Genuine Tripartite Entanglement Research Articles

Moments based entanglement criteria and measures

Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures.

Genuine tripartite entanglement and geometric quantum discord in entangled three-body Unruh–DeWitt detector system

Genuine tripartite entanglement and geometric quantum discord in entangled three-body Unruh–DeWitt detector system

Squeezing and entangling two microwave modes of electro-optomechanical systems with two driving lasers

We propose an effective scheme to generate the squeezed vacuum states of two microwave fields, bipartite and genuine tripartite entanglement in a compound four-mode electro-optomechanical system with two driving lasers of different amplitudes. We find that two microwave fields can be squeezed simultaneously when the effective coupling constants between mechanical oscillator and two microwave fields are chosen appropriately. In particular, the squeezing of one microwave mode can be larger than 3 dB even at high temperature. We also find that bipartite and genuine tripartite entanglement can be generated in this system which are robust against thermal fluctuations. Our scheme may have potential applications in quantum information processing and quantum metrology.

Nonreciprocal macroscopic tripartite entanglement in atom-optomagnomechanical system

We investigate how to generate the nonreciprocal macroscopic tripartite entanglement among the atomic ensemble, ferrimagnetic magnon and mechanical oscillator in a hybrid atom-optomagnomechanical system, where an ensemble of two-level atoms and a yttrium iron garnet micro-bridge supporting the magnon and mechanical modes are placed in a spinning optical resonator driven by a laser field. The phonon being the quantum of the mechanical mode interacts with the magnon and the optical photon via magnetostriction and radiation pressure, respectively, and meanwhile the photon couples to the atomic ensemble. The results show that not only all bipartite entanglements but also the genuine tripartite entanglement among the atomic ensemble, magnon and phonon could be generated at the steady state. Moreover, the nonreciprocity of atom-magnon-phonon entanglement can be obtained with the aid of the optical Sagnac effect by spinning the resonator, in which the entanglement is present in a chosen driving direction but disappears in the other direction. The nonreciprocal macroscopic tripartite entanglement is robust against temperature and could be flexibly controlled by choosing the system parameters. Our work enriches the study of macroscopic multipartite quantum states, which may have potential applications in the development of quantum information storage and the construction of multi-node chiral quantum network.

Detection and measure of genuine entanglement based on the realignment of density matrices for tripartite quantum states

As one of the important types of entanglement, genuine multipartite entanglement plays a key role in both foundational and practical aspects of quantum information theory. In this manuscript, we study the genuine multipartite entanglement in tripartite quantum systems based on the enhanced realignment criterion. A family of sufficient conditions for detecting genuine tripartite entanglement are presented. Moreover, lower bounds of the genuine multipartite entanglement concurrence are derived. The detection power and advantages of our results are illustrated through several examples.

Monogamy relations for bipartite and tripartite entanglement via intracavity spontaneous parametric down-conversion

Quantum entanglement is an important resource for quantum information processing, quantum communication, quantum computation and quantum sensing. Hence, several proposals have focused on the generation and characterization of entanglement. Some of those proposals are based on intracavity nonlinear processes. Here, we investigate bipartite and tripartite continuous variable entanglement generated by three intracavity spontaneous parametric down-conversion processes. In the model, three beams interact with a nonlinear medium inside a resonant cavity, as well as through the nonlinear process, creating three output fields. We use the positive-P phase-space method to analyze this system and to obtain the steady-states solutions. We also calculate the intracavity fluctuation spectra and utilize different continuous-variable entanglement criteria to certify bipartite/tripartite entanglement. Our results show the frequency regime where bipartite and genuine tripartite entanglement are present in the system. For this system, we also analyze the regimes where the monogamy relations hold.

Effect of relativistic acceleration on tripartite entanglement of Gaussian states

The performance of quantum information protocols can be impacted by the noninertial motion of parties such as in a gravitational field. Previous studies have primarily focused on the degradation of entanglement for global modes, revealing that bipartite entanglement vanishes in the limit of large acceleration, whereas tripartite entanglement does not. In this study, we examine the impact of acceleration on tripartite Gaussian resource states encoded in spatially localized wave packets. Contrarily to prior findings, we observe that genuine tripartite entanglement (GTE) vanishes in the limit of large acceleration for various initial states and observer trajectories.

Manipulating bipartite and tripartite quantum correlations of mechanical oscillators via optomechanical interaction.

The entanglement of macroscopic mechanical oscillators is always an interesting domain. How to entangle multiple mechanical oscillators is still not well answered. In this paper, we investigate the bipartite and tripartite quantum correlations among three distinct mechanical oscillators interacting with one cavity pumped by a multi-tone driving laser. Floquet cavity modes, resulting from different frequency components of the multi-tone driven cavity, are used to construct channels for quantum correlations between mechanical oscillators. By modulating the effective optomechanical coupling, we can manipulate the mechanical entanglement and EPR steering. The numerical results show that the two-tone driving widely employed is not enough to generate tripartite entanglement, while three- and four-tone driving can be employed to generate and enhance genuine tripartite entanglement. All bipartite entanglement can also be modulated. In addition, we demonstrate the monogamous relation of tripartite EPR steering and manipulate the asymmetry of steering. This work provides a method for manipulating the quantum correlation among multiple macroscopic objects.

Detecting multipartite entanglement via complete orthogonal basis

We study genuine tripartite entanglement and multipartite entanglement in arbitrary n-partite quantum systems based on complete orthogonal basis (COB). While the usual Bloch representation of a density matrix uses three types of generators, the density matrix with COB operators has one uniformed type of generators which may simplify related computations. We take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement and multipartite entanglement. We first convert the general states to simpler forms by using the relationship between general symmetric informationally complete measurements and COB. Then we derive an operational criteria to detect genuine tripartite entanglement. We study multipartite entanglement in arbitrary dimensional multipartite systems. By providing detailed examples, we demonstrate that our criteria can detect more genuine entangled and multipartite entangled states than the previously existing criteria.

Nonreciprocal tripartite entanglement based on magnon Kerr effect in a spinning microwave resonator

We present a scheme to generate the ideal nonreciprocal tripartite entanglement in a cavity magnonic system where a yttrium iron garnet sphere is placed in a spinning microwave resonator. Based on Kerr nonlinearities of magnons, the photon, the Kittel and the higher-order magnetostatic modes are entangled with each other and the genuine tripartite entanglement also could be achieved. By spinning the resonator, the Sagnac effect directly leads to the nonreciprocity of tripartite entanglement, where the entanglement is present in one chosen propagating direction but disappears in another. Our work could be applied in constructing chiral quantum networks.

Hawking effect can generate physically inaccessible genuine tripartite nonlocality

We explore the acceleration effect on the genuine tripartite nonlocality (GTN) for one or two accelerated detector(s) coupled to the vacuum field with initial mixed tripartite states. We show that the Hawking radiation degrades the physically accessible GTN, which suffers from “sudden death” at certain critical Hawking temperature. An novel phenomenon has been observed first time that the Hawking effect can generate the physically inaccessible GTN for fermion fields in curved spacetime, the “sudden birth” of the physically inaccessible GTN. This result shows that the GTN can pass through the event horizon of black hole for certain mixed initial states. We also derived analytically the tradeoff relations of genuine tripartite entanglement (GTE) and quantum coherence under the influence of Hawking effect.

Experimental entanglement generation using multiport beam splitters

Multipartite entanglement plays a central role in optical quantum technologies. One way to entangle two photons is to prepare them in orthogonal internal states, for example, in two polarisations, and then send them through a balanced beam splitter. Post-selecting on the cases where there is one photon in each output port results in a maximally entangled state. This idea can be extended to schemes for the post-selected generation of larger entangled states. Typically, switching between different types of entangled states requires different arrangements of beam splitters and so a new experimental setup. Here, we demonstrate a simple and versatile scheme to generate different types of genuine tripartite entangled states with only one experimental setup. We send three photons through a three-port splitter and vary their internal states before post-selecting on certain output distributions. This results in the generation of tripartite W, G and GHZ states. We obtain fidelities of up to with regard to the respective ideal states, confirming a successful generation of genuine tripartite entanglement.

Detecting genuine tripartite entanglement via general symmetric informationally complete measurements.

We study multipartite entanglement and genuine tripartite entanglement based on general symmetric informationally complete positive operator valued measurements (GSIC-POVMs). By representing the bipartite density matrices in terms of GSIC-POVMs, we obtain the lower bound of the sum of squares of the corresponding probability. We then construct a special matrix with the correlation probability of GSIC-POVMs to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. Detailed examples show that the new method can detect more entangled and genuine entangled states than previous criteria.

Enhanced the Bi-(Tri-)partite entanglement between three magnons in a cavity magnomechanics system

We propose a scheme to generate steady-state bipartite and tripartite entanglement in the cavity magnomechanical system, which consists of a microwave (MW) cavity field, three magnons, and a phonon mode. The three magnons are coupled to the MW cavity via the magnetic dipole interaction, and one of them is also coupled to the phonon mode through the magnetostrictive force. By utilizing the nonlinearity of the magnetostrictive force and the cavity-magnon interaction, the three magnons become mutually entangled, and the steady-state of the system displays a genuine tripartite entanglement. We found that there are optimum parameters, including the detunings and the cavity-magnon coupling, which lead to maximum entanglement. Moreover, the entanglement is robust against thermal effects.

Quantum feedback induced genuine magnon–photon–magnon entanglement and steering in a cavity magnonical system

We present an alternative scheme to generate genuine tripartite entanglement and steering among one photon and two magnons in a cavity magnonical system, where two yttrium iron garnet spheres are respectively placed inside two microwave cavities driven by a two-mode squeezed field and subjected to homodyne-measurement feedback. It is found that quantum feedback on two cavities plays a crucial role in enhancing quantum correlations of photons and magnons. In the absence of measurement feedback, only bipartite entanglement between two magnons is existent. In contrast, when the continuous measurement feedback is present, two magnons are strongly entangled and magnon–photon entanglement also appears. More importantly, the stable genuine magnon–photon–magnon tripartite entanglement and steering could be obtained based on the homodyne-measurement feedback on two microwave cavities, which are robust against the thermal fluctuations. The work we present provides a feasible way to manipulate the multipartite quantum correlations including entanglement and steering in hybrid quantum systems.

Monogamy inequality and entanglement sharing in optomechanics

In this paper, we quantitatively study the dynamics of the tripartite entanglement of the three-mode Gaussian state in a cavity-free optomechanical system. After deriving the explicit form of the evolved state matrix covariance, we elucidate in detail the evidence of entanglement monogamy in different mode partitions, based on Coofman–Kundu–Wotters inequalities, using the Gaussian Contangle quantifying bipartite entanglement. Next, we focus on the genuine tripartite entanglement quantified by means of the Residual Gaussian Contangle.

Enhancement of magnon–photon–phonon entanglement in a cavity magnomechanics with coherent feedback loop

In this paper, we present a coherent feedback loop scheme to enhance the magnon–photon–phonon entanglement in cavity magnomechanics. We provide a proof that the steady state and dynamical state of the system form a genuine tripartite entanglement state. To quantify the entanglement in the bipartite subsystem and the genuine tripartite entanglement, we use the logarithmic negativity and the minimum residual contangle, respectively, in both the steady and dynamical regimes. We demonstrate the feasibility of our proposal by implementing it with experimentally realizable parameters to achieve the tripartite entanglement. We also show that the entanglement can be significantly improved with coherent feedback by appropriately tuning the reflective parameter of the beam splitter and that it is resistant to environmental thermalization. Our findings pave the way for enhancing entanglement in magnon–photon–phonon systems and may have potential applications in quantum information.

Genuine Tripartite Non-Gaussian Entanglement.

Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a set of sufficient and necessary conditions for separability of the broad family of spontaneously generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.

Genuine tripartite entanglement of W state subject to Hawking effect of a Schwarzschild black hole

We study the genuine tripartite entanglement (GTE), one-tangle and two-tangle of W state of fermionic fields in the background of a Schwarzschild black hole. We find that, with the increase of the Hawking temperature, the GTE of W state first decreases and then tends to zero, while the GTE of GHZ state first decreases and then freezes. We also find that the Hawking effect can completely destroy the two-tangle of W state, while one-tangle first decreases and then the freezing phenomenon appears with the growth of the Hawking temperature. These results are helpful to guide us to select appropriate quantum states and quantum resources to deal with relativistic quantum information tasks.

Unification of coherence and quantum correlations in tripartite systems

In quantum resource theories (QRTs), there exists evidences of intrinsic connections among different measures of quantum resources, including entanglement, coherence, quantum steering, and so on. However, building the relations among different quantum resources is a vital yet challenging task in multipartite quantum systems. Here, we focus on a unified framework of interpreting the interconversions among different quantum resources in tripartite systems. In particular, an exact relation between the generalized geometric measure and the genuinely multipartite concurrence are derived for tripartite entanglement states. Then we obtain the tradeoff relation between the first-order coherence and the genuine tripartite entanglement by the genuinely multipartite concurrence and concurrence fill. Furthermore, the tradeoff relation between the maximum steering inequality violation and concurrence fill for an arbitrary three-qubit pure state is found. In addition, we investigate the close relation between the maximum steering inequality violation and the first-order coherence. The results show that these quantum resources are intrinsic related and can be converted to each other in the framework of QRTs, although they are still regarded to be different.