Search

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]

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]

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 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]

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]

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]

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]