Pairwise Concurrence Research Articles

Stability of spatial dependence structure of extreme precipitation and the concurrent risk over a nested basin

Extreme low and high precipitation can cause natural disasters (e.g., drought and flood events) which have devastatingeffects on natural environment and the human society. In this study, we present a framework for assessing the stability of spatial dependence of extreme precipitation and their concurrence probability in a nested catchment. The Pearl River basin was used as a case study to test the applicability of the framework. This framework is threefold. This first part involves modeling spatial dependence of both summer maxima and winter minima precipitation between pairs of scattered gauges over the basin by employing the pair-copula constructions as a baseline model. The second part of this framework aims to identify the variability of spatial dependence as a result of the effects of external drivers. Specifically, variations in the spatial dependence of extreme precipitation in the Pearl River basin over different periods associated with the influence of large-scale climate signals were examined. The final part quantifies the probability of occurring extreme precipitation-related events simultaneously over broader areas related to a specific event at a given gauge and the possible spatial extents being affected. The results indicate that the presented framework is able to capture the large-scale spatial dependence structures of both summer maxima and winter minima precipitation. It also allows for explicitly estimating the pairwise concurrence probability of extreme high and low precipitation events and event-impacted areas across the basin.

Exact one- and two-site reduced dynamics in a finite-size quantum Ising ring after a quench: A semianalytical approach

We study the non-equilibrium dynamics of a homogeneous quantum Ising ring after a quench, in which the transverse field $g$ suddenly changes from zero to a nonzero value. The long-timescale reduced dynamics of a single spin and of two nearest-neighbor spins, which involves the evaluation of expectation values of odd operators that break the fermion parity, is exactly obtained for finite-size but large rings through the use of a recently developed Pfaffian method [N. Wu, Phys. Rev. E 101, 042108 (2020)]. Time dependence of the transverse and longitudinal magnetizations, single-spin purity, expectation value of the string operator $X_j=\prod^{j-1}_{l=1}\sigma^z_l\sigma^x_j$, several equal-time two-site correlators, and pairwise concurrence after quenches to different phases are numerically studied. Our main findings are that (i) The expectation value of a generic odd operator approaches zero in the long-time limit; (ii) $\langle X_j\rangle_t$ exhibits $j$-independent exponential decay for a quench to $g=1$ and the time at which $\langle X_j\rangle_t$ reaches its first maximum scales linearly with $j$; (iii) The single-spin purity dynamics is mainly controlled by $\langle\sigma^x_j\rangle_t$ ($\langle\sigma^z_j\rangle_t$) for a quench to $g<1$ ($g\geq 1$). For quenches to the disordered phase with $g\gg1$, the single-spin tends to be in the maximally mixed state and the transverse and longitudinal correlators $\langle\sigma^z_j\sigma^z_{j+1}\rangle_t$ and $\langle\sigma^x_j\sigma^x_{j+1}\rangle_t$ respectively approaches $-0.25$ and $0.5$ in the thermodynamic limit; (iv) The nearest-neighbor entanglement acquires a finite plateau value that increases with increasing $g$, and approaches a saturated value $\sim0.125$ for $g\gg1$.

Plasmonic-modulated dissipative-driven multiqubit entanglement under asymmetric detuning

A dissipative-driven system can generate steady-state entanglement robust to control parameters, while a quantum plasmonic system has the advantages of being strongly coupled to qubits and manipulation of electromagnetic waves in the subwavelength regime. We propose an effective multiqubit dissipative-driven entanglement model for a plasmonic system which takes into account coupling of the plasmonic cavity and qubits as well as the direct coupling between any two qubits and develop a numerical solution of the effective model on a scalable composite plasmonic structure. In this structure, the multiqubit entanglement under asymmetric detuning, especially for those combinations containing pairs of antisymmetric detuning qubits, achieves stronger steady-state entanglement measured by negativity and pairwise concurrence. The robustness of multiqubit entanglement against variations of the control parameters is also presented. In addition, the phenomenon of entanglement sudden death caused by the driving field in entanglement dynamics is investigated. Our model shows evidence that quantum plasmonics has great potential in multiqubit entanglement.

Pairwise concurrence in cyclically symmetric quantum states

We provide an initial characterization of pairwise concurrence in quantum states which are invariant under cyclic permutations of party labeling. We prove that maximal entanglement can be entirely described by adjacent pairs, then give explicit descriptions of those states in specific subsets of 4 and 5 qubit states - X states. We also construct a monogamy bound on shared concurrences in the same subsets in 4 and 5 qubits, finding that above non-maximal entanglement thresholds, no other entanglements are possible.

Local entanglement and string order parameter in dimerized models

In this letter, we propose an application of string order parameter (SOP), commonly used in quantum spin systems, to identify symmetry-protected topological phase (SPT) in fermionic systems in the example of the dimerized fermionic chain. As a generalized form of dimerized model, we consider a one-dimensional spin-1/2 XX model with alternating spin couplings. We employ Jordan–Wigner fermionization to map this model to the spinless Su–Schrieffer–Heeger fermionic model (SSH) with generalized hopping signs. We demonstrate a phase transition between a trivial insulating phase and the Haldane phase by the exact analytical evaluation of reconstructed SOPs which are represented as determinants of Toeplitz matrices with the given generating functions. To get more insight into the topological quantum phase transition (tQPT) and microscopic correlations, we study the pairwise concurrence as a local entanglement measure of the model. We show that the first derivative of the concurrence has a non-analytic behaviour in the vicinity of the tQPT, like in the second order trivial QPTs.

Probabilities of Concurrent Extremes

ABSTRACTThe statistical modeling of spatial extremes has been an active area of recent research with a growing domain of applications. Much of the existing methodology, however, focuses on the magnitudes of extreme events rather than on their timing. To address this gap, this article investigates the notion of extremal concurrence. Suppose that daily temperatures are measured at several synoptic stations. We say that extremes are concurrent if record maximum temperatures occur simultaneously, that is, on the same day for all stations. It is important to be able to understand, quantify, and model extremal concurrence. Under general conditions, we show that the finite sample concurrence probability converges to an asymptotic quantity, deemed extremal concurrence probability. Using Palm calculus, we establish general expressions for the extremal concurrence probability through the max-stable process emerging in the limit of the component-wise maxima of the sample. Explicit forms of the extremal concurrence probabilities are obtained for various max-stable models and several estimators are introduced. In particular, we prove that the pairwise extremal concurrence probability for max-stable vectors is precisely equal to the Kendall’s τ. The estimators are evaluated from simulations and applied to study temperature extremes in the United States. Results demonstrate that concurrence probability can be used to study, for example, the effect of global climate phenomena such as the El Niño Southern Oscillation (ENSO) or global warming on the spatial structure and areal impact of extremes.

Thermal entanglement in a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction

In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.

Symmetric three-qubit-state invariants

For pure symmetric 3-qubit states there are only three algebraically independent entanglement measures; one choice is the pairwise concurrence $\mathcal C$, the 3-tangle $\tau$, and the Kempe invariant $\kappa$. Using a canonical form for symmetric $N$-qubit states derived from their Majorana representation, we derive the explicit achievable region of triples $(\mathcal C,\tau,\kappa)$.

Effect of three-spin interaction on thermal entanglement in Heisenberg XXZ model

The effect of three-spin interaction k on thermal entanglement between alternate qubits is studied using pairwise concurrence C and energy level diagram. It is found that k breaks the symmetry about the effect of magnetic field h on C. It shifts a dip structure and gradually effaces a boot structure when |k|<|J| (J is spin exchange coupling). A peak with C maintains 1 appears and expands, elbowing the dip backwards when |k|>|J|. A sudden change of the concurrence occurs around |k|=|J|, h=-k. Similar conclusions about nearest-neighbor qubits are directly given.

Contrasting distributions of pairwise entanglement and mutual information in Heisenberg spin systems

The correlations between a pair of spins in a many-spin state encoded in the diagonal and off-diagonal spin–spin correlation functions. These spin functions determine the quantum correlation measures, like pair-wise concurrence, quantum discord and other measures of quantum information. We show that for isotropic and translationally invariant states, the quantum correlations depend only on the diagonal spin correlation function. The pair concurrence shows a strict short-ranged behavior. The distribution of concurrence for a random W-like state exhibits a long tail for both time-reversal invariant states and for states that break the time reversal. The quantum discord can be related to the diagonal spin correlation function. As the spin function is long range close to a critical point, analogously the quantum discord exhibits a long range behavior. For the isotropic state, the conditional entropy distribution is a Dirac delta function, whereas it has a twin-peak structure for the anisotropic model.

Towards photonic quantum simulation of ground states of frustrated Heisenberg spin systems

Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. Recent experiments have shown that photonic quantum systems have the advantage to exploit quantum interference for the quantum simulation of the ground state of Heisenberg spin systems. Here we experimentally characterize this quantum interference at a tuneable beam splitter and further investigate the measurement-induced interactions of a simulated four-spin system by comparing the entanglement dynamics using pairwise concurrence. We also study theoretically a four-site square lattice with next-nearest neighbor interactions and a six-site checkerboard lattice, which might be in reach of current technology.

Tuning Entanglement Patterns in Qubits Clusters

We identify patterns of ground state entanglement, or quantum discord, in qubit clusters with three and four qubits, that are induced by varying the couplings between next-nearest neighbors in the clusters. We show that these entanglement patterns can be associated with continuous multiply connected regions in parameter space, on which entanglement quantifiers, such as the pairwise concurrence, exhibit a particular type of behavior as a function of the couplings between next-nearest neighbors in the cluster. We present the distinct patterns in diagrams in parameter space with continuous boundary lines and we associate each pattern to a specific type of pure quantum correlation. We propose this procedure as a simple method to identify useful classes of pure quantum correlations in qubit networks.

Thermal entanglement in a {Cu3} single molecular magnet in the magnetic field

We have investigated the properties of thermal entanglement in a triangular spin ring of the single molecular magnet (SMM) Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O in a magnetic field, and the pairwise concurrences of arbitrary two Cu2+ ion qubits are calculated numerically, hereafter abbreviated as C12, C23 and C13, respectively. Results show that the magnitude and direction of magnetic field as well as temperature have important effects on the pairwise thermal entanglement. Moreover, C12, C23 and C13 have difference variations with the change of the parameters. We also plot the changes of the critical temperatures Tc of C12, C23 and C13 with the magnetic fields along three different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the ranges of parameters in which the pairwise thermal entanglement in a triangular spin ring of the SMM exists. Therefore, the pairwise entanglement can be controlled and enhanced in the SMM by choosing appropriate magnitude and direction of magnetic field and temperature.

Entanglement between Two Tavis-Cummings Systems with N=2

We consider two non interacting two-atoms Tavis -Cummings systems and examine the entanglement among four two-state atoms. For our purpose, we assume that one atom fro m each system are entangled init ially and we obtain time-dependent concurrence among atoms. There are six pairwise concurrences among atoms and in this paper, we focus on remote atoms . We show that initially non-entangled atoms 2 A and 2 B becomes entangled by passing time, the process

Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements

We consider two entangled qubits, each of which is coupled to its own reservoir, so that their entanglement degrades with time. To enhance the qubits' entanglement at a time during the evolution we propose a proper combination of pre- and postmeasurements to be performed locally on individual qubits. The premeasurements are weak measurements, but the postmeasurements may be either quantum measurement reversals or weak measurements again, depending on the situation at the time they are applied. Given the parameters of the initial qubits' state, the premeasurements' strength, and the evolution time, we establish the optimal conditions for the postmeasurements so that the qubits' entanglement becomes the largest possible. Actually, by our scheme, less entangled qubits can evolve into more entangled ones with a finite probability, or even into a near-maximally entangled state but with a vanishingly low probability. We also examine the entanglement distribution among different pairs of subsystems involved and find out that the pairwise concurrence dynamics in our scheme differs strikingly from that in the situation without any control actions.

Conservation issue of pairwise quantum discord and entanglement of two coupled qubits in a two-mode vacuum cavity

The conservation issues of pairwise quantum discord and entanglement of two qubits coupled to a two-mode vacuum cavity are investigated by considering the dipole–dipole interaction between two qubits. It is found that the sum of the square of the pairwise quantum discords and the sum of the square of the pairwise concurrences are both conserved in the strong dipole-dipole interaction limit. However, in the middle dipole-dipole and weak dipole-dipole interaction limits, the sum of the square of the pairwise concurrences is still conserved while the sum of the square of the pairwise discords is not. The crucial reason for this is that the quantum discords are not equivalent if the measurements are performed on different subsystems in a general situation. So it is very important for quantum computation depending on the quantum discord to select the target performed by the measurements.

Entanglement of polar molecules in pendular states

In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.

Thermal entanglement in the four-qubit Heisenberg XXZ model with the Dzyaloshinskii-Moriya interaction

In this paper, we study the property of thermal entanglement in four-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered, and investigate the pairwise concurrences of two nearest-neighbor qubits and two next-neighbor qubits to study this entanglement property. The result shows that for the two-next-neighbor-qubit case, there exists pairwise concurrence neigher in ferromagnetic model nor in antiferromagnetic model; but for the two-nearest-neighbor-qubits case, the DM interaction and the parameter of the anisotropy exchange coupling have a significant influence on the pairwise entanglement and critical temperature Tc. Moreover, the pairwise concurrence will decrease with the increase of temperature. When the temperature execeds its critical value, the pairwise concurrence disappears. Therefore, the pairwise entanglement can be controlled and enhanced by choosing the appropriate parameters of the DM interaction and the anisotropy exchange coupling.

Conservation rules for entanglement transfer between qubits

We consider an entangled but non-interacting qubit pair a1 and b1 that is independently coupled to a set of local qubit systems, aI and bJ, of 0 bit value, respectively. We derive rules for the transfer of entanglement from the pair a1–b1 to an arbitrary pair aI–bJ, for the case of qubit-number conserving local interactions. It is shown that the transfer rule depends strongly on the initial entangled state. If the initial entanglement is in the form of the Bell state corresponding to anti-correlated qubits, the sum of the square of the nonlocal pairwise concurrences is conserved. If the initial state is the Bell state with correlated qubits, this sum can be reduced, even to zero in some cases, to reveal a complete and abrupt loss of all nonlocal pairwise entanglement. We also identify that for the nonlocal bipartitions A–bJ involving all qubits at one location, with one qubit bJ at the other location, the concurrences satisfy a simple addition rule for both cases of the Bell states that the sum of the square of the nonlocal concurrences is conserved.

Entanglement dynamics of W-like states in an open system

The pairwise entanglement dynamics in a multipartite open system consisting of three entangled cavity photons locally coupled with independent N-mode reservoirs is studied via concurrence. The initial states of cavity photons are prepared in two types of W-like states while the corresponding reservoirs are prepared in the factorable vacuum state. The result shows that all the pairwise concurrences of the total system including cavities and reservoirs undergo qualitatively different dynamical behaviors. Among the two W-like states, only one could exhibit entanglement sudden death (ESD) leading the corresponding reservoirs to exhibit entanglement sudden birth. In addition, by taking the entanglement of the corresponding reservoirs into account, entanglement invariants are constructed for the W-like state that does not undergo ESD.