When Is a Genuine Multipartite Entanglement Measure Monogamous?

A crucial issue in quantum communication tasks is characterizing how quantum resources can be quantified and distributed over many parties. Consequently, entanglement has been explored extensively. However, there are few genuine multipartite entanglement measures and whether it is monogamous is so far unknown. In this work, we explore the complete monogamy of genuine multipartite entanglement measure (GMEM) for which, at first, we investigate a framework for unified/complete GMEM according to the unified/complete multipartite entanglement measure we proposed in 2020. We find a way of inducing unified/complete GMEM from any given unified/complete multipartite entanglement measure. It is shown that any unified GMEM is completely monogamous, and any complete GMEM that is induced by given complete multipartite entanglement measure is completely monogamous. In addition, the previous GMEMs are checked under this framework. It turns out that the genuinely multipartite concurrence is not as good of a candidate as GMEM.     

Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model

Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89 (2002) 060401] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Since this model can be simulated with nuclear magnetic resonance, our results provide a fresh approach to experimental test of GME.     

多粒子纠缠的保护方案

量子纠缠是量子信息的重要物理资源. 然而当量子系统与环境相互作用时, 会不可避免地产生消相干导致纠缠下降, 因此保护纠缠不受环境的影响具有重要意义. 振幅衰减是一种典型的衰减机制. 如果探测环境保证没有激发从系统中流出, 即视为对系统的一种弱测量. 本文基于局域脉冲序列和弱测量, 提出了一种可以保护多粒子纠缠不受振幅衰减影响的有效物理方案, 保护的对象是在量子通信和量子计算中发挥重要作用的Cluster态和Maximal slice态.     

Entangled three-qubit states without concurrence and three-tangle

We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this "monogamy" can be lifted for mixed states by virtue of vanishing tangle measures.     

Unextendible Product Bases,Uncompletable Product Bases and Bound Entanglement

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.     

Local indistinguishability: more nonlocality with less entanglement

We provide a first operational method for checking local indistinguishability of orthogonal states. It originates from that in Ghosh et al. [Phys. Rev. Lett. 87, 5807 (2001)]], though we deal with pure states. Our method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product. Also, it leads to local indistinguishability of a set of orthogonal pure states of 3 multiply sign in circle 3, which shows that one can have more nonlocality with less entanglement, where "more nonlocality" is in the sense of "increased local indistinguishability of orthogonal states." This is, to our knowledge, the only known example where d orthogonal states in d multiply sign in circle d are locally indistinguishable.     

Revised Geometric Measure of Entanglement for Multipartite and Continuous Variable Systems

Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.     

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Schmidt Number Entanglement Measure for Multipartite k-nonseparable States

In this paper, an entanglement measure for multipartite quantum states with respect to k-partition was introduced, which is called Schmidt number entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-ME SN. We show that this measure is well-defined, i.e., it satisfies some basic properties as an entanglement measure. In addition, we give a super bound and lower bound of k-ME SN for multipartite pure states according to the definition of joint k-Schmidt number with respect to k-partition. Furthermore, we give some examples to show that Schmidt number entanglement measure can quantify the strength of entanglement for multipartite quantum states.

     

Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement.     

Measures of genuine multipartite entanglement for graph states

Graph states are special multipartite entangled states that have been proven useful in a variety of quantum information tasks. We address the issue of characterizing and quantifying the genuine multipartite entanglement of graph states up to eight qubits. The entanglement measures used are the geometric measure, the relative entropy of entanglement, and the logarithmic robustness, have been proved to be equal for the genuine entanglement of a graph state. We provide upper and lower bounds as well as an iterative algorithm to determine the genuine multipartite entanglement.     

Entanglement detection in the vicinity of arbitrary Dicke states

Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.     

Preparation of entangled squeezed states and quantification of their entanglement

We propose a scheme for generating bipartite and multipartite entangled squeezed states via the Jaynes－Cummings model with large detuning. Bipartite entanglement of these entangled states is quantified by the concurrence. We also use the N-tangle to compute multipartite entanglement of these multipartite entangled squeezed states. Finally we discuss two limiting cases which arise from r→∞ and r→0, in which the multipartite entangled squeezed state reduces correspondingly into an N-qubit Greenberger－Horne－Zeilinger state and an N-qubit W state.     

Experimental detection of multipartite entanglement using witness operators

We present the experimental detection of genuine multipartite entanglement using entanglement witness operators. To this aim, we introduce a canonical way of constructing and decomposing witness operators so that they can be directly implemented with present technology. We apply this method to three- and four-qubit entangled states of polarized photons, giving experimental evidence that the considered states contain true multipartite entanglement.     

Detection of the quantum states containing at most k-1 unentangled particles

There are many different classifications of entanglement for multipartite quantum systems, one of which is based on the number of the unentangled particles. In this paper, we mainly study the quantum states containing at most k-1 unentangled particles and provide several entanglement criteria based on the different forms of inequalities, which can both identify quantum states containing at most k-1 unentangled particles. We show that these criteria are more effective for some states by concrete examples.     

A New Multipartite Entanglement Measure for Arbitrary <Emphasis Type="Italic">n</Emphasis>-qudit Pure States

In this paper, we propose a multipartite entanglement measure for arbitrary pure states, which is presented based on reduced density matrices of multi-qudit pure states. We review some multipartite entanglement measures based on density matrices. This is helpful for us to introduce a new good entanglement measure, which is vanishing if and only if a state is separable, invariant under local unitary transformations and non-increasing under local operations assisted by classical communication. We apply our entanglement measure for some explicit examples. It demonstrates that our entanglement measure is practical and convenient for computation. It can also distinguish the relatively high entanglement and the maximal entanglement. In short, our entanglement measure is good at characterizing multipartite entanglement.     

A Reversible Theory of Entanglement and its Relation to the Second Law

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein’s Lemma, giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.     

Tractable Quantification of Entanglement for Multipartite Pure States

We present kth-order entanglement measure and global kth-order entanglement measure for multipartite pure states, and extend Bennett＇s measure of partial entropy for bipartite pure states to a multipaxtite case. These measures are computable and can effectively classify and quantify the entanglement of multipartite pure states.     

Verifying genuine high-order entanglement

High-order entanglement embedded in multipartite multilevel quantum systems (qudits) with many degrees of freedom (DOFs) plays an important role in quantum foundation and quantum engineering. Verifying high-order entanglement without the restriction of system complexity is a critical need in any experiments on general entanglement. Here, we introduce a scheme to efficiently detect genuine high-order entanglement, such as states close to genuine qudit Bell, Greenberger-Horne-Zeilinger, and cluster states as well as multilevel multi-DOF hyperentanglement. All of them can be identified with two local measurement settings per DOF regardless of the qudit or DOF number. The proposed verifications together with further utilities such as fidelity estimation could pave the way for experiments by reducing dramatically the measurement overhead.