Realignment criteria for recognizing multipartite entanglement of quantum states

By multiple realignments of density matrices, we present a new separability criterion for the multipartite quantum state, which includes the computable cross-norm or realignment criterion and the multipartite partial realignment criterion as special cases. An example is used to show that the new criterion can be more efficient than the corresponding multipartite realignment criteria given in Horodecki et al. (Open Syst Inf Dyn 13:103–111, 2006) and Shen et al. (Phys Rev A 92:042332, 2015).     

Examining the dimensionality of genuine multipartite entanglement

Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite states by the number of degrees of freedom being entangled. In this regard, we derive computable and experimentally friendly criteria for arbitrary multipartite qudit systems that enable to examine in how many degrees of freedom a mixed state is genuine multipartite entangled.     

Quantifying entanglement of two relativistic particles using optimal entanglement witness

In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin- \frac12{\frac{1}{2}} particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p ₁ and p ₂) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied.     

A new method for quantifying entanglement of multipartite entangled states

We propose a new way for quantifying entanglement of multipartite entangled states which have a symmetrical structure and can be expressed as valence-bond-solid states. We put forward a new concept ‘unit.’ The entangled state can be decomposed into a series of units or be reconstructed by multiplying the units successively, which simplifies the analyses of multipartite entanglement greatly. We compute and add up the generalized concurrence of each unit to quantify the entanglement of the whole state. We verify that the new method coincides with concurrence for two-partite pure states. We prove that the new method is a good entanglement measure obeying the three necessary conditions for all good entanglement quantification methods. Based on the method, we compute the entanglement of multipartite GHZ, cluster and AKLT states.     

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW??s are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance.     

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, we search for highly entangled qubit states to show the applicability of this method.     

High-efficiency multipartite entanglement purification of electron-spin states with charge detection

We present a high-efficiency multipartite entanglement purification protocol (MEPP) for electron-spin systems in a Greenberger–Horne–Zeilinger state based on their spins and their charges. Our MEPP contains two parts. The first part is our normal MEPP with which the parties can obtain a high-fidelity N-electron ensemble directly, similar to the MEPP with controlled-not gates. The second one is our recycling MEPP with entanglement link from N′-electron subsystems (2 < N′ < N). It is interesting to show that the N′-electron subsystems can be obtained efficiently by measuring the electrons with potential bit-flip errors from the instances which are useless and are just discarded in all existing conventional MEPPs. Combining these two parts, our MEPP has the advantage of the efficiency higher than other MEPPs largely for electron-spin systems.     

Emergence of multipartite optomechanical entanglement in microdisk cavities coupled to nanostring waveguide

In this paper, we propose a scheme to show signatures of multipartite optomechanical entanglement, which is based on two high quality factor (high- $Q$ ) silicon nitride ( $\text{ Si }_{3}\text{ N }_{4}$ ) microdisk cavities coupled to a nanostring waveguide via evanescent field. Genuine tripartite optomechanical entanglement is shared in the subsystem even though the two fields of microdisk cavities do not have direct interaction. In addition, we study the behaviors of the bipartite entanglement between the pairs of the system constituents by numerical simulation.     

Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource

Recently, the method that using an entanglement as a resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has brought into focus. Zhang et al. (Sci Rep 6:30493, 2016) presented protocols which use an entanglement to distinguish some classes of orthogonal product states in \(\mathbb {C}^m\otimes \mathbb {C}^n\). In this paper, we mainly study the local distinguishability of multipartite product states. For the class of locally indistinguishable multipartite product states constructed by Wang et al. (Quantum Inf Process 16:5, 2017), we present a protocol that distinguishes perfectly these quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.     

Genuine multipartite entanglement as the indicator of quantum phase transition in spin systems

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.     

Optimal multipartite entanglement concentration of electron-spin states based on charge detection and projection measurements

We propose an optimal entanglement concentration protocol (ECP) for nonlocal $N$ -electron systems in a partially entangled Greenberger–Horne–Zeilinger (GHZ) pure state, resorting to charge detection and the projection measurement on an additional electron. For each nonlocal $N$ -electron system in a partially entangled GHZ state, one party in quantum communication, say Alice first entangles it with an additional electron, and then, she projects the additional electron into an orthogonal basis for dividing the $N$ -electron systems into two groups. In the first group, the $N$ parties obtain a subset of $N$ -electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled $N$ -electron systems which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, the theoretical limit of an ECP as it just equals to the entanglement of the partially entangled state, far higher than others. Moreover, this ECP for an $N$ -electron GHZ-type state requires only one additional electron, not two or more, and it does not resort to a collective unitary evolution, far different from others, which may decrease the difficulty for its implementation in experiment. When it is used for an $N$ -electron W-type state, $N-1$ additional electrons are required only.     

Entanglement witness criteria of strong-<Emphasis Type="Italic">k</Emphasis>-separability for multipartite quantum states

Let \(H_{1}, H_{2},\ldots ,H_{n}\) be separable complex Hilbert spaces with \(\dim H_{i}\ge 2\) and \(n\ge 2\). Assume that \(\rho \) is a state in \(H=H_1\otimes H_2\otimes \cdots \otimes H_n\). \(\rho \) is called strong-k-separable \((2\le k\le n)\) if \(\rho \) is separable for any k-partite division of H. In this paper, an entanglement witnesses criterion of strong-k-separability is obtained, which says that \(\rho \) is not strong-k-separable if and only if there exist a k-division space \(H_{m_{1}}\otimes \cdots \otimes H_{m_{k}}\) of H, a finite-rank linear elementary operator positive on product states \(\Lambda :\mathcal {B}(H_{m_{2}}\otimes \cdots \otimes H_{m_{k}})\rightarrow \mathcal {B}(H_{m_{1}})\) and a state \(\rho _{0}\in \mathcal {S}(H_{m_{1}}\otimes H_{m_{1}})\), such that \(\mathrm {Tr}(W\rho )<0\), where \(W=(\mathrm{Id}\otimes \Lambda ^{\dagger })\rho _{0}\) is an entanglement witness. In addition, several different methods of constructing entanglement witnesses for multipartite states are also given.     

Matched filters for bin picking

Currently, a major difficulty for the widespread use of robots in assembly and material handling comes from the necessity of feeding accurately positioned workpieces to robots. ``Bin picking' techniques help reduce this constraint. This paper presents the application of matched filters for enabling robots with vision to acquire workpieces randomly stored in bins. This approach complements heuristic methods already reported. The concept of matched filter is an old one. Here, however, it is redefined to take into account robot end-effector features, in terms of geometry and mechanics. In particular, the proposed filters match local workpiece structures where the robot end-effector is likely to grasp successfully and hold workpieces. The local nature of the holdsites is very important as computation costs are shown to vary with the fifth power of structure size. In addition, the proposed filters tend to have a narrow angular bandwidth. An example, which features a parallel-jaw hand is developed in detail, using both statistical and Fourier models. Both approaches concur in requiring a very small number of filters (typically four), even if a good orientation accuracy is expected (two degrees). Success rates of about 90 percent in three or fewer attempts have been experimentally obtained on a system which includes a small minicomputer, a 128 × 128 pixel solidstate camera, a prototype Cartesian robot, and a ``universal' parallel-jaw hand.     

Equation of motion for entanglement

We review an evolution equation for quantum entanglement for 2 × 2 dimensional quantum systems, the smallest system that can exhibit entanglement, and extend it to higher dimensional systems. Furthermore, we provide statistical evidence for the equation’s applicability to the experimentally relevant domain of weakly mixed states.     

A lower bound of concurrence for multipartite quantum systems

We present a lower bound of concurrence for four-partite systems in terms of the concurrence for \(M\, (2\le M\le 3)\) part quantum systems and give an analytical lower bound for \(2\otimes 2\otimes 2\otimes 2\) mixed quantum sates. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. Furthermore, our approach can be generalized to multipartite quantum systems.     

Protecting single-photon entanglement with practical entanglement source

Single-photon entanglement (SPE) is important for quantum communication and quantum information processing. However, SPE is sensitive to photon loss. In this paper, we discuss a linear optical amplification protocol for protecting SPE. Different from the previous protocols, we exploit the practical spontaneous parametric down-conversion (SPDC) source to realize the amplification, for the ideal entanglement source is unavailable in current quantum technology. Moreover, we prove that the amplification using the entanglement generated from SPDC source as auxiliary is better than the amplification assisted with single photons. The reason is that the vacuum state from SPDC source will not affect the amplification, so that it can be eliminated automatically. This protocol may be useful in future long-distance quantum communications.     

Bounds on multipartite concurrence and tangle

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.     

Local cloning of multipartite entangled states

No cloning theorem is a very fundamental issue in quantum mechanics. But the issue is much more involved if we consider quantum state shared among two or more than two parties and allow only local operation and classical communication. In the context of the fact that no known bipartite entangled state can be cloned by local operation and classical communication (LOCC) without assistance of extra entangled state, the cloning of unknown orthogonal entangled state becomes meaningful when there is some supply of free entanglement. With restriction on supply of free entanglement, various cases have been studied. In this paper, we try to give an overview of the subject and results that have been obtained across the literature along with a new result on probabilistic LOCC cloning of four Bell states.