Multipartite Quantum Correlations Research Articles

Generation of entanglement and quantum steering via Josephson parametric amplifier in a dual cavity-magnon system

In the two microwave (MW) cross-shaped cavity magnon system, we describe a method to produce multipartite entanglement and quantum steering. To achieve squeezed states of the magnons, a Josephson parametric amplifier (JPA) creates a squeezed vacuum field that drives the two cavities. We theoretically demonstrate that the cavity-cavity entanglement can be generated at the resonance point, however, increasing the cavity and magnon decay rates generate the cavity-magnon entanglement. By changing the squeezing parameter and increasing the decay rates, we can transfer the cavity-cavity entanglement to cavity-magnon entanglement. Furthermore, the cavity-cavity entanglement (survive up to 2.8 K) was not only found to be much stronger but also more robust as compared to cavity-magnon entanglement (survive up to 0.4 K). More importantly, the genuine photon-magnon-photon tripartite entanglement could be achieved, which is robust against thermal fluctuations and depends strongly on the squeezing parameter. Furthermore, for the current dual cavity-magnon system, two-way quantum steering is found when the optomagnonical couplings are equal. The current study offers a straightforward and practical method for achieving multipartite quantum correlations.

A computable quantification of multi-mode Gaussian coherence and complete monogamy relation

We propose a quantification CνGn of n-mode Gaussian coherence. The value of CνGn only depends on the covariance matrices and displacement vectors of continuous-variable states without any optimization procedures, and thus is easily calculated. For n=1, CνG1 is a proper Gaussian coherence measure of single-mode CV system. For n≥2, CνGn is invariant under any permutation of submodes, nonincreasing under any n-mode local incoherent Gaussian channels, vanishes at incoherent Gaussian states, and, satisfies the unification condition and the hierarchy condition that a multi-partite quantum correlation measure should obey. Thus CνGn is a multi-partite Gaussian correlation measure, which reveals, though the quantum coherence lives in single-partite systems, that the multi-mode coherence for continuous-variable systems can be regarded as a multipartite Gaussian correlation between modes, and such multi-partite Gaussian correlation is also a quantum resource. Moreover, we show that CνGn is completely monogamous as a multipartite Gaussian correlation measure. This means that the n-mode Gaussian coherence subjects to the principles of resource allocation. In addition, CνGn is an upper bound of the geometric-based single-mode Gaussian coherence measure CBu by the Bures distance at pure Gaussian states of mode ≤2 and can be used to detect coherence in any n-mode Gaussian states more efficiently.

Bipartite and tripartite steering by a nonlinear medium in a cavity

Nonlocal quantum correlations are important for potential applications in quantum optics and quantum information. Multipartite quantum correlations are relevant to access to high-dimensional systems such as qudits. There are also different proposals for the generation of quantum steering based on nonlinear systems and cavities. Here, we consider the Hamiltonian of a triple photon parametric down-conversion process to investigate the regions where bipartite and tripartite steering are generated. In this model, three beams interact with a nonlinear medium inside a cavity through the process of parametric down-conversion, creating three output fields. The positive P representation is used to analyze this system and steady-state solutions are obtained. We calculated the intracavity fluctuation spectra to analyze steering in the frequency domain and used different criteria to certify this quantum correlation. We certified bipartite steering for the three output fields from the cavity. In the case of full tripartite two-way steering inseparability, it is also present for all the bipartitions under consideration. Our results show regimes where bipartite and tripartite steering is certified for this model.

Multipartite nonlocality and symmetry breaking in one-dimensional quantum chains

Multipartite nonlocality is a measure of multipartite quantum correlations. In this paper we investigate the influence of symmetry-breaking perturbations upon ground-state nonlocality by considering several typical finite-size quantum models, including the transverse-field Ising chains, the $XY$($XX$) chains, and the $XXZ$ chains. We find that even a slight perturbation can reshape the nonlocality curve dramatically. For instance, in the $XY$ chains, a perturbation can induce an oscillation behavior in the nonlocality curve. A clear microscopic mechanism for the results is proposed. Furthermore, we also connect the behaviors to the macroscopic symmetry properties of the chains and make some predictions on general models.

Complete monogamy of multipartite quantum mutual information

Quantum mutual information not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here two alternatives of the multipartite quantum mutual information (MQMI) based on the von Neumann entropy according to the framework of the complete measure of the multiparticle quantum system. We show that these two MQMIs are complete and are monogamous on pure states, and one of them (we call it type-1) is not only completely monogamous but also tightly complete monogamous, while the other one (we call it type-2) is not. Moreover, we present another two MQMIs by replacing the von Neumann entropy with the Tsallis $q$-entropy from the former two ones. It is proved that one of them displays some degree of ``completeness'' as a measure of the multiparticle quantum system, but the other one is not even non-negative and thus it cannot be an alternative of MQMI. We also discuss the triangle relation for these three alternatives of MQMI. It is shown that the triangle inequalities hold for the former two MQMIs as that of entanglement measure but the later one fails. We thus can conclude that the type-1 von Neumann entropy MQMI is a ``fine'' measure of multipartite quantum correlation.

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.

Continuous variable quantum conference network with a Greenberger–Horne–Zeilinger entangled state

Quantum conference (QC) is a cryptographic task in secure communications that involves more than two users wishing to establish identical secret keys among N users. The Greenberger–Horne–Zeilinger (GHZ) entangled state is the basic resource for quantum cryptographic communication due to the existence of multipartite quantum correlations. An unconditional and efficient quantum network can be established with a continuous variable (CV) GHZ entangled state because of its deterministic entanglement. Here, we report an implementation of QC scheme using a CV multipartite GHZ entangled state. The submodes of a quadripartite GHZ entangled state are distributed to four spatially separated users. The proposed QC scheme is proved to be secure even when the entanglement is distributed through lossy quantum channels and the collective Gaussian attacks are in the all lossy channels. The presented QC scheme has the capability to be directly extended to a larger scale quantum network by using entangled states with more submodes.

Distributing Multipartite Entanglement over Noisy Quantum Networks

A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.

Enhancement of quadripartite quantum correlation via phase-sensitive cascaded four-wave mixing process

Multipartite quantum correlation is important for both fundamental science and quantum information processing. Its enhancement is critical to improve the performance of physical systems. Therefore, it is of great practical significance to study the enhancement of multipartite quantum correlation. Here, we theoretically investigate a scheme for enhancing quadripartite quantum correlation by utilizing a phase-sensitive cascaded four-wave mixing (CFWM) process. We find that the intensity-difference squeezing (IDS) among the four output beams generated by the phase-insensitive CFWM process can be largely enhanced by introducing the phase-sensitive CFWM process. We also find that our phase-sensitive CFWM process can be used to generate intensity-sum squeezing (ISS), which cannot be generated by the phase-insensitive CFWM process. Moreover, we find that the maximum squeezing value of ISS is equal to that of IDS when the intensity gains of the three four-wave mixing processes are equal in the phase-sensitive cascaded scheme. In the end, we discuss the effects of the losses and the phase fluctuations on the squeezing values of our phase-sensitive CFWM process and the corresponding phase-insensitive CFWM process with the same intensity gains. It can be seen that the squeezing enhancement of our phase-sensitive CFWM process holds also in presence of the losses and the phase fluctuations. Our results pave the way for experimental implementation and may find applications in quantum metrology and quantum communication.

Entangled multiplets and spreading of quantum correlations in a continuously monitored tight-binding chain

We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semi-classical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and continuous monitoring. We unveil the existence of multipartite quantum correlations which are inconsistent with an entangled-pair structure and which, within a quasiparticle picture, would require the presence of larger multiplets. We also observe that quantum information is highly delocalized, as it is shared in a collective {\it nonredundant} way among adjacent regions of the many-body system. Our results shed new light onto the behavior of correlations in quantum stochastic dynamics and further show that these may be enhanced by a (weak) continuous monitoring process.

Open quantum rotors: Connecting correlations and physical currents

We consider a finite one-dimensional chain of quantum rotors interacting with a set of thermal baths at different temperatures. When the interaction between the rotors is made chiral, such a system behaves as an autonomous thermal motor, converting heat currents into non-vanishing rotational ones. Such a dynamical response is strongly pronounced in the range of the Hamiltonian parameters for which the ground state of the system in the thermodynamic limit exhibits a quantum phase transition. Such working points are associated with large quantum coherence and multipartite quantum correlations within the state of the system. This suggests that the optimal operating regime of such quantum autonomous motor is one of maximal quantumness.

Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 XY chain

We study the properties of multipartite quantum correlation (MQC) in a one-dimensional spin-1/2 $XY$ chain, where the three-spin reduced states are focused on and the four introduced MQC measures are based on entanglement negativity and entanglement of formation. It is found that, even in the Ising case, the three-spin subsystems have long-range MQCs and the tripartite quantum correlations beyond the nearest-neighbor three spins can detect the quantum phase transition and obey the finite-size scaling around the critical point. Furthermore, in the $XY$ model, we show that the two selected MQCs can indicate exactly the factorization point of the ground state for the anisotropic model in the thermodynamic and finite-size cases. Moreover, the spatial distribution of MQC based on entanglement negativity can attain a much larger range by tuning the anisotropic parameter, and the newly defined MQC based on entanglement of formation can detect the bound entanglement in the three-spin subsystems when the entanglement negativity loses its efficacy.

Coordinately assisted distillation of quantum coherence in multipartite system

We investigate the issue of assisted coherence distillation in the asymptotic limit, by coordinately performing the identical local operations on the auxiliary systems of each copy. When we further restrict the coordinate operations to projective measurements, the distillation process branches into many sub-processes. Finally, a computable measure of the assisted distillable coherence is derived as the maximal average coherence of the residual states with the maximization taken over all the projective measurements on the auxiliary. The measure can be conveniently used to evaluate the assisted distillable coherence in experiments, especially suitable for the case that the system and its auxiliary are in mixed states. By using the measure, we for the first time study the assisted coherence distillation in multipartite systems. Monogamy-like inequalities are derived to constrain the distribution of the assisted distillable coherence in the subsystems. Taking a three-qubit system for example, we experimentally prepare two types of tripartite correlated states, i.e., the W-type and GHZ-type states in a linear optical setup, and experimentally test the assisted distillable coherence. Theoretical and experimental results agree well to verify the distribution inequalities given by us. Three measures of multipartite quantum correlation are also considered. The close relationship between the assisted coherence distillation and the multipartite correlation is revealed.

Multipartite nonlocality and topological quantum phase transitions in a spinless fermion quantum wire with uniform and incommensurate potentials

Multipartite nonlocality and Bell-type inequalities are used to characterize topological quantum phase transitions (QPTs) in a spinless fermion quantum wire, where both uniform potentials and incommensurate potentials are considered. First, the nonlocality measures show clear signals at the critical points in both the uniform model and the incommensurate model. It indicates that these QPTs are accompanied by dramatic changes of multipartite quantum correlations in the ground states. Second, finite-size scaling analysis is carried out. In particular, in the incommensurate model where translation invariance is broken, with some rescaling techniques, we successfully establish the scaling formula in the large-$L$ limit. Finally, the full phase diagram of the model with mixed potentials is figured out. We find a region which is featured with strong randomness in the large-$L$ limit. The structure of this region is revealed by analyzing the energy spectrum, and an efficient approach to characterize this region is proposed.

Computable multipartite multimode Gaussian quantum correlation measure and the monogamy relations for continuous-variable systems

In this paper, definitions of the unification condition, the hierarchy condition, and three kinds of monogamy relations for multipartite quantum correlation measures are given and discussed. A computable multipartite multimode Gaussian quantum correlation measure ${\mathcal{M}}^{(k)}$ is proposed for any $k$-partite multimode continuous-variable systems with $k\ensuremath{\ge}2$. The value of ${\mathcal{M}}^{(k)}$ only depends on the covariance matrices of continuous-variable states, is invariant under any permutation of subsystems, has no ancilla problem, is nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite locally Gaussian unitary operations), and vanishes on $k$-partite product states. For a $k$-partite Gaussian state $\ensuremath{\rho}, {\mathcal{M}}^{(k)}(\ensuremath{\rho})=0$ if and only if $\ensuremath{\rho}$ is a $k$-partite product state. Moreover, ${\mathcal{M}}^{(k)}$ satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that ${\mathcal{M}}^{(k)}$ is not strongly monogamous but completely monogamous and tightly monogamous.

Multi-User Distillation of Common Randomness and Entanglement From Quantum States

We construct new protocols for the tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communication (LOCC). The former task is known as common randomness (CR) distillation, and it requires offsetting the amount of classical communication against the randomness created. We obtain a new lower bound on the “distillable common randomness,” an operational measure of the total genuine (classical) correlations in a quantum state. Our proof relies on a generalization of communication for omniscience (CO) [Csiszár and Narayan, IEEE Trans. Inf. Theory 50:3047-3061, 2004], and our contribution here is a novel simultaneous decoder for the compression of correlated classical sources by random binning with quantum side information at the decoder. For the latter task, we derive two lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in “making coherent” the proposed CR distillation protocols and recycling of resources [Devetak <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> IEEE Trans. Inf. Theory 54(10):4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65(9):5945-5958, 2019], which is based on a combinatorial method to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation.

Multipartite quantum correlations in a two-mode Dicke model

We analyze multipartite correlations in a generalized Dicke model involving two optical modes interacting with an ensemble of two-level atoms. In particular, we examine correlations beyond the standard bipartite entanglement and derive exact results in the thermodynamic limit. The model presents two superradiant phases involving the spontaneous breaking of either a ${\mathbb{Z}}_{2}$ or a U(1) symmetry. The latter is characterized by the emergence of a Goldstone excitation, found to significantly affect the correlation profiles. Focusing on the correlations between macroscopic subsystems, we analyze both the mutual information and the entanglement of formation for all possible bipartitions among the optical and matter degrees of freedom. It is found that while each mode entangles with the atoms, the bipartite entanglement between the modes is zero, and they share only classical correlations and quantum discord. We also study the monogamy of multipartite entanglement and show that there exists genuine tripartite entanglement, i.e., quantum correlations that the atoms share with the two modes but that are not shared with them individually, only in the vicinity of the critical lines. Our results elucidate the intricate correlation structures underlying superradiant phase transitions in multimode systems.

Multipartite nonlocality in one-dimensional quantum spin chains at finite temperatures

Multipartite nonlocality is an important measure of multipartite quantum correlations. In this paper, we show that the nonlocal $n$-site Mermin-Klyshko operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}}_{n}$ can be exactly expressed as a matrix product operator with a bond dimension $D=2$, and then the calculation of nonlocality measure $\mathcal{S}$ can be simplified into standard one-dimensional (1D) tensor networks. With the help of this technique, we analyze finite-temperature multipartite nonlocality in several typical 1D spin chains, including an $XX$ model, an $XXZ$ model, and a Kitaev model. For the $XX$ model and the $XXZ$ model, in a finite-temperature region, the logarithm measure of nonlocality (${log}_{2}\mathcal{S}$) is a linear function of the temperature $T$, i.e., ${log}_{2}\mathcal{S}\ensuremath{\sim}\ensuremath{-}aT+b$. It provides us with an intuitive picture about how thermodynamic fluctuations destroy multipartite nonlocality in 1D quantum chains. Moreover, in the $XX$ model $\mathcal{S}$ presents a magnetic-field-induced oscillation at low temperatures. This behavior has a nonlocal nature and cannot be captured by local properties such as the magnetization. Finally, for the Kitaev model, we find that in the limit $T\ensuremath{\rightarrow}0$ and $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the nonlocality measure may be used as an alternative order parameter for the topological-type quantum phase transition in the model.

Three‐Mode Squeezing of Simultaneous and Ordinal Cascaded Four‐Wave Mixing Processes in Rubidium Vapor

AbstractMultipartite quantum correlation plays a vital role in potential applications of quantum technologies. In this paper, using energy‐level cascaded four‐wave mixing (EC‐FWM) process, a scheme to produce quantum correlated three‐mode light beams within a single device of hot atomic medium of rubidium is proposed. Two‐ and three‐mode amplitude, phase quadrature squeezing and intensity difference squeezing using energy‐level simultaneous cascaded FWM (ESC‐FWM) method and energy‐level ordinal cascaded FWM (EOC‐FWM) method, respectively, is theoretically reported. Via investigating their covariance matrix properties, the comparison has been made between the two methods, which shows the ESC‐FWM method has a more stable mode structure than EOC‐FWM method. Moreover, versatile gain dependent squeezing via EC‐FWM is studied and analytical expressions are given. These results show a simplified and efficient experimental scheme producing multipartite quantum correlation among multiple spatially separated beams.

Operational characterization of multipartite nonlocal correlations

Nonlocality, one of the most puzzling features of multipartite quantum correlation, has been identified as a useful resource for device-independent quantum information processing. Motivated by the resource theory of quantum entanglement recently an operational framework have been proposed by Gallego et al. [\href{https://doi.org/10.1103/PhysRevLett.109.070401}{Phys. Rev. Lett. 109, 070401 (2012)}] and Bancal et al. [\href{https://doi.org/10.1103/PhysRevA.88.014102}{Phys. Rev. A 88, 014102 (2013)}] that characterizes the nonlocal resource present in multipartite quantum correlations. While the bipartite no-signaling correlations allows a dichotomous classification -- local vs. nonlocal, in multipartite scenario the authors have shown existence of several types of nonlocality that are inequivalent under the proposed operational framework. In this work we present a finer characterization of multipartite no-signaling correlations based on the same operational framework. We also clarify a statement in Gallego et al.'s work that could be misinterpreted and make the conclusions of that work more precise here.