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Quantum entanglement plays a pivotal role in quantum information processing. Quantifying quantum entanglement is a challenging and essential research area within the field. This manuscript explores the relationships between bipartite entanglement concurrence, multipartite entanglement concurrence, and genuine multipartite entanglement (GME) concurrence. We derive lower bounds on GME concurrence from these relationships, demonstrating their superiority over existing results through rigorous proofs and numerical examples. Additionally, we investigate the connections between GME concurrence and other entanglement measures, such as tangle and global negativity, in multipartite quantum systems. [ABSTRACT FROM AUTHOR]

We present proper genuine multipartite entanglement (GME) measures for arbitrary multipartite and dimensional systems. By using the volume of concurrence regular polygonal pyramid, we first derive the GME measure of four-partite quantum systems. From our measure, it is verified that the GHZ state is more entangled than the W state. Then, we study the GME measure for multipartite quantum states in arbitrary dimensions. A well-defined GME measure is constructed based on the volume of the concurrence regular polygonal pyramid. Detailed example shows that our measure can characterize better the genuine multipartite entanglements. [ABSTRACT FROM AUTHOR]

Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the "genuine" requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems. [ABSTRACT FROM AUTHOR]

Xie and Eberly introduced a genuine multipartite entanglement (GME) measure ‘concurrence fill’ (Xie and Eberly, 2021) for three-party systems. It is defined as the area of a triangle whose side lengths represent squared concurrence in each bi-partition. However, it has been recently shown that concurrence fill is not monotonic under LOCC, hence not a faithful measure of entanglement. Though it is not a faithful entanglement measure, it encapsulates an elegant geometric interpretation of bipartite squared concurrences. There have been a few attempts to generalize GME quantifier to four-party settings and beyond. However, some of them are not faithful, and others simply lack an elegant geometric interpretation. The recent proposal from Xie et al.. constructs a concurrence tetrahedron, whose volume gives the amount of GME for four-party systems; with generalization to more than four parties being the hypervolume of the simplex structure in that dimension. Here, we show by construction that to capture all aspects of multipartite entanglement, one does not need a more complex structure, and the four-party entanglement can be demonstrated using 2D geometry only. The subadditivity together with the Araki-Lieb inequality of linear entropy is used to construct a direct extension of the geometric GME quantifier to four-party systems resulting in quadrilateral geometry. Our quantifier can be geometrically interpreted as a combination of three quadrilaterals whose sides result from the concurrence in one-to-three bi-partition, and diagonal as concurrence in two-to-two bipartition.

A genuine multipartite entanglement measure based on the geometric method is investigated in this paper. This measure has desirable properties for quantifying the genuine multipartite entanglement. A lower bound of the genuine multipartite entanglement measure derived with the fidelity‐based method is then presented. The advantages of the measure proposed here with other measures are also presented. At last, examples are presented to show that the genuine entanglement measure has distinct entanglement ordering from other measures. [ABSTRACT FROM AUTHOR]

Entanglement represents “the” key resource for several applications of quantum information processing, ranging from quantum communications to distributed quantum computing. Despite its fundamental importance, deterministic generation of maximally entangled qubits represents an on- going open problem. Here, we design a novel generation scheme exhibiting two attractive features, namely, i) deterministically generating different classes - particularly, GHZ-like, W-like and graph states - of genuinely multipartite entangled states, ii) not requiring any direct interaction between the qubits. Indeed, the only necessary condition is the possibility of coherently controlling - according to the indefinite causal order framework - the causal order among the unitaries acting on the qubits. Through the paper, we analyze and derive the conditions on the unitaries for deterministic generation, and we provide examples for unitaries practical implementation. We conclude the paper by discussing the scalability of the proposed scheme to higher dimensional genuine multipartite entanglement (GME) states and by introducing some possible applications of the proposal for quantum networks.

We study detection of genuine multipartite entanglement based on one-particle loss operator. We obtain a criterion on detecting genuine pure tripartite entanglement. The results are then generalized to arbitrary pure multipartite states. For mixed states by using the correlation tensors of the Bloch representation of density matrices, we obtain an effective criterion of arbitrary dimensional genuine tripartite entanglement. Detailed examples are given to show that our criterion is able to detect more genuine tripartite entanglement states than some existing criteria. [ABSTRACT FROM AUTHOR]

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We characterize the metrological usefulness by determining how much the state outperforms separable states. We identify a large class of entangled states that become maximally useful for metrology in the limit of large number of copies, even if the state is weakly entangled and not even more useful than separable states. This way we activate metrologically useful genuine multipartite entanglement. Remarkably, not only that the maximally achievable metrological usefulness is attained exponentially fast in the number of copies, but it can be achieved by the measurement of few simple correlation observables. We also make general statements about the usefulness of a single copy of pure entangled states. We surprisingly find that the multiqubit states presented in Hyllus et al (2010 Phys. Rev. A 82 012337), which are not useful, become useful if we embed the qubits locally in qutrits. We discuss the relation of our scheme to error correction, and its possible use for quantum metrology in a noisy environment.

It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in Curchod et al (2019 New J. Phys. 21 023016) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deliver finer Bell inequalities for detection of GMNL. Remarkably, we then prove one of the improved Bell inequalities to be powerful enough to detect GMNL in every three-qubit genuinely entangled state. We also generalize some of these inequalities to detect not only GMNL but also nonlocality depth in multipartite states and we present a possible way of generalizing them to the case of more outcomes.

We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use the trace norm of the whole correlation tensor as a measurement to detect genuine multipartite entanglement. By detailed examples, we show our result can detect more genuinely entangled states. Furthermore, we generalize the genuine multipartite entanglement criterion to tripartite higher-dimensional systems. [ABSTRACT FROM AUTHOR]

Entanglement of high-dimensional multipartite systems plays an important role both in quantum foundation and applications of quantum physics. Inspired by the genuine high-dimensional entanglement (Kraft et al. in Phys Rev Lett 120:060502, 2018), we first propose a new criterion to characterize genuine entangled states in arbitrary finite dimensional systems. We further define two decomposable models by using embedding method for featuring experimentally untrusted parties. We show that the equivalence of local decomposability and embedded decomposability holds under special conditions for entangled pure states. For mixed states, we show the decomposability may be changed in embedded space. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

Anonymous entanglement refers to the construction of entangled channel between two parties among the quantum network, while keeping the identities of these two parties unknown to other parties. A recent work of [A. Unnikrishnan et al., Phys. Rev. Lett. 122, 240501 (2019)] proposed the first anonymous entanglement protocol in the presence of malicious parties and untrusted source. However, the correctness of the original protocol will be threatened, considering that the generated entangled channel can be destroyed by malicious parties without being detected. In this paper, we propose an improved protocol, which ensures the anonymity of the parties and the correctness of shared entanglement channel simultaneously. Furthermore, we consider the noisy measurement in the security analysis, which makes our protocol practical and rigorous. Based on the security analysis, genuine multipartite entanglement could be certified in the untrusted quantum network with our protocol. [ABSTRACT FROM AUTHOR]

Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavor. We prove that nonvanishing quantum correlations, both bipartite and genuine multipartite entanglement, are required for solving nontrivial linear systems of equations in the Harrow-Hassidim-Lloyd (HHL) algorithm. Moreover, we find a nonvanishing l 1 -norm quantum coherence of the entire system and the register qubit which turns out to be related to the success probability of the algorithm. Quantitative analysis of the quantum resources reveals that while a significant amount of bipartite entanglement is generated in each step and required for this algorithm, multipartite entanglement content is inversely proportional to the performance indicator. In addition, we report that when imperfections chosen from Gaussian distribution are incorporated in controlled rotations, multipartite entanglement increases with the strength of the disorder, albeit error also increases while bipartite entanglement and coherence decreases, confirming the beneficial role of bipartite entanglement and coherence in this algorithm. • Role of quantum resources required for successfully executing the Harrow–Hassidim–Lloyd (HHL) algorithm. • Successful implementation of HHL algorithm requires non-vanishing genuine multipartite entanglement. • Quantum coherence is directly related to the success probability of the HHL algorithm. [ABSTRACT FROM AUTHOR]

A multipartite state that is not the convex sum of bipartite product states is said to be a genuine multipartite entangled (GME) state, which offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy n-partite W state when n = 3 , 4 , 5 and 6 and find that the criterion can detect more noisy W states when n ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of 3-qutrit states. The result is stronger than that based on GME concurrence and Fisher information. [ABSTRACT FROM AUTHOR]

Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example. [ABSTRACT FROM AUTHOR]

We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical and sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary multipartite systems. [ABSTRACT FROM AUTHOR]

In this paper, the genuine multipartite entanglement (GME) and quantum criticality property of spin systems with staggered Dzyaloshinskii-Moriya (DM) interaction are investigated by exploiting quantum renormalization group method. The results show that the GME can indicate quantum phase transitions at critical points after several iterations of the renormalization. Moreover, the DM interaction effectively restores the spoiled GME via creation of quantum fluctuations, while it also changes the critical points. At last, the nonanalytic and scaling behaviors of GME are analyzed in detail. [ABSTRACT FROM AUTHOR]

We present an analytical lower bound of multipartite concurrence based on the generalized Bloch representations of density matrices. It is shown that the lower bound can be used as an effective entanglement witness of genuine multipartite entanglement. Tight lower and upper bounds for multipartite tangles are also derived. Since the lower bounds depend on just part of the correlation tensors, the result is experimentally feasible. [ABSTRACT FROM AUTHOR]

We propose a scheme to control the dynamics of genuine multipartite entanglement and purity of qubits within spatially separated thermal baths using the bang-bang pulses with finite period. The qubits are initially entangled and have no direct interactions. The genuine multipartite entanglement of the system is measured by an entanglement monotone based on a generalization of the Peres-Horodecki criterion to multipartite systems. We first derive a master equation to describe the non-Markovian dynamics of an arbitrary number of qubits within their baths with decoherence and dynamical decoupling. Then, we calculate the entanglement monotone and purity of three qubits in super-Ohmic, sub-Ohmic, and Ohmic baths numerically. The effects of the period of pulses on the non-Markovian dynamics of qubits are discussed. We show the genuine multipartite entanglement and purity can be simultaneously improved by applying the bang-bang pulses with finite period. In particular, the bang-bang pulses with finite period are more efficient when the qubits are put into the sub-Ohmic or Ohmic baths than the case of the super-Ohmic bath. [ABSTRACT FROM AUTHOR]

Quantum entanglement is an essential resource for quantum information processing, either for quantum communication or for quantum computation. The multipartite case of entanglement, especially the so called genuine multipartite entanglement, has significant importance for multipartite quantum information protocols. Thus, it is a natural requirement to experimentally verify multipartite quantum entanglement when performing many quantum information tasks. However, this is often technically challenging due to the difficulty of building a shared reference frame among all involved parties, especially when these parties are distant from each other. In this paper, we experimentally verify the genuine tripartite entanglement of a three-photon Greenberger-Horne-Zeilinger state without shared reference frames. A high probability 0.79 of successfully verifying the genuine tripartite entanglement is achieved when no reference frame is shared. In the case of sharing only one common axis, an even higher success probability of 0.91 is achieved. [ABSTRACT FROM AUTHOR]

In this paper, we present the separability criteria to identify non- k-separability and genuine multipartite entanglement in mixed multipartite states using elements of density matrices. Our criteria can detect the non- k-separability of Dicke class of states, anti W states and mixtures thereof and higher dimensional W class of states. We then investigate the performance of our criteria by considering N-qubit Dicke states with arbitrary excitations added with white noise and mixture of N-qudit W state with white noise. We also study the robustness of our criteria against white noise. Further, we demonstrate that our criteria are experimentally implementable by means of local observables such as Pauli matrices and generalized Gell-Mann matrices. [ABSTRACT FROM AUTHOR]

• GE subspaces from bipartite ones by reducing the number of separated parties. • Easy control of the characteristics of the obtained subspaces. • Applications in detecting genuine entanglement of mixed states. • Construction of distillable multipartite subspaces. 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. [ABSTRACT FROM AUTHOR]

Long-term preservation of quantum coherence and entanglement is indispensable for practical quantum computation. We study the evolution of quantum coherence and genuine multipartite concurrence of extended Werner like states transmitted through correlated amplitude damping (AD), phase damping (PD) and depolarizing (DP) channels. The results show that the decay rate of coherence is curtailed in the presence of correlation between successive actions of the channel. It is shown that the fragility of genuine multipartite entanglement due to decoherence can be protected to some significant amount by using the correlated channels. In fact, for even qubit Werner like states, coherence and entanglement exhibit freezing phenomenon, in which it remains intact against decohering environment in perfectly correlated phase damping and depolarizing channels. For multipartite GHZ-class states in a perfectly correlated channel, it is shown that entanglement sudden death (ESD) is circumvented in amplitude damping channel, and there is an entanglement sudden birth (ESB) for odd qubit systems in depolarizing channel. Further, we have established analytical relation between coherence and entanglement for completely uncorrelated and fully correlated quantum channels. [ABSTRACT FROM AUTHOR]

Abstract: How can one prove that a given quantum state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented. [Copyright &y& Elsevier]

We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy. While for a finite number of systems there is a maximal temperature allowing for the creation of entanglement, we show that genuine multipartite entanglement—the strongest form of entanglement in multipartite systems—can be created at any finite temperature when sufficiently many systems are considered. This approach may find applications, e.g. in quantum information processing, for physical platforms in which thermodynamic considerations cannot be ignored.

• The criterion of M -separable W state is given based on QFI. • The criteria of visibility for genuine N -qubit W state, GHZ state and Twin-Fock state in the white noise model are presented. • An extremum v W N = 1 / 3 is found in the limit of large N for observing partial entanglement. We study the entanglement detection of three classes of state in the white noise model: N -qubit W state, Greenberger-Horne-Zeilinger state and Twin-Fock state. Taking advantage of Quantum Fisher information, we first present how to witness M -separable W state (M ≤ N) in the ideal situation, and then derive the criteria for detecting genuine W state, Greenberger-Horne-Zeilinger state and Twin-Fock state in the noisy model. Meanwhile, the bounds for M -separable W state, k -partite entangled GHZ state and k -partite entangled Twin-Fock state are also investigated. The results show that with the increase of the number of particles, the requirement of visibility V for genuine multipartite entanglement becomes more and more stringent, while it is relaxed for partial entanglement. Specially, an extremum value of V W N = 1 / 3 is found in the limit of large N. [ABSTRACT FROM AUTHOR]