Spin Squeezing and Quantum Fisher Information in Generalized Two-Axis Twisting Model

We investigated spin squeezing and quantum Fisher information in generalized two-axis twisting model; which generalizes the two-axis twisting model including a linear interaction controlled by an external field. In particular, we are interested in the dependence of spin squeezing and quantum Fisher information on the external field. By adopting frozen-spin approximation, we derive the theoretical and numerical results for spin squeezing and quantum Fisher information. Except certain special conditions, the stronger external field induces to stronger squeezing. Spin squeezing parameter and the reciprocal of the mean quantum Fisher information per particle are periodic function; but the external field has not important effect on the period.     

基于量子费希尔信息的纠缠判据

对于几类常见的量子态, 对自旋压缩和量子Fisher信息进行了比较研究.得到量子Fisher信息的表达式,以Fisher信息为基础,给出了量子纠缠的判据,结果表明:比较于自旋压缩,该判据有明显的优势.(1).对于两个Qubit的对称态,该判据与自旋压缩,concurrence完全等价;(2).对于两个Qubit的非对称态的纠缠,自旋压缩不能检验其纠缠,但对于部分态,该判据也能检验;(3).对于Dicke态, 自旋压缩不能检验其纠缠,但该判据能检验且完全等价于concurrence.     

基于量子费希尔信息的纠缠判据

对于几类常见的量子态, 对自旋压缩和量子Fisher信息进行了比较研究.得到量子Fisher信息的表达式,以Fisher信息为基础,给出了量子纠缠的判据,结果表明:比较于自旋压缩,该判据有明显的优势.(1).对于两个Qubit的对称态,该判据与自旋压缩,concurrence完全等价;(2).对于两个Qubit的非对称态的纠缠,自旋压缩不能检验其纠缠,但对于部分态,该判据也能检验;(3).对于Dicke态, 自旋压缩不能检验其纠缠,但该判据能检验且完全等价于concurrence.     

Entangled Property in Cloned Superposition State

With spin squeezing and quantum Fisher information we investigate the entangled property of the cloned superposition state which is superposed by two states. We first derive the mean spin direction, the optimally squeezed angle and the anti-squeezed angle. Then we numerically calculate the dependence of spin squeezing parameter and the reciprocal of the mean quantum Fisher information on the superposed coefficients and the relative phase. Its shown that the entangled degree is determined by the superposed coefficients and the relative phase.     

Spin Squeezing and Quantum Fisher Information in One-Axis Twisting Model with Decay

We investigate spin squeezing and the reciprocal of the mean quantum Fisher information per particle (RMQFI) of a collective spin governed by a one-axis twisting Hamiltonian with decay. In particular, we are interesting in the dependence of spin squeezing and RMQFI on the decay rate. The larger decay rate induces to stronger squeezing in certain regime and the larger period of RMQFI.     

Quantum Fisher information and spin squeezing in one-axis twisting model

We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 （2009） 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near- Heisenberg limit 2IN in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0- π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEE     

Controlling Many-Body Entanglement with an External Field

We investigate how an appropriate choice of the external field allows one to control many-body entanglement characterized by spin squeezing and the reciprocal of mean quantum Fisher information per particle (RMQFI). By adopting frozen-spin approximation, we succussed in obtaining analytical expressions of the spin squeezing parameter and RMQFI. The stronger external field induces stronger squeezing, the smaller value of RMQFI and the larger period.     

光与物质相互作用系统中的量子Fisher信息和自旋压缩

Fisher信息是估计理论中的重要概念,最近发现与量子信息中的纠缠判据具有密切联系.非旋波近似条件下,Dicke模型经典相空间表现为混沌动力学特征.本文详细考察了Dicke模型描述的光与物质相互作用系统中量子Fisher信息和自旋压缩动力学特性.结果表明:在短时瞬态情况下,无论初态处于规则区域还是混沌区域系统均表现为纠缠性质;但在长时稳态情况下,初态处于规则区域时系统纠缠消失,而初态处于混沌区域时系统则一直存在纠缠.通过与系统自旋压缩动力学性质相比较,发现量子Fisher信息可以更有效地刻画量子混沌.进一步考察初态处于规则和混沌区域时系统密度矩阵和纯度的动力学演化特性,发现混沌导致系统退相干现象发生,说明量子Fisher信息对混沌更敏感.     

Coherence and Entanglement in Spinor Bose-Einstein Condensate

We propose a scheme to generate and detect quantum coherence and quantum entanglement in a spin-1 Bose-Einstein condensate with the help of spin squeezing parameter and quantum Fisher information. It is shown that quantum coherence and quantum entanglement are independent of the Rabi frequency and the better entanglement can be achieved by increasing the number of atoms.     

Phonon-induced Quantum Entanglement in Diamond Nanostructures

We consider the quantum entanglement such as spin squeezing and the reciprocal of the mean quantum Fisher information per particle(RMQFIP) resulted from the phonon-induced spin-spin interactions in diamond nanoresonator. The entangled state can be generated by adjusting the near-resonant coupling and the single phonon coupling strength and the better entanglement and a longer entangled time interval can be achieved by increasing the number of charged nitrogen-vacancy (NV) centers.     

Generating Multi-particle Entangled State with Matter-Wave Interferometer

We put forward a realizable scheme for generating multi-particle entangled state with matter-wave interferometer, where the entangled properties are characterized by spin squeezing parameter and the reciprocal of the mean quantum Fisher information per particle (RMQFIP). The multi-particle entangled state can be generated by adjusting phase difference between two input ports of the interferometer and the better entanglement can be achieved by increasing the number of the total particles.     

Quantum Fisher Information Gap for Systems with Nonlinear Hamiltonians

Quantum Fisher information(QFI) gap characterizes the stability of QFI to space directions. We study the QFI distributions and QFI gap for quantum states generated from nonlinear Hamiltonians for both spin and bosonic systems. We find that the same spin-squeezing parameter(or principle squeezing parameter) corresponds to two different values QFI gap, and the locations of all extreme points of the QFI are explicitly given.     

Spin Squeezing and Quantum Fisher Information for Mixed Hamiltonian Model

We investigate spin squeezing and the mean quantum Fisher information per particle χ ² for mixed Hamiltonian model. By adopting frozen-spin approximation, we first derive a analytical expression of spin squeezing parameter ξ ² and then numerically calculate ξ ² and χ ². It is shown that most of the time the spin squeezing appears alternatively in the x and y directions, but it cannot appear simultaneously in the two directions. It is also shown that the smaller external field strength induces better entanglement and larger period.     

量子混沌系统中的自旋压缩性质

量子信息是21世纪的一门新兴交叉学科,现已经成为世界关注的热门研究领域.近年来,量子计算机的研究正成为大家十分感兴趣的课题.在寻找量子计算的实现方案过程中,量子混沌引起了研究人员的极大关注,因为在量子计算机执行一些量子运算法则的过程中可能产生量子混沌,并可能破坏量子计算机的运算操作条件.近期有关量子纠缠与量子混沌之间的关系已经有所报道,而自旋压缩作为另外一种典型的纯量子效应,是否也与量子混沌之间存在一定关系呢?讨论了量子混沌研究中一个非常典型的QKT模型,研究了量子混沌系统中自旋压缩的性质.通过数值模拟计算,给出了两种不同定义的自旋压缩系数与混沌系数κ之间的变化关系,结果发现在经典相空间中,如果在规则区域占优势的情况下,当初始自旋相干态波包位于椭圆形中心时,随着时间的演化,系统压缩行为表现得非常强;而对于经典相空间中混沌区域占优势的情况下,初始自旋相干态波包同样位于椭圆形中心,则系统的压缩行为表现得非常弱,说明自旋压缩对相应的经典混沌非常敏感.通过比较还发现,采用Wineland等定义的自旋压缩系数比采用Kitagawa和Ueda等定义的自旋压缩系数对经典混沌更敏感一些,从而得出用自旋压缩可以刻画量子混沌的结论.     

Quantum Fisher Information of a 3-Qubit State

We investigate the properties of quantum Fisher information in a general superposition of a 3-qubit GHZ state and two W states. Numerical calculation for quantum Fisher information of the 3-qubit state is given. It is shown that the mean spin direction, the length of mean spin and quantum Fisher information are determined by the coefficients of superposition and the relative phase between the GHZ state and the W states.     

Environmental parameter estimation with the two-level atom probes

A novel scheme is proposed to estimate three environmental parameters, the detuning, the temperature and the squeezing strength with one-qubit or two-qubit probes. Quantum Fisher information and the fidelity of the atom probes are calculated. When the detuning between the frequency of cavity field and the atomic transition frequency is estimated, the dynamics of quantum Fisher information shows oscillatory and rising behaviors. To estimate the temperature of the thermal reservoir, the one-qubit probe with the superposition initial state is more favorable than the two-qubit probe with the entangled initial state. When the squeezing strength of the squeezed vacuum reservoir is estimated, we find that the estimation precision is significantly improved by utilizing the two-qubit probe with the maximal entangled initial state. Our work provides a potential application in the open quantum system and quantum information processing.     

Quantum Fisher information width in quantum metrology

In scenarios of quantum metrology, the unitary parametrization process often depends on space directions. How to characterize the sensitivity of parameter estimation to space directions is a natural question. We propose the concept of the quantum Fisher information(QFI) width, which is the difference between the maximum and minimum values of the QFI, to quantitatively study the sensitivity. We find that Fock states, the bosonic coherent states, and the displaced Fock states all have zero widths, indicating that QFI is completely inert over all directions, while the width for the spin state with all spins down or up is equal to the number of particles, so this concept will enable us to choose appropriate directions to make unitary transformation to obtain larger QFI.The QFI width of the displaced quantum states is found to be independent of the magnitude of the displacement for both spin and bosonic systems. We also find some relations between the QFI width and squeezing parameters.     

Quantum Fisher Information in the Symmetric Pure Three-Qubit State

We investigate the quantum Fisher information in the symmetric pure three-qubit state. It is shown that the quantum Fisher information and the mean spin direction are determined by the probability amplitudes and the relative phase of the symmetric pure three-qubit state; while the length of mean spin is only determined by the probability amplitudes.     

Estimation of the Parameters in a Two-State System Coupled to a Squeezed Bath

Estimation of the phase and weight parameters of a two-state system in a squeezed bath by calculating quantum Fisher information is investigated. The results show that, both for the phase estimation and for the weight estimation, the quantum Fisher information always decays with time and changes periodically with the phases. The estimation precision can be enhanced by choosing the proper values of the phases and the squeezing parameter. These results can be provided as an analysis reference for the practical application of the parameter estimation in a squeezed bath.     

Global and Local Spin Squeezing in Coupled Quantum Kicked Tops Model

We investigate the global and the local spin squeezing in a weakly coupled quantum kicked tops system. Two different situations are considered: (i) N=1 and (ii) N=30 for each subsystem, corresponding to quantum and classical cases, respectively. In the first case, since the two subsystems have no spin squeezing, the global squeezing completely originates from quantum correlations. For the second one, the global spin squeezing is enhanced over the local one. Due to the chaotic nature of the system, the spin squeezing is sensitive to the initial state. In chaotic region, the squeezing vanished time is much shorter than that in the regular region.