S. Shelly Sharma
We present a single step scheme to generate, experimentally, maximally entangled tripartite GHZ state in a single ion, using trapped ion interacting simultaneously with a resonant external laser field and red sideband tuned quantized cavity field. Besides the simplicity of execution and short operation time, GHZ state generation is reduction free. Pacs: 03.67.-a, 42.50.-p, 03.67.Dd
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The paper titled "Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states", (Physical Review Letters 102, 250404 (2009)), does very important work on studying the nature of Svetlichny Inequalities (which are Bell-type inequalities) and sheds light on some important properties and relationship between Svetlichny inequality and tripartite entanglement. It derives a result for the maximum expectation value of Svetlichny operator for GGHZ and MS states. In this comment, it is put forth that there is probably a mistake in the central result derived in the paper.
We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for 3-qubit pure states in the GHZ class. We consider a family of states known as the generalized GHZ states and derive an analytical expression relating the 3-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with 3-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states do …
We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. Milburn equation is solved for this tripartite system to obtain the time evolution of density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of unitary time step relative to the time scale determined by system parameters. Starting with the system prepared initially in a separable state, density matrix is used to calculate the probability of tripart…
In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of superposition and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel p…
We investigate economic protocol to securely encoding classical information among three users via entangled GHZ states. We implement the scheme in cavity QED with atomic qubits where the atoms interact simultaneously with a highly detuned cavity mode with the assistance of a classical field. The scheme is insensitive to the cavity decay and the thermal field, thus based on cavity QED techniques presently it might be realizable.
The paper presents the detailed study of controlled dense coding scheme for different types of $3$ and $4-$ particle states. It consists of GHZ state, GHZ type states, Maximal Slice state, Four particle GHZ state and W class of states. It is shown that GHZ-type states can be used for controlled dense coding in a probabilistic sense. We have shown relations among parameter of GHZ type state, concurrence of the shared bipartite state by two parties with respect to GHZ type and Charlie's measurement angle $θ$. We have seen that tripartite W state and quadripartite W state cannot be used in contro…
The existence and nature of tripartite entanglement of a noninteracting Fermi gas (NIFG) is investigated. Three new classes of parameterized entanglement witnesses (EWs) are introduced with the aim of detecting genuine tripartite entanglement in the three-body reduced density matrix and discriminating between the presence of the two types of genuine tripartite entanglement, W\B and GHZ\W. By choosing appropriate EW operators, the problem of finding GHZ and W EWs is reduced to linear programming. Specifically, we devise new W EWs based on a spin-chain model with periodic boundary conditions, an…
The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleportrd state by controlling on Bell measurements, analyzer angle and channel's strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the deca…
We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator …
Experimental free-will or measurement independence is one of the crucial assumptions in derivation of any nonlocal theorem. Any nonlocal correlation obtained in quantum world can have a local deterministic explanation if there is no experimental free-will in choosing the measurement settings. Recently, in [Phys. Rev. Lett. {\bf105}, 250404 (2010)] it has been shown that to obtain a local deterministic description for singlet state correlation one does not need to give up measurement independence completely, but a partial measurement dependence suffices. In three party scenario considering GHZ …
We present a scheme for joint remote state preparation (JRSP) of three-particle state via three tripartite Greenberger-Horne-Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We use eight-qubit mutually orthogonal basis vector as measurement point of departure. The likelihood of success for this scheme has been found to be $1/8$. However, by putting some special cases into consideration, the chances can be ameliorated to $1/4$ and $1$. The effects of amplitude-damping noise, phase-damping noise and depolarizing noise on this scheme have been scrutinized and the analy…
We study the tripartite entanglement for a class of mixed states defined by the mixture of GHZ and W states, ρ=p|GHZ><GHZ|+(1-p)|W><W|. Based on the Caratheodory theorem and the periodicity assumption, the possible optimal decomposition of the states has been derived, which is not independent on the detailed measure of entanglement. We find that, according to p, there are two different decompositions containing 3 or 4 quantum states in the decomposition respectively. When the decomposition contains 3 quantum states, the tripartite entanglement of the mixed state is simply the entanglement of s…
The multipartite Greenberger-Horne-Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme can be considered as an extension of a recent work [T. M. Wintermantel, Y. Wang, G. Lochead, \textit{et al}, {Phys. Rev. Lett. \textbf{124}, 070503 (2020)}]. By virtue of the polychromatic driving fields and the engineered spontaneous emission, a multipartite GHZ state with odd numbers of atoms are generated with a high effic…
We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own non-Markovian environment. First, we consider three GHZ-type initial states, all of which have GHZ symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding $π$-tangles, one of the tripartite entanglement measure, are analytically computed at arbitrary time. The revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also c…
We investigate minimal control power (MCP) for controlled dense coding defined by the channel capacity. We obtain MCPs for extended three-qubit Greenberger-Horne-Zeilinger (GHZ) states and generalized three-qubit $W$ states. Among those GHZ states, the standard GHZ state is found to maximize the MCP and so does the standard $W$ state among the $W$-type states. We find the lower and upper bounds of the MCP and show for pure states that the lower bound, zero, is achieved if and only if the three-qubit state is biseparable or fully separable. The upper bound is achieved only for the standard GHZ …
In tripartite discrete systems, two classes of genuine tripartite entanglement have been discovered, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. To date, much research effort has been concentrated on the polarization entangled three-photon GHZ and W states. Most studies of continuous variable multiparticle entanglement have been focused on Gaussian states. In this Brief Report, we examine two classes of three-photon entangled states in space and time. One class is a three-mode three-photon entangled state and the other is a two-mode triphoton state. These states show b…
Local unitary decomposition of tripartite arbitrary leveled qudit stabilizer states into $p$-level-qudit EPR and GHZ state
本文提出利用 Clifford 群外局域幺正和子系统相位矩阵，将任意维素数幂三体 qudit 稳定子态分解为 $p$ 能级 GHZ、EPR 与未纠缠 qudit。
Hardy-type self-testing and exposedness of tripartite GHZ correlations
研究三体两输入两输出场景中Hardy型悖论的自检验，证明最大Hardy成功概率关联自检验GHZ态和测量，且该关联是量子关联集的极点和暴露点，与Mermin不等式最大违反点重合。
We embarked upon the task of experimental protection of different classes of tripartite entangled states, namely the maximally entangled GHZ and W states and the ${\rm W \bar{W}}$ state, using dynamical decoupling. The states were created on a three-qubit NMR quantum information processor and allowed to evolve in the naturally noisy NMR environment. Tripartite entanglement was monitored at each time instant during state evolution, using negativity as an entanglement measure. It was found that the W state is most robust while the GHZ-type states are most fragile against the natural decoherence …
We present a family of tri-partite entangled states that, in an asymptotical sense, can be reversibly converted into EPR states shared by only two of parties (say B and C), and tripartite GHZ states. Thus we show that bipartite and genuine tripartite entanglement can be reversibly combined in several copies of a single tripartite state. For such states the corresponding fractions of GHZ and of EPR states represent a complete quantification of their (asymptotical) entanglement resources. More generally, we show that the three different kinds of bipartite entanglement (AB, AC and BC EPR states) …
Maximally entangled states are of utmost importance to quantum communication, dense coding, and quantum teleportation. With a trapped ion placed inside a high finesse optical cavity, interacting with field of an external laser and quantized cavity field, a scheme to generate a maximally entangled three qubit GHZ state, is proposed. The dynamics of tripartite entanglement is investigated, using negativity as an entanglement measure and linear entropy as a measure of mixedness of a state. It is found that (a) the number of modes available to the subsystem determines the maximum entanglement of a…
The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. We study this topic in three-qubit systems considering the entanglement classification of stochastic local operations and classical communication (SLOCC). The equivalence under SLOCC divides threequbit states into separable, biseparable, W, and Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of genuine tripartite entanglement.We adopt the family of GHZ-symmetric states as a research subject, which share the symmetries of the GHZ state and have…
We introduce a suit of simple entangling protocols for generating tripartite GHZ and W states in systems with anisotropic exchange interaction g(XX+YY)+g'ZZ. An interesting example is provided by macroscopic entanglement in Josephson phase qubits with capacitive (g'=0) and inductive (0<|g'/g|<0.1) couplings.
We investigate the influence of photon excitations on quantum correlations in tripartite Glauber coherent states of Greenberger-Horne-Zeilinger type. The pairwise correlations are measured by means of the entropy-based quantum discord. We also analyze the monogamy property of quantum discord in this class of tripartite states in terms of the strength of Glauber coherent states and the photon excitation order.
Methods for distilling maximally entangled tripartite (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillation. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems, a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selecti…
We propose an experimentally feasible scheme to demonstrate quantum nonlocality, using Greenberger-Horne-Zeilinger (GHZ) and $W$ entanglement between atomic ensembles generated by a new developed method based on laser manipulation and{} single-photon detection.
Channels composed by Einstein-Podolsky-Rosen (EPR) pairs are capable of teleporting arbitrary multipartite states. The question arises whether EPR channels are also optimal against imperfections. In particular, the teleportation of Greenberger-Horne-Zeilinger states (GHZ) requires three EPR states as the channel and full measurements in the Bell basis. We show that, by using two GHZ states as the channel, it is possible to transport any unknown three-qubit state of the form $c_0|000\rangle+c_1|111\rangle$. The teleportation is made through measurements in the GHZ basis, and, to obtain determin…
In this article the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits and profound impact of DM interaction is studied on the initial entan…
As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. Greenberger-Horne-Zeilinger (GHZ) state plays important role in quantum communication network. By reconstructing the covariance matrix of a continuous variable tripartite GHZ state, we fully quantify the amount of bipartite steering under Gaussian measurements. We demonstrate that the (1+1)-mode steerability is not exist in the tripartite GHZ state, only the collectively steerability exist between the (1+2)-mode and (2+1)-mode partitions. These p…
We consider the problem of extracting tripartite entanglement through single local instantaneous interactions of a separable target system A-B-C with a scalar field. We find, non-perturbatively, that tripartite entanglement is easily extracted in this scenario, in strong contrast to bipartite extraction, which is not possible due to a no-go theorem. The tripartite entanglement is of the GHZ-type, and an optimal value of the coupling exists that admits maximal extraction.
Generation of tripartite entangled states with fermionic systems
本文提出基于隧穿与粒子探测的协议，在三阱势中3个不可区分费米子间生成三体纠缠，成功制备费米子w型态但无法生成ghz型态，揭示两类纠缠态的根本不等价性，为不可区分粒子多体纠缠的量子信息应用提供新思路。
Nonlinear Tripartite Coupling of Trapped Electrons with Magnons in a Hybrid Quantum System
研究提出在混合量子系统中通过受限电子与磁子的非线性三元耦合实现量子模拟与信息处理，利用电子的电荷和自旋自由度与磁子模式相互作用，实现可调强的自旋-磁子-运动耦合，用于制备少体纠缠态。
We investigate schemes for quantum secret sharing and quantum dense coding via tripartite entangled states. We present a scheme for sharing classical information via entanglement swapping using two tripartite entangled GHZ states. In order to throw light upon the security affairs of the quantum dense coding protocol, we also suggest a secure quantum dense coding scheme via W state in analogy with the theory of sharing information among involved users.
We study how to control the dynamics of tripartite entanglement among optical cavities using non-Markovian baths. In particular, we demonstrate how the reservoir engineering through the utilization of non-Markovian baths with different types of Lorentzian and ohmic spectral densities can lead to an entanglement survival for longer times and in some cases considerable regain of seemingly lost entanglement. Both of these behaviors indicate a better sustainability of entanglement (in time) compared to the usual Markovian bath situations which assumes a flat spectrum of the bath around the system …
Tripartite quantum Rabi model with trapped Rydberg ions
本文提出三方量子 Rabi 模型（TQRM），研究玻色子与双自旋的耦合机制，解析推导本征谱，并指出可在囚禁里德堡离子量子模拟器中实现，为探索自旋与运动自由度的新关联和纠缠提供新机遇。
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localiz…
A measure for genuine tripartite entanglement
提出一个基于四个三量子比特关联期望值的实值泛函，将GHZ代数悖论转化为真正三方纠缠的定量判据，并证明其最大值为2，仅在GHZ态时达到。
Demonstration of tripartite cat states in two distinct classes of entanglement
研究通过三个微波谐振器与辅助超导跨导量子比特耦合，实现两类宏观三方纠缠猫态，利用跨导量子比特能级生成态并重构，获不同保真度，验证不同纠缠类，为宏观多体纠缠和容错量子信息处理研究提供测试平台。
It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a non-separable, tripartite GHZ-like state of path, polarization and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by…
Entanglement is a well-known resource in quantum information, in particular it can be exploited for quantum key distribution (QKD). In this paper we define a two-way QKD scheme employing GHZ-type states of three qubits obtaining an extension of the standard E91 protocol with a significant increasing of the number of shared bits. Eavesdropping attacks can be detected measuring violation of the CHSH inequality and the secret key rate can be estimated in a device-independent scenario.
We propose an experimentally feasible scheme for dissipative preparation of tripartite entangled state with atoms separately trapped in an array of three coupled cavities. The combination of coherent driving fields and quantum-jump-based feedback control will drive the system into a non-equilibrium steady state, which has a nearly perfect overlap with the genuine three-atom singlet state. Different control strategies are investigated and the corresponding optimal parameters are confirmed. Moreover, the fidelity of target state is insensitive to detection inefficiencies, and it oversteps 90\% f…
Tripartite State Characterization via Activated Bipartite Entanglement
提出基于激活的二部纠缠（ABE）识别和分类纯3-qubit态中真正三部分纠缠的程序，证明ABE能区分GHZ与W类态，并通过线性光学电路实验验证其有效性。
Sharing tripartite nonlocality sequentially using only projective measurements
本文研究仅用投影测量和共享经典随机性共享三方非定域性，发现无偏测量下两个Charlie可共享标准非定域性，有偏测量可将共享真正非定域性的Charlie增至两个。
For a tripartite pure state of three qubits, it is well known that there are two inequivalent classes of genuine tripartite entanglement, namely the GHZ-class and the W-class. Any two states within the same class can be transformed into each other with stochastic local operations and classical communication (SLOCC) with a non-zero probability. The optimal conversion probability, however, is only known for special cases. Here, we derive new lower and upper bounds for the optimal probability of transformation from a GHZ-state to other states of the GHZ-class. A key idea in the derivation of the …
Tripartite Entanglement dynamics: the influence of intrinsic decoherence and decoherence channels
本研究探讨了三耦合量子比特系统在XXZ Heisenberg链中的纠缠动力学，发现内禀退相干抑制纠缠，且不同退相干通道对GHZ态和W态的纠缠演化有显著影响。
Tripartite measurement uncertainty in Schwarzschild space-time
本研究分析了 Schwarzschild 黑洞背景下 Hawking 辐射对三方测量不确定性的影响，发现测量不确定性随 Hawking 温度升高而增加，且 GHZ 态比 W 态表现出更强的鲁棒性。
An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this s…
We describe the transfer of quantum information and entanglement from three flying (radiation) to three localized (atomic) qubits via cavity modes resonantly coupled to the atoms, in the presence of a common reservoir. Upon addressing the full dynamics of the resulting nine-qubit open system, we find that once the cavities are fed, fidelity and transferred entanglement are optimal, while their peak values exponentially decrease due to dissipative processes. The external radiation is then turned off and quantum correlations oscillate between atomic and cavity qubits. For a class of mixtures of …
By exploiting a system of three distant cavities, we propose a scheme for constructing tripartite entangled coherent GHZ and W states which are robust due to the photon losses in the cavities. Each of cavities is doped with a semiconductor quantum dot. By the dynamics, the excitonic modes of quantum dots are enabled to exhibit entan-gled coherent GHZ and W states. Apart from the exciton losses, the master equation approach shows that when the populations of the field modes in the cavities are negli-gible the destruction of entanglement due to decoherence arises from photon losses, is effective…
Lemniscate phase trajectories for high-fidelity GHZ state preparation in trapped-ion chains
本文提出一种莱姆斯曲线脉冲，通过特殊相位轨迹降低GHZ态制备保真度误差，使20离子链的保真度可达10^-4。
We describe the transfer of quantum information and correlations from an entangled tripartite bosonic system to three separate qubits through their local environments also in the presence of various dissipative effects. Optimal state mapping and entanglement transfer are shown in the framework of optical cavity quantum electrodynamics involving qubit-like radiation states and two-level atoms via the mediation of cavity modes. For an input GHZ state mixed with white noise we show the occurrence of sudden death and birth of entanglement that is discontinuously exchanged among the tripartite subs…
The conventional approach to perform two-qubit gate operations in trapped ions relies on exciting the ions on motional sidebands with laser light, which is an inherently slow process. One way to implement a fast entangling gate protocol requires a suitable pulsed laser to increase the gate speed by orders of magnitude. However, the realization of such a fast entangling gate operation presents a big technical challenge, as such the required laser source is not available off-the-shelf. For this, we have engineered an ultrafast entangling gate source based on a frequency comb. The source generate…
True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications (SLOCC). Such states can be classified in two categories: GHZ states and W-states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype W-state cannot be. However, we show that there is a class of W-states that can be used for perfect teleportation and superdense coding.
Tripartite Entanglement in Multimode Cavity Quantum Electrodynamics
研究多模腔量子电动力学中量子比特三体纠缠的生成与动力学，揭示退化效应及损耗对纠缠的影响，为量子网络和存储器发展提供新思路。
Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single NV center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive…
Sharing tripartite nonlocality sequentially by arbitrarily many independent observers
本文针对三方纠缠态的顺序共享非定域性问题，证明任意多个顺序测量的Charlie均可与单个Alice、Bob共同观测到Mermin不等式违反对应的标准非定域性及真无信号非定域性，突破了此前GHZ态真非定域性最多两个Charlie共享的结论。
The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the W- and GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstrac…
We analyze an entangling protocol to generate tripartite Greenberger-Horne-Zeilinger states in a system consisting of three superconducting qubits with pairwise coupling. The dynamics of the open quantum system is investigated by taking into account the interaction of each qubit with an independent bosonic bath with an ohmic spectral structure. To this end a microscopic master equation is constructed and exactly solved. We find that the protocol here discussed is stable against decoherence and dissipation due to the presence of the external baths.
Practical scheme for efficient distillation of GHZ states
本文提出一种基于后选择非线性变换和迭代过程的LOCC方案，以子指数收敛高效蒸馏GHZ态，纠正任意小误差，兼具操作简单性与实用性。
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.
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