Tripartite States Research Articles

Generation of tripartite squeezed state by cascaded four-wave mixing in single hot rubidium atomic system

We report the quantum correlated triple beams via cascaded four-wave mixing (CFWM) amplified in single hot atomic vapor. Experimentally, we show that strong quantum correlation of three light beams, among them any two’s quantum correlation is characterized by the maximum value of intensity-difference squeezing (IDS) about −7.8 ± 0.3 dB. We found there is IDS between two idler beams, because two pairs of Einstein–Podolsky–Rosen injections potentially exist in our system. Besides, CFWM can emit three-mode beams at three different frequencies, in which these beams can be well separated in the spatial domain. Moreover, much difference with other methods, the injecting probe field can manipulate the gain and IDS of output three-mode light beams, which is resulting from competition relationship between cascaded two four-wave mixing processes. More interestingly, Autler–Townes splitting of gain peaks of output signals due to dressing effect of pumping fields, will lead to the evolution of measured two- and three-mode IDS from single-mode to multi-mode at frequency domain. This result will provide a multimode quantum resource which can potentially realize multimode entanglement and quantum networks.

Recoupling Corporate Culture with New Political Discourse in China’s Platform Economy: The Case of Alibaba

Previous research on the corporate culture construction in China primarily highlights how Chinese firms draw on its traditional culture and socialist heritages as two crucial intellectual resources. The highly marketised high-tech sector with declining employment security and changing political environment renders a new context and dual process for the ‘engineering’ of corporate culture in China’s platform economy. An ethnographic study of Alibaba unveils the resources the management draws on to construct its culture, including not only the founder’s entrepreneurial stories but also the economic and social changes allegedly brought by Alibaba’s platforms and technologies. This article theorises a new tripartite state–employer–employee relationship manifested through corporate culture by showcasing how the discourses of market meritocracy in China’s reform era and national renaissance based on technological progressivism have both fuelled the corporate culture construction, delineating its simultaneous yet paradoxical decoupling from and recoupling with the national political discourse in China’s high-tech industries.

On ergotropic gap of tripartite separable systems

Extracting work from quantum system is one of the important areas in quantum thermodynamics. As a significant thermodynamic quantity, the ergotropy gap characterizes the difference between the global and local maximum extractable works. We derive an analytical upper bound of the ergotropic gap with respect to [Formula: see text] tripartite separable states. This bound also provides a necessary criterion for the separability of tripartite states. Detailed examples are presented to illustrate the efficiency of this separability criterion.

Probing Genuine Multipartite Einstein–Podolsky–Rosen Steering and Entanglement Under an Open Tripartite System

Einstein–Podolsky–Rosen steering is a peculiar quantum nonlocal correlation and has unique physical characteristics and a wide application prospect. Even more importantly, multipartite steerable states have more vital applications in the future quantum information field. Thus, in this work, we explored the dynamics characteristics of both genuine multipartite steering (GMS) and genuine multipartite entanglement (GME) and the relations of both under an open tripartite system. Specifically, the tripartite decoherence system may be modeled by the three parties of a tripartite state that undergo the noisy channels. The conditions for genuine entangled and steerable states can be acquired for the initial tripartite state. The results showed that decoherence noises can degrade the genuine multipartite entanglement and genuine multipartite steering and even induce its death. Explicitly, GME and GMS disappear with the increase in the decoherence strength under the phase damping channel. However, GME and GMS rapidly decay to death with the increase in the channel-noise factor and then come back to life soon after in the bit flip channel. Additionally, the results indicate that GMS is born of GME, but GME does not imply GMS, which means that the set of genuine multipartite steerable states is a strict subset of the set of genuine multipartite entangled states. These conclusions may be useful for discussing the relationship of quantum nonlocal correlations (GME and GMS) in the decoherence systems.

Two-dimensional quantum motion of a levitated nanosphere

We report on the two-dimensional (2D) dynamics of a levitated nanoparticle in an optical cavity. The motion of the nanosphere is strongly coupled to the cavity field by coherent scattering and heavily cooled in the plane orthogonal to the tweezer axis. Due to the characteristics of the 2D motion and the strong optomechanical coupling, the motional sideband asymmetry that reveals the quantum nature of the dynamics is not limited to mere scale factors between Stokes and anti-Stokes peaks, as customary in quantum optomechanics, but assumes a peculiar spectral dependence. We introduce and discuss an effective thermal occupancy that quantifies how close the system is to a minimum uncertainty state and allows us to consistently characterize the particle motion. By rotating the polarization angle of the tweezer beam we tune the system from a 1D cooling regime, where we achieve a best thermal occupancy of $0.51\ifmmode\pm\else\textpm\fi{}0.05$, to a regime in which the fully 2D dynamics of the particle exhibit strong nonclassical properties. We achieve a strong 2D confinement with thermal occupancy of $3.4\ifmmode\pm\else\textpm\fi{}0.4$ along the warmest direction and around one in the orthogonal one. These results represent a major improvement over previous experiments considering both the 1D and the 2D motion and pave the way toward the preparation of tripartite optomechanical entangled states and novel applications to directional force and displacement quantum sensing.

Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties

Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of bipartite entangled subspaces under joining of their adjacent subsystems. In addition, it is shown that direct sums of such constructions under certain conditions are genuinely entangled. These facts are then used in detecting entanglement of tensor products of mixed states and constructing subspaces that are distillable across every bipartite cut, where for the former application we include an example with the analysis of genuine entanglement of a tripartite state obtained from two Werner states.

Detection of Multipartite Entanglement Based on Heisenberg-Weyl Representation of Density Matrices

We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria.

Local Unitary Equivalence of Generic Multi-qubits Based on the CP Decomposition

The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral decomposition of matrices to higher-order tensors. In this paper we use the CP decomposition to study unitary equivalence of higher order tensors and construct several invariants of local unitary equivalence for general higher order tensors. Based on this new method, we study the coefficient tensors of $3$-qubit states and obtain a necessary and sufficient criterion for local unitary equivalence of general tripartite states in terms of the CP decomposition. We also generalize this method to obtain some invariants of local unitary equivalence for general multi-partite qudits.

Demonstration of entanglement and coherence in GHZ-like state when exposed to classical environments with power-law noise

We investigate the dynamics and protection of entanglement and coherence in three non-interacting qubits that are initially prepared as mixed entangled GHZ-like state when coupled with external classical fields. A type of Gaussian noise, namely power-law (PL) noise, controls the external local fields in three different configurations with single, double, and triple noise sources. When influenced by a single PL noise source, the GHZ-class state remains partially entangled and coherent indefinitely, in contrast to the multiple PL noise sources. However, long-term non-local correlations and coherence are still possible in the presence of multiple noise sources. In classical fluctuating environments, the PL noise restricts the entanglement sudden death and birth phenomenon, thereby preventing the conversion of free states to resource states. In addition to the noise phase, parameter optimization in local fields regulates disorders, noise effects, and memory properties. Unlike the bipartite and tripartite W-type states, the GHZ-like state has shown positive traits of preserving entanglement and coherence in the presence of PL noise.

There exist infinitely many kinds of partial separability/entanglement

In tri-partite systems, there are three basic biseparability, A-BC, B-CA, and C-AB, according to bipartitions of local systems. We begin with three convex sets consisting of these basic biseparable states in the three-qubit system, and consider arbitrary iterations of intersections and/or convex hulls of them to get convex cones. One natural way to classify tri-partite states is to consider those convex sets to which they belong or do not belong. This is especially useful to classify partial entanglement of mixed states. We show that the lattice generated by those three basic convex sets with respect to convex hull and intersection has infinitely many mutually distinct members to see that there are infinitely many kinds of three-qubit partial entanglement. To do this, we consider an increasing chain of convex sets in the lattice and exhibit three-qubit Greenberger–Horne–Zeilinger diagonal states distinguishing those convex sets in the chain.

Quantum discords of tripartite quantum systems

The quantum discord of bipartite systems is one of the best-known measures of non-classical correlations and an important quantum resource. In the recent work appeared in [Phys. Rev. Lett 2020, 124:110401], the quantum discord has been generalized to multipartite systems. In this paper, we give analytic solutions of the quantum discord for tripartite states with fourteen parameters.

Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polygamy inequalities of the $\beta$th ($\beta\geq \max\{1, s\}, 0\leq s\leq s_0, 0\leq s_0\leq\sqrt{2}$) power of the entanglement of formation for $2\otimes2\otimes2$ and $n$-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies.

A New Parameterized Monogamy Relation between Entanglement and Equality

AbstractA generalized definition of the monogamy relation for entanglement measures is provided. A monogamy equality rather than the usual inequality is presented based on the monogamy weight, from which monogamy relations are given satisfied by the αth power of the entanglement measures. Taking concurrence as an example, the significance and advantages of these relations are further demonstrated. In addition, it is shown that monogamy relations can be recovered by considering multiple copies of states for every non‐additive entanglement measure that violates the inequalities. It is also demonstrated that such relations for tripartite states can be generalized to multipartite systems.

The “ER = EPR” Conjecture and Generic Gravitational Properties: A Universal Topological Linking Model of the Correspondence between Tripartite Entanglement and Planck-Scale Wormholes

The “ER = EPR” conjecture, conceived by Maldacena and Susskind, is grounded on the notion that a gravitational theory in the bulk is dual to the corresponding quantum field theory on the boundary in accordance to the AdS/CFT correspondence. The conjecture pertains to the idea that Einstein-Rosen (ER) spacetime bridges and Einstein-Podolsky-Rosen (EPR) quantum entanglement may be considered as dually equivalent. Since ER bridges refer to the connectivity between black holes, the “ER = EPR” conjecture implies that black holes connected by ER bridges are entangled, and conversely, that entangled black holes are connected by ER bridges. However, the instance of the maximally entangled tripartite (GHZ) quantum state points to the necessity of devising a model of non-classical Planck scale ER bridges going beyond the standard description of these bridges in spacetime. Based on the topological structure of the maximally entangled GHZ state, we propose that a universal topological link, called the Borromean rings, furnishes a particular linking structure that is able to unravel the equavalence between entanglement and wormholes, and thus, to address the validity of the “ER = EPR” conjecture beyond the initial context of the AdS/CFT correspondence. As a consequence, we propose the explicit construction of distinguishable extensions of the smooth classical spacetime manifold taking place in the transition to the quantum gravity regime according to a naturally induced physical criterion of gravitational generic properties following from this intrinsic topological qualification of the “ER = EPR” conjecture.

The tripartite quantum-memory-assisted entropic uncertainty relation and upper bound on shareability of quantum discord

Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. By using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different parties of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be generalized and an upper bound for the shareability of quantum discord for multipartite states is derived.

Detection of genuine tripartite entanglement based on Bloch representation of density matrices

We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria.

Tripartite high-dimensional magnon-photon entanglement in phases with broken PT -symmetry of a non-Hermitian hybrid system

Hybrid systems that combine spin ensembles and superconducting circuits provide a promising platform for implementing quantum information processing. We propose a non-Hermitian magnon-circuit-QED hybrid model consisting of two cavities and an yttrium iron garnet (YIG) sphere placed in one of the cavities. Abundant exceptional points (EPs), parity-time ($\mathcal{PT}$)-symmetry phases, and $\mathcal{PT}$-symmetry broken phases are investigated in the parameter space. Tripartite high-dimensional entangled states can be generated steadily among modes of the magnon and photons in $\mathcal{PT}$-symmetry broken phases, corresponding to which the stable quantum coherence exists. Results show that the tripartite high-dimensional entangled state is robust against the dissipation of hybrid system, independent of a certain initial state, and insensitive to the fluctuation of magnon-photon coupling. Further, we propose to simulate the hybrid model with an equivalent $LCR$ circuit. This paper may provide prospects for realizing multipartite high-dimensional entangled states in the magnon-circuit-QED hybrid system.

Entanglement witnesses of four-qubit tripartite separable quantum states* *Supported by the National Natural Science Foundation of China (Grant No: 61871347).

A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.

Review of “Social Capital in Singapore: The Power of Network Diversity”

Vincent Chua and his colleagues, Gillian Koh, Tan Ern Ser, and Drew Shih, exerted collective effort in organizing a monograph entitled Social Capital in Singapore: The Power of Network Diversity published under the Politics in Asia series of the Routledge. Considering the relative dearth of a relevant literature regarding the particular theme, readers who are interested in how social capital has been formed in Singapore, a multiethnic and economically affluent city state, will find the book an essential reading. As the book befittingly devotes the whole first chapter to explicate intricate characteristics of the Singaporean polity, it is impossible to comprehend the process of social capital production at the interpersonal and organizational levels if one is ignorant about the state-society and state-citizens relationship in Singapore. The tripartite state policies that underpin the Singaporean society are public housing, meritocracy, and racial harmony as stipulated in Chapters 1, 3, 4, and 7....

Detection of genuine multipartite entanglement based on principal basis matrix representations

We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.