stabilization mechanism leads to v…
We study mechanisms that allow one to synchronize the quantum phase of two qubits relative to a fixed basis. Starting from one qubit in a fixed reference state and the other in an unknown state, we find that contrary to the impossibility of perfect quantum cloning, the quantum-phase can be synchronized perfectly through a joined unitary operation. When both qubits are initially in a pure unknown state, perfect quantum-phase synchronization through unitary operations becomes impossible. In this situation we determine the maximum average quantum-phase synchronization fidelity, the distribution o…
We introduce methods for clock synchronization that make use of the adiabatic exchange of nondegenerate two-level quantum systems: ticking qubits. Schemes involving the exchange of N independent qubits with frequency $ω$ give a synchronization accuracy that scales as $(ω\sqrt{N})^{-1}$, i.e., as the standard quantum limit. We introduce a protocol that makes use of N coherent exchanges of a single qubit at frequency $ω$, leading to an accuracy that scales as $(ωN)^{-1}\log N$. This protocol beats the standard quantum limit without the use of entanglement, and we argue that this scaling is the f…
The phase synchronization of a single qubit in a dissipative bath in the absence of driving field is demonstrated. Using the Husimi $Q$-function we show that the phase preference is present in the long time limit only during non-Markovian evolution with a finite detuning. This happens due to the information backflow signifying that non-Markovianity is a resource for quantum synchronization. To quantify synchronization we use the shifted phase distribution as well as its maximal value. From the maximal value of the shifted phase distribution we observe the signatures of quantum synchronization …
The clock synchronization problem is to determine the time difference $Δ$ between two spatially separated clocks. When message delivery times between the two clocks are uncertain, $O(2^{2n})$ classical messages must be exchanged between the clocks to determine $n$ digits of $Δ$. On the other hand, as we show, there exists a quantum algorithm to obtain $n$ digits of $Δ$ while communicating only O(n) quantum messages.
We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for such "quantum-state synchronization", prove tight lower bounds on the dimension of the environment's Hilbert space in two main classes of quantum-state synchronizers, and give an analytical solution for their construction. The functioning of the found quantum-state synchronizer of two qubits is demonstrated experimentally on an IBM quantum computer and we sh…
Mediated Transmission of Quantum Synchronization in Star Networks
Renmin University of China（中国人民大学）；School of Physics, Renmin University of China（中国人民大学物理学院）；Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学量子态构建与操控教育部重点实验室）
We reveal the emergence of environment-induced spontaneous synchronization between two spin-1/2 quantum objects in a collision model setting. In particular, we determine the conditions for the dynamical establishment of synchronous evolution between local spin observables of a pair of spins undergoing open-system dynamics in the absence of an external drive. Exploiting the versatility of the collision model framework, we show that the formation of quantum or classical correlations between the principal spin pair are of no significant relevance to the manifestation of spontaneous quantum synchr…
The phenomenon of spontaneous synchronization is universal and only recently advances have been made in the quantum domain. Being synchronization a kind of temporal correlation among systems, it is interesting to understand its connection with other measures of quantum correlations. We review here what is known in the field, putting emphasis on measures and indicators of synchronization which have been proposed in the literature, and comparing their validity for different dynamical systems, highlighting when they give similar insights and when they seem to fail.
The phenomenon of spontaneous synchronization arises in a broad range of systems when the mutual interaction strength among components overcomes the effect of detuning. Recently it has been studied also in the quantum regime with a variety of approaches and in different dynamical contexts. We review here transient synchronization arising during the relaxation of open quantum systems, describing the common enabling mechanism in presence of either local or global dissipation. We address both networks of harmonic oscillators and spins and compare different synchronization measures.
Spontaneous synchronization is a significant collective behavior of weakly coupled systems. Due to their inherent nonlinear nature, optomechanical systems can exhibit self-sustained oscillations which can be exploited for synchronizing different mechanical resonators. In this paper, we explore the synchronization dynamics of two membranes coupled to a common optical field within a cavity, and pumped with a strong blue-detuned laser drive. We focus on the system quantum dynamics in the parameter regime corresponding to synchronization of the classical motion of the two membranes. With an approp…
To establish a time reference frame between two users in quantum key distribution, a synchronization calibration process is usually applied for the case of using gated mode single-photon detectors (SPDs). Traditionally, the synchronization calibration is independently implemented by the line length measurement for each SPD. However, this will leave a loophole which has been experimentally demonstrated by a special attack. Here, we propose an alternative synchronization scheme by fixing the relative delay of the signal time window among all SPDs and jointly performing the line length measuremen…
A multi-party protocol for distributed quantum clock synchronization has been claimed to provide universal limits on the clock accuracy, viz. that accuracy monotonically decreases with the number n of party members. But, this is only true for synchronization when one limits oneself to W-states. This work shows that usage of Zen-states, a generalization of W-states, results in improved accuracy, having a maximum when \lfloor n/2 \rfloor of its members have their qubits with a |1> value.
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing that the ability of the system to synchronize is related to the existence of disparate decay rates and is accompanied by robust quantum discord and mutual information between the oscillators, preventing the leak of information from the system.
Signatures of Environment-Induced Quantum Synchronization Transitions via Two-body Dissipator Engineering
The Chinese University of Hong Kong（香港中文大学）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）；The Chinese University of Hong Kong Shenzhen Research Institute（香港中文大学（深圳）研究院）
We present a multi-party quantum clock synchronization protocol that utilizes shared prior entanglement and broadcast of classical information to synchronize spatially separated clocks. Notably, it is necessary only for any one party to publish classical information. Consequently, the efficacy of the method is independent of the relative location of the parties. The suggested protocol is robust and does not require precise sequencing of procedural steps.
We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In contrast to classical synchronization schemes, the accuracy of our protocol is independent of Alice or Bob's knowledge of their relative locations or of the properties of the intervening medium.
The quantum clock synchronization algorithm proposed by I. L. Chuang (Phys. Rev. Lett, 85, 2006(2000)) has been implemented in a three qubit nuclear magnetic resonance quantum system. The effective-pure state is prepared by the spatial averaging approach. The time difference between two separated clocks can be determined by reading out directly through the NMR spectra.
We show the emergence of spontaneous synchronization between a pair of detuned quantum oscillators within a harmonic network. Our model does not involve any nonlinearity, driving, or external dissipation, thus providing the simplest scenario for the occurrence of local coherent dynamics in an extended harmonic system. A sufficient condition for synchronization is established by building upon the Rayleigh normal mode approach to vibrational systems. Our results show that mechanisms favoring synchronization, even between oscillators that are not directly coupled to each other, are transient ener…
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 study the quantum phase synchronization of a driven two-level system (TLS) coupled to a structured environment and demonstrate that quantum synchronization can be enhanced by the classical driving field. We use the Husimi $Q$-function to characterize the phase preference and find the in-phase and anti-phase locking phenomenon in the phase diagram. Remarkably, we show that the in-phase classical driving enables a TLS to reach stable anti-phase locking in the Markovian regime. However, we find that the synergistic action of classical driving and non-Markovian effects significantly enhances th…
We propose Qubit4Sync, a synchronization method for Quantum Key Distribution (QKD) setups, based on the same qubits exchanged during the protocol and without requiring additional hardware other than the one necessary to prepare and measure the quantum states. Our approach introduces a new cross-correlation algorithm achieving the lowest computational complexity, to our knowledge, for high channel losses. We tested the robustness of our scheme in a real QKD implementation.
Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to detectable Byzantine agreement (DBA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm that solves the DBA and achieves …
The interaction of a quantum system, which is not accessible by direct measurement, with an external probe can be exploited to infer specific features of the system itself. We introduce a probing scheme based on the emergence of spontaneous quantum synchronization between an out-of-equilibrium qubit, in contact with an external environment, and a probe qubit. Tuning the frequency of the probe leads to a transition between synchronization in phase and antiphase. The sharp transition between these two regimes is locally accessible by monitoring the probe dynamics alone and allows one to reconstr…
Quantum phase synchronisation enhanced via Coulomb interaction in an optomechanical system
University of Yaounde I（雅温得第一大学）；University of Ngaoundere（恩冈德雷大学）；Nantong University（南通大学）；Government College University（政府学院大学）；IIT Kharagpur（印度理工学院卡拉格普尔分校）；University of Bisha（比沙大学）；Akal University（阿卡尔大学）
