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 synchronization in quantum level, we show that one can prepare a state, which describes two synchronized oscillators with no entanglement between them. Thus, the entanglement resource is not necessary in the occurrence of the ideal phase synchronization, and also the reason for this phenomenon is discussed.
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…
We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $σ$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is smaller than $σ$; otherwise the difference is beyond $σ$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $σ\simπ/{(ω(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condit…
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…
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…
We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator. The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy for suppressing measurement-induced fluctuations by a…
A very explicit analytic formula of the separability criterion of two-party Gaussian systems is given. This formula is compared to the past formulation of the separability criterion of continuous variables two-party Gaussian systems.
An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all the Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.
A general and computable criterion for k-(in)separability in continuous multipartite quantum systems is presented. The criterion can be experimentally implemented with a finite and comparatively low number of local observables. We discuss in detail how the detection quality can be optimised.
The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable states. For all bipartite Gaussian states, the Peres-Horodecki criterion turns out to be necessary and sufficient condition for separability.
We show that the existing argument on the non-classicality of the continuous variable quantum teleportation (CVQT) experiment by the average fidelity criterion is incomplete therefore so far it is still unclear whether the CVQT experiment(Furusawa et al, Science,282, 706(1998)) is really non-classical.
We present a class of non-Gaussian two-mode continuous variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case.
The separability of bipartite non-Gaussian states is studied by applying the realignment criterion with the technique of functional analysis. The realignment criterion is given as one inequality in contrast to the infinitive number of inequalities based on the moments. We give the necessary and sufficient condition of inseparability for non-Gaussian states prepared by photon subtraction or addition from symmetric Gaussian states. The entanglement criterion of non-Gaussian states evolved in thermal noise and amplitude damping environment is also obtained.
We introduce a weak form of the realignment separability criterion which is particularly suited to detect continuous-variable entanglement and is physically implementable (it requires linear optics transformations and homodyne detection). Moreover, we define a family of states, called Schmidt-symmetric states, for which the weak realignment criterion reduces to the original formulation of the realignment criterion, making it even more valuable as it is easily computable especially in higher dimensions. Then, we focus in particular on Gaussian states and introduce a filtration procedure based o…
We use matched quantum entanglement witnesses to study the separable criteria of continuous variable states. The witness can be written as an identity operator minus a Gaussian operator. The optimization of the witness then is transformed to an eigenvalue problem of a Gaussian kernel integral equation. It follows a separable criterion not only for symmetric Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from symmetric Gaussian states. Based on Fock space numeric calculation, we obtain an entanglement witness for more general two-mode s…
We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable systems. Using the derived fine-grained uncertainty relation, we formulate stronger steering criterion that is able to reveal the steerability of N00N states that has hitherto not been possible using other criteria. We further obtain a monogamy relation for our steering inequality which leads to an, in principle, improved lower bound on the secret key rate of a on…
Continuous variable quantum key distribution (CV-QKD) is a promising emerging technology for the distribution of secure keys for symmetric encryption. It can be readily implemented using commercial off-the-shelf optical telecommunications components. A key requirement of the CV-QKD receiver is the ability to measure the quantum states at the correct time instance and rate using the correct orthogonal observables, referred to as synchronization. We propose a digital synchronization procedure for a modern CV-QKD system with locally generated local oscillator for coherent reception. Our proposed …
By using the algebraic separability criterion of R. Simon, we present an explicit determination of squeezing parameters for which the P-representation condition saturates the $Sp(2,R)\otimes Sp(2,R)$ invariant separability condition for continuous variable two-party Gaussian systems. We thus give for the first time the explicit analytic formulas of squeezing parameters which establish the equivalence of the separability condition with the P-representation condition. The implications of our algebraic analysis on some of the past related works are discussed.
Photon subtraction and addition are experimental means of generating non-Gaussian states from Gaussian states. Coherent subtraction or addition is a combination of photon subtractions or additions. The resultant states are quite general non-Gaussian states. The states can be photon number entangled states with arbitrary coefficients. We derive the entanglement conditions for several classes of coherent subtraction or coherent addition bipartite continuous variable states. One of the entanglement conditions is necessary and sufficient.
Currently available separability criteria for continuous-variable states are generally based on the covariance matrix of quadrature operators. The well-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leaves many entangled non-Gaussian states undetected. Here, we introduce an improvement of this criterion that enables a stronger entanglement detection. The improved condition is based on the knowledge of an additi…
Quantum state reconstruction for continuous-variable systems such as the radiation field poses challenges which arise primarily from the large dimensionality of the Hilbert space. Many proposals for state reconstruction exist, ranging from standard reconstruction protocols to applications of machine learning. No universally applicable protocol exists, however, for extracting the Wigner function from the optical tomogram of an arbitrary state of light. We establish that nonclassical effects such as entanglement changes during dynamical evolution and the onset of quantum synchronization are mirr…
The problem of constructing a necessary and sufficient condition for establishing the separability of continuous variable systems is revisited. Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)] pointed out that such a criterion may be constructed by drawing a parallel between the Peres' partial transpose criterion for finite dimensional systems and partial time reversal transformation for continuous variable systems. We generalize the partial time reversal transformation to a partial scaling transformation and re-examine the problem using a tomographic description of the continuous variable q…
We experimentally demonstrate synchronization between two distinct ensembles of cold atoms undergoing steady state superradiance within a single longitudinal and transverse mode of the same optical cavity. The synchronization process is studied first in terms of the time dynamics of re-synchronization when the phase alignment of the two oscillators is abruptly broken. We also observe the steady state behavior of the lasers as their relative frequency is continuously varied. This system has the potential to realize a non-equilibrium quantum phase transition and could inform future implementatio…
