Tripartite Negativity Research Articles

Evidence of a significant full tripartite entanglement in a mixed spin-(1/2,1) Heisenberg tetramer

We rigorously analyze the full tripartite entanglement of a mixed spin-(1/2,1) Heisenberg tetramer in the presence of an external magnetic field. The tetramer consists of two mixed spin-(1/2,1) dimers arranged to form a square plaquette, with distinct exchange couplings J and J1 between spins from the same and different dimers, respectively. The full tripartite entanglement is classified according to the tripartite negativity NABC defined as a geometric mean of all possible bipartite negativities NA|BC, NB|AC, and NC|AB, when the degrees of freedom of the fourth spin D of the tetrapartite system ABCD are traced out. We demonstrate that for J1/J>1, both trimeric subsystems 1/2-1-1 and 1/2-1/2-1 exhibit tripartite entanglement mediated through the central spin. This entanglement becomes more robust upon the application of an external magnetic field. The opposite limit J1/J<1 leads to the spontaneous emergence of full tripartite entanglement solely within the subsystem 1/2-1-1. However, the increasing magnetic field swiftly disrupts the three-particle correlation across the relevant ground-state phase boundary. Additionally, we identify that in the isotropic limit J1/J=1, the ground-state degeneracy significantly reduces the strength of full tripartite entanglement and favors nontrivial subtypes of full nonseparable states with none or just one spin-dimer entanglement. Finally, we discuss in detail the thermal stability of all fully tripartite nonseparable states.

Distribution of Bipartite and Tripartite Entanglement within a Spin-1/2 Heisenberg Star in a Magnetic Field.

The spatial distribution of entanglement within a spin-1/2 Heisenberg star composed from a single central spin and three peripheral spins is examined in the presence of an external magnetic field using the Kambe projection method, which allows an exact calculation of the bipartite and tripartite negativity serving as a measure of the bipartite and tripartite entanglement. Apart from a fully separable polarized ground state emergent at high-enough magnetic fields, the spin-1/2 Heisenberg star exhibits at lower magnetic fields three outstanding nonseparable ground states. The first quantum ground state exhibits the bipartite and tripartite entanglement over all possible decompositions of the spin star into any pair or triad of spins, whereby the bipartite and tripartite entanglement between the central and peripheral spins dominates over that between the peripheral spins. The second quantum ground state has a remarkably strong tripartite entanglement between any triad of spins in spite of the lack of bipartite entanglement. The central spin of the spin star is separable from the remaining three peripheral spins within the third quantum ground state, where the peripheral spins are subject to the strongest tripartite entanglement arising from a two-fold degenerate W-state.

Quantum Information Scrambling in Non-Markovian Open Quantum System.

In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.

Tripartite Entanglement in Quantum Memristors

We study the entanglement and memristive properties of three coupled quantum memristors. We consider quantum memristors based on superconducting asymmetric SQUID architectures which are coupled via inductors. The three quantum memristors are arranged in two different geometries: linear and triangular coupling configurations. We obtain a variety of correlation measures, including bipartite entanglement and tripartite negativity. We find that, for identical quantum memristors, entanglement and memristivity follow the same behavior for the triangular case and the opposite one in the linear case. Finally, we study the multipartite correlations with the tripartite negativity and entanglement monogamy relations, showing that our system has genuine tripartite entanglement. Our results show that quantum correlations in multipartite memristive systems have a non-trivial role and can be used to design quantum memristor arrays for quantum neural networks and neuromorphic quantum computing architectures.

Tripartite Entanglement for Three-Qubit System in the Generalized Coleman-Hepp Model

Based on the solvable dynamical model for quantum measurement process, we consider three uncoupled particles interacting with their local one-dimensional (1D) spin arrays. Here the 1D spin arrays can be regarded as the local phase decoherence environments for the particles. To demonstrate the dynamics of quantum entanglement among three particles in measuring process, the tripartite negativity is introduced. Our study indicates that the tripartite negativity is determined jointly by the initial states and the dephasing factors for four kinds of initial states, including GHZ-type states, W-type states, Weiner-GHZ states, and Weiner-W states. We find the particle-spin array interaction can destroy the tripartite negativity, and the tripartite negativity is the same for the family of entangled GHZ states or the family of entangled W states. Furthermore, there exists the sudden death of tripartite negativity when the initial states are Weiner-GHZ states or Weiner-W states.

Structure of quantum entanglement at a finite temperature critical point

We propose a scheme to characterize long-range quantum entanglement close to a finite temperature critical point using tripartite entanglement negativity. As an application, we study a model with mean-field Ising critical exponents and find that the tripartite negativity does not exhibit any singularity in the thermodynamic limit across the transition. This indicates that the long-distance critical fluctuations are completely classical, allowing one to define a `quantum correlation length' that remains finite at the transition despite a divergent physical correlation length. Motivated by our model, we also study mixed state entanglement in tight-binding models of bosons with $U(1)$ and time-reversal symmetry. By employing Glauber-Sudarshan `P-representation', we find a surprising result that such states have zero entanglement.

Tripartite Entanglement Dynamics in the System Consisting of Three Damping Jaynes-Cummings Models

In this paper we consider the situation that three identical two-level atoms resonantly interact with three distant single-mode optical cavities via a one-photon hopping separately, and there exist the phenomena of atom-decay and cavity-decay. Under Jaynes-Cummings model the time evolution of the system is given. The tripartite negativity is used to quantify the degree of tripartite entanglement. The tripartite entanglement dynamics among atoms and among cavities are studied. The influences of the atom-decay and the cavity-decay on tripartite entanglement are discussed. The results obtained using the numerical method show that the tripartite entanglement among atoms and that among cavities all display damping oscillation behavior. On the other hand, as the atomic decay rate increases, their decays are accelerated, and so do they with the increase of cavity decay rate.

Multipartite entanglement transfer in spin chains

We investigate the transfer of genuine multipartite entanglement across a spin-12 chain with nearest-neighbour XX-type interaction. We focus on the perturbative regime, where a block of spins is weakly coupled at each edge of a quantum wire, embodying the role of a multiqubit sender and receiver, respectively. We find that high-quality multipartite entanglement transfer is achieved at the same time that three excitations are transferred to the opposite edge of the chain. Moreover, we find that both a finite concurrence and tripartite negativity is attained at much shorter time, making GHZ-distillation protocols feasible. Finally, we investigate the robustness of our protocol with respect to non-perturbative couplings and increasing lengths of the quantum wire.

Classification of Classical Non-Gaussian Noises with Respect to Their Detrimental Effects on the Evolution of Entanglement Using a System of Three-Qubit as Probe

A system of three non-interacting qubits is used as a quantum probe to classify three classical non-Gaussian noises namely, the static noise (SN), colored noise (pink and brown spectrum) and random telegraph noise (RTN), according to their detrimental effects on the evolution of entanglement of the latter. The probe system is initially prepared in the GHZ state and coupled to the noises in independent environments. Seven configurations for the qubit-noise coupling (QNC) are considered. To estimate the destructive influence of each kind of noise, the tripartite negativity is employed to compare the evolution of entanglement in these QNC configurations to each other with the same noise parameters. It is shown that the evolution of entanglement is drastically impacted by the QNC configuration considered as well as the properties of the environmental noises and that the SN is more detrimental to the survival of entanglement than the RTN and colored noise, regardless of the Markov or non-Markov character of the RTN and the spectrum of the colored noise. On the other hand, it is shown that pink noise is more fatal to the system than the RTN and that the situation is totally reversed in the case of brown noise. Finally, it is demonstrated that these noises, in descending order of destructive influence, can be classified as follows: SN > pink noise > RTN > brown noise.

Dynamical evolution of entanglement of a three-qubit system driven by a classical environmental colored noise

The effects of $$ 1/f^{\alpha } (\alpha =1,2)$$ noise stemming from one or a collection of random bistable fluctuators (RBFs), on the evolution of entanglement, of three non-interacting qubits are investigated. Three different initial configurations of the qubits are analyzed in detail: the Greenberger–Horne–Zeilinger (GHZ)-type states, W-type states and mixed states composed of a GHZ state and a W state (GHZ-W). For each initial configuration, the evolution of entanglement is investigated for three different qubit–environment (Q-E) coupling setups, namely independent environments, mixed environments and common environment coupling. With the help of tripartite negativity and suitable entanglement witnesses, we show that the evolution of entanglement is extremely influenced not only by the initial configuration of the qubits, the spectrum of the environment and the Q-E coupling setup considered, but also by the number of RBF modeling the environment. Indeed, we find that the decay of entanglement is accelerated when the number of fluctuators modeling the environment is increased. Furthermore, we find that entanglement can survive indefinitely to the detrimental effects of noise even for increasingly larger numbers of RBFs. On the other hand, we find that the proficiency of the tripartite entanglement witnesses to detect entanglement is weaker than that of the tripartite negativity and that the symmetry of the initial states is broken when the qubits are coupled to the noise in mixed environments. Finally, we find that the 1 / f noise is more harmful to the survival of entanglement than the $$ 1/f^{2} $$ noise and that the mixed GHZ-W states followed by the GHZ-type states preserve better entanglement than the W-type ones.

Tripartite Entanglement Among Atoms in Cavity Quantum Electrodynamics when Atom Off-resonantly Interacting with Cavity Field

The tripartite Negativity is adopted to quantify the degree of entanglement among three subsystems. The situation is considered that three identical two-level atoms are trapped in a single-mode optical cavity, and each atom off-resonantly interacts with cavity field via a one-photon hopping. When there is a dipole-dipole interaction between atoms, the tripartite entanglement dynamics among atoms is studied. The influences of detuning between atom and cavity field and the strength of dipole-dipole interaction of two atoms on the tripartite entanglement are discussed. The calculation results indicate that the tripartite entanglement among atoms is strengthened with increasing of the detuning, and it is also strengthened with increasing of the strength of dipole-dipole interaction of two atoms. Under the case of large detuning, the tripartite entanglement among atoms exhibits quasi-periodic oscillations, and its oscillation frequency is accelerated with increasing of the strength of dipole-dipole interaction between two atoms.

Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise

We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.

Maximum nonlocality in the (3,2,2) scenario

We identify the simplest combinations of entanglement and incompatibility giving the maximum quantum violation for each of the 46 classes of tight Bell inequalities for the (3,2,2) scenario, i.e., three parties, two measurements per party, and two outcomes per measurement. This allows us to classify the maximum quantum nonlocality according to the simplest resources needed to achieve it. We show that entanglement and incompatibility only produce maximum nonlocality when they are combined in specific ways. For each entanglement class there is, in most cases, just one incompatibility class leading to maximum nonlocality. We also identify two interesting cases. We show that the maximum quantum violation of \'Sliwa inequality 23 only occurs when the third party measures the identity, so nonlocality cannot increase when we add a third party to the bipartite case. Almost quantum correlations predict that adding a new party increases nonlocality. This points out that either almost quantum correlations violate a fundamental principle or that there is a form of tripartite entanglement which quantum theory cannot account for. The other interesting case is the maximum quantum violation of \'Sliwa inequality 26, which, like the Mermin inequality, requires maximum incompatibility for all parties. In contrast, it requires a specific entangled state which has the same tripartite negativity as the W state.

Tripartite entanglement of {Cu3} single molecular magnet with magnetic field in thermal equilibrium

Quantum entanglement is one of the most fundamental properties of quantum mechanics. Because of the nonlocality, quantum entanglement is widely used in quantum computation and quantum information. Considering the fact that thermal fluctuation suppresses quantum effects, the concept of thermal entanglement is introduced to refer to the idea that the effect of temperature should be viewed as external control in the preparation of entangled state. It has been found that nanoscale single molecular magnet has a novel quantum effect at low temperature. Furthermore, single-molecular magnet is viewed as a promising candidate for realizing encoding and manipulation of quantum information. Na9[Cu3Na3(H2O)9(-AsW9O33)2]26H2O (denoted as {Cu3} for convenience) is one of the typical representatives of nanoscale single molecular magnets. In this paper, we will theoretically analyze the properties of tripartite entanglement in {Cu3} with an external magnetic field in thermal equilibrium. The tripartite negativity is used to characterize the tripartite entanglement. The tripartite negativity of {Cu3} single molecular magnet is calculated numerically by using the equivalent spin model and experimental fitting parameters. We consider the magnetic fields along the vertical and the parallel directions of triangular spin ring, respectively, and the case with a tilted magnetic field is also discussed in this paper. It is shown that the magnitude and direction of magnetic field, and temperature have importance effects on the tripartite negativity of the system. It is found that the larger extra strong magnetic field will inhibit the generation of the quantum state of tripartite entanglement at higher temperature. In addition, compared with the magnetic field along the parallel direction of triangular spin ring and the tilted magnetic field, the magnetic field along the vertical direction of triangular spin ring obtains larger values of tripartite negativity under the same temperature and magnetic field. We also plot the variations of the critical temperature with the magnetic field along different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the range of parameters in which the tripartite entanglement of the system exists. We also find that entanglement revival behaviors may occur in the specific range of parameters. Therefore, the properties of the tripartite entanglement in the {Cu3} triangular spin ring can be controlled and enhanced by choosing appropriate magnitude and direction of the magnetic field and temperature.

Entanglement dynamics of a three-qubit system with different interatomic distances**Project supported by the National Natural Science Foundation of China (Grant Nos. 61178012, 11204156, and 11304179), the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant Nos. 20133705110001 and 20123705120002), and the Natural Science Foundation of Shandong Province, China (Grant Nos. BS2013DX034, ZR2012FQ024, and ZR2014AP009).

We investigate the tripartite entanglement dynamics of three two-level atoms in a multi-mode vacuum field. By considering the influences of the interatomic distance and the initial condition on the lower bound of concurrence and the tripartite negativity, we show that an optimal interatomic distance can be found to minimize the collective damping. Interestingly, at the same optimal distance, the tripartite entanglement would be maximized in the open dynamics process. In the case of shorter interatomic distance, the tripartite entanglement can display the oscillatory behavior in the initial short-time limit and be trapped in a stationary value in the long-time limit. In addition, the tripartite entanglement for the general situation with different interatomic distances is also discussed.

Quantum correlations of three-qubit states driven by a classical random external field

In this paper, we exploit the notions of tripartite quantum discord , tripartite negativity , and entanglement witnesses (EWs), respectively, as a measure of quantum correlations in a model of three noninteracting qubits subject to a classical random external field. We compare the dynamics of with that of entanglement for the initial entangled pure or mixed GHZ- and W-type states. We find that the quantum correlations dynamics depend on the input configuration of the purity of the initial states. The results show that may be more robust than entanglement and no sudden death of the occurs, whereas entanglement displays periodically sudden death and revivals in the regions for GHZ- and W-type states driven by a classical random external field. Furthermore, we also show that the survival partial entanglement can be detected by means of the suitable EWs.

Entanglement evolution of three interacting twolevel atoms within a common environment

Entanglement dynamical evolution of three two-level atoms coupled to a common environment is investigated. We utilize the tripartite negativity to quantify entanglement and analyze the effect of the initial state, pairwise dipole-dipole interactions on the entanglement dynamical properties of the system by means of numerical calculations. Results show that a novel quantum interference can be controlled by the relative phase of initially entangled states of the atoms. And the excited-state population can be trapped in the long time limit. Besides, the tripartite entanglement can be enhanced by choosing the appropriate conditions.

Three-qubit entanglement generation of quantum states dissipating into a common environment

In this paper, we investigate the dynamics of entanglement of three-qubit states of a system dissipating into a common environment. By using the tripartite negativity as entanglement measure, our results imply that the three-qubit entanglement can be generated among the three qubits which have no interaction with each other, but interact with the common environment independently. From our analysis, we find that the three-qubit entanglement increases from zero to a stable value which varies with the size of the system with the increasing of the scaled time. Additionally, the extension of the entanglement generation to an arbitrary size of a subsystem is made and some discussion is given.

Tripartite quantum correlations of polar molecules in pendular states

Cold polar molecules have long coherence time and strong dipole-dipole interaction and thus are regarded as a promising quantum carrier for quantum information processing. In this paper, by employing the pendular states of polar molecules as qubit, we investigate the properties of three types of tripartite quantum correlations for three linear polar molecules and numerically analyze the relations of tripartite negativity, measurement-induced disturbance (MID), and tripartite quantum discord (TQD) to three dimensionless reduced variables that relate to external field strength, dipole moment, rotational constant, dipole-dipole coupling, and temperature. The result shows that if the values of the other parameters are fixed, the three quantum correlations decrease with the increase of the field strength, and the three quantum correlations first increase to their respective maxima and then diminish gradually as the dipole-dipole coupling becomes larger. Moreover, as the temperature increases, both tripartite negativity and TQD become small, but with the variation of temperature there exhibit different evolution tendencies for MID between the influence of the electric field strength and that of the dipole-dipole coupling. In addition, the three quantum correlations of polar molecules in pendular state can be manipulated by tuning the external electric field strength, dipole-dipole coupling, and temperature.

Tripartite correlations in a Heisenberg [formula omitted] spin ring in thermal equilibrium

Tripartite correlations are investigated at length by various witnesses such as tripartite negativity, genuine tripartite entanglement, total tripartite correlations and genuine tripartite correlations. Their behaviors following various tunable system parameters as well as their connections with quantum phase transitions (QPTs) in a three-qubit Heisenberg XXZ spin ring with three-spin interaction in thermal equilibrium are discussed. The results show that these tripartite correlation witnesses can faithfully detect the critical points associated with QPTs at zero temperature limit in this model. In addition, total tripartite correlations and genuine tripartite correlations can even signal critical points with respect to anisotropy Δ at finite low temperatures.