arXiv subjects
Publications and source records attributed to Jing-Ling Chen.
In this paper, by searching the relation between the radial part of Higgs harmonic oscillator in the two-dimensional curved space and the generalized CRS harmonic oscillator model, we can find a series of quasi-exact models in two-dimensional curved space based on this relation.
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.
Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of convenient substitute, i.e. squeezed light in present paper. Squeezed light is very important in the field of quantum optics and the corresponding transformation can be regarded as the coherent state of SU(1; 1). In this paper, the connection between the squeezed operator and Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of Wigner rotation are deduced as well.
We propose a sufficient criterion ${S}=λ_1+λ_2-(λ_1-λ_2)^2<0$ to detect Einstein-Podolsky-Rosen steering for arbitrary two-qubit density matrix $ρ_{AB}$. Here $λ_1,λ_2$ are respectively the minimal and the second minimal eigenvalues of $ρ^{T_B}_{AB}$, which is the partial transpose of $ρ_{AB}$. By investigating several typical two-qubit states such as the isotropic state, Bell-diagonal state, maximally entangled mixed state, etc., we show this criterion works efficiently and can make reasonable predictions for steerability. We also present a mixed state of which steerability always exists, and compare the result with the violation of steering inequalities.
We investigate the Einstein-Podolsky-Rosen (EPR) steering and its criticality in quantum phase transition. It is found that the EPR steerability function of the ground state of XY spin chain exhibits nonanalytic feature in the vicinity of a quantum phase transition by showing that its derivative with respect to anisotropy parameter diverges at the critical point. We then verify the universality of the critical phenomena of the EPR steerability function in the system. We also use two-qubit EPR-steering inequality to explore the relation between EPR steering and quantum phase transition.
The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A 162, 25 (1992)]. A lower bound of the local weight is proved being connected with the concurrence of the state $p_L^{\max}= 1-\mathcal{C}(ρ)$. The local probability distributions for two families of mixed states are constructed independently, which accord with the lower bound.
Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party correlations in two families of $n$-qutrit Greenberger-Horne-Zeilinger type states. For the pure states in one of the families, the irreducible 2-party, $n$-party and $(n-m)$-party ($0< m < n-2$) correlations are nonzero, which is different from the $n$-qubit case. We also derive the correlation distributions in the $n$-qutrit maximal slice state, which can be uniquely determined by its $(n-1)$-qutrit reduced density matrices among pure states. It is proved that there is no irreducible $n$-qutrit correlation in the maximal slice state. This enlightens us to give a discussion about how to characterize the pure states with irreducible $n$-party correlation in arbitrarily high-dimensional systems by the way of the continuity approach.
By use of Reid's criterion and entropic criterion, we investigate the Einstein-Podolsky-Rosen (EPR) steering for some entangled continuous variable wavefunctions. We find that not all of the entangled states violate Reid's EPR inequality and the entropic inequality, this in turn suggests that both criteria are not necessary and sufficient conditions to detect the EPR steering.
We investigate the connection between quantum no-cloning theorem and Bell's theorem. Designing some Bell's inequalities, we show that quantum no-cloning theorem can always be certified by Bell's theorem, and this fact in turn reflects that our physical world is essentially nonlocal.
We investigate the relation between Bell function values (BFV) of the reduced density matrix and the topological quantum phase transitions in the Kitaev-Castelnovo-Chamon model. % [Phys. Rev. B \textbf{77}, %054433 (2008)]. We find that the first order derivative of BFV exhibits singular behavior at the critical point and we propose that it can serve as a good and convenient marker for the transition point. More interestingly, the value of the critical point can be analytically obtained in this approach. Since the BFV serves as a measure of nonlocality when it is greater than the classical bound of the correlation functions, our work has established a link between quantum nonlocality and phase transitions.
We use two different approaches to derive multipartite Leggett-type inequalities, which are generalizations of the two-qubit Leggett-type inequality obtained in [Nature Phys. \textbf{4}, 681 (2008)]. The first approach is based on the assumption that the probability distributions should be non-negative. The second approach is based on a very simple algebraic equation and is, to some extent, easier than the first approach. Although these inequalities might not be the optimal ones in the sense that their quantum violations may not be the strongest, our results make the first step of generalizing Leggett-type inequality to multi-qubit systems and provide the possibility to experimentally test non-local realism in such systems. Moreover, the two approaches here may shed new light on the challenging problem of obtaining stronger multipartite Leggett-type inequalities.
Based on maximally entangled states in the full- and sub-spaces of two qutrits, we present an alternative decomposition of two-qutrit pure states in a form $|Ψ>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>) +\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{iθ}|02>$. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter $p_1$ is shown to be an entanglement invariant.
We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled coherent states, several interesting results followed by considering different cases for the parameters. The effects of entanglement and harmonic potential on the geometric phase are discussed.
The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper-lower bound are determined analytically.
We investigate the transfer of entanglement from source particles (SP) to target particles (TP) in the Heisenberg interaction $ H=\vec s_{1} \cdot \vec s_{2}$. In our research, TP are two qubits and SP are two qubits or qutrits. When TP are two qubits, we find that no matter what state the TP is initially prepared in, at the specific time $t=π$, the entanglement of TP can attain to 1 after interaction with SP which stay on the maximally entangled state. For the TP are two qutrits, we find that the maximal entanglement of TP after interaction is relative to the initial state of TP and always cannot attain to 1 to almost all of initial states of TP. But we discuss an iterated operation which can make the TP to the maximal entangled state.
The Virial Theorem in the one- and two-dimensional spherical geometry are presented, in both classical and quantum mechanics. Choosing a special class of Hypervirial operators, the quantum Hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman Theorem, these relations can be used to formulate a \emph{perturbation theorem without wave functions}, corresponding to the Hypervirial-Hellmann-Feynman Theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method.
We introduce an intuitive measure of genuine multipartite entanglement which is based on the well-known concurrence. We show how lower bounds on this measure can be derived that also meet important characteristics of an entanglement measure. These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.
While the detection of entanglement has been proved already to be quite a difficult task, experimental quantification of entanglement is even more challenging. In this work, we derive an analytical lower bound for the concurrence of a bipartite mix quantum state in arbitrary dimension. The lower bound is experimentally implementable in a feasible way, which enabling quantification of entanglement in a broad variety of cases