Sergio Albeverio, Shao-Ming Fei, Tong-qiang Song
The multipartite entangled state $|p,ξ_2,ξ_2,...,ξ_n>$ for the total momentum and relative coordinates of n particles is constructed. The corresponding quantum mechanical operator with respect to the classical transformation $p\to e^{λ_1} p$, $ξ_i\to e^{λ_i} ξ_i$, $i=1,...,n$, in the state $|p,ξ_2,ξ_2,...,ξ_n>$ is investigated.
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Entanglement witnesses based on first and second moments exist in the form of spin-squeezing criteria for the detection of particle entanglement from collective measurements, and in form of modified uncertainty relations for the detection of mode entanglement or steering. By revealing a correspondence between them, we show that metrologically useful spin squeezing reveals multimode entanglement in symmetric spin states that are distributed into addressable modes. We further derive tight state-independent multipartite entanglement bounds on the spin-squeezing coefficient and point out their con…
In this paper, we study entanglement distillation of multipartite continuous-variable Gaussian entangled states. Following Opatrný \emph{et al.}'s photon subtraction (PS) scheme, the probability of successful distillation decreases exponentially with the number of parties $N$. However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with $N$. Our protocol employs several local squeezers, but it requires only a single PS operation. Using the logarithmic negativity as a measure of entanglement, we find that both the success probability an…
Continuous-variable (CV) multipartite unlockable bound-entangled states is investigated in this paper. Comparing with the qubit multipartite unlockable bound-entangled states, CV multipartite unlockable bound-entangled states present the new and different properties. CV multipartite unlockable bound-entangled states may serve as a useful quantum resource for new multiparty communication schemes. The experimental protocol for generating CV unlockable bound-entangled states is proposed with a setup that is at present accessible.
Genuine multipartite entanglement is of great importance in quantum information, especially from the experimental point of view. Nevertheless, it is difficult to construct genuine multipartite entangled states systematically, because the genuine multipartite entanglement is unruly. We propose another product based on the Kronecker product in this paper. The Kronecker product is a common product in quantum information with good physical interpretation. We mainly investigate whether the proposed product of two genuine multipartite entangled states is still a genuine entangled one. We understand …
Via the Weyl correspondence approach, we construct multipartite entangled state which is the common eigenvector of their center-of-mass coordinate and mass-weighted relative momenta. This approach is concise and effective for setting up the Fock representation of continuous multipartite entangled states. The technique of integration within an ordered product (IWOP) of operators is also essential in our derivation.
We propose a scheme for generating multipartite entangled coherent states via entanglement swapping, with an example of a physical realization in ion traps. Bipartite entanglement of these multipartite states is quantified by the concurrence. We also use the $N$--tangle to compute multipartite entanglement for certain systems. Finally we establish that these results for entanglement can be applied to more general multipartite entangled nonorthogonal states.
We study the relation between distillability of multipartite states and violation of Bell's inequality. We prove that there exist multipartite bound entangled states (i.e. non-separable, non-distillable states) that violate a multipartite Bell inequality. This implies that (i) violation of Bell's inequality is not a sufficient condition for distillability and (ii) some bound entangled states cannot be described by a local hidden variable model.
The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states which admit a fully local hidden variable model, i.e. where all parties are separated. Hence, although these states are entangled in the strongest possible sense, they cannot lead to Bell inequality violation considering general non-sequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing …
We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover,two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased.
Building upon the results of [R. Augusiak et al., Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite Hilbert spaces are applied to local subsystems of bipartite entangled or multipartite genuinely entangled quantum states. To prove that entanglement of the resulting …
We study maximally multipartite entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n<=7.
Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. Here we use methods from quantum metrology to microscopically characterize the entanglement structure of multimode continuous-variable states in all possible multi-partitions and in all reduced distributions. From experimentally measured covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with controllable losses, we extract the metrological sensitivity as well as an …
Fully entangled fraction is a definition for bipartite states, which is tightly related to bipartite maximally entangled states, and has clear experimental and theoretical significance. In this work, we generalize it to multipartite case, we call the generalized version multipartite fully entangled fraction (MFEF). MFEF measures the closeness of a state to GHZ states. The analytical expressions of MFEF are very difficult to obtain except for very special states, however, we show that, the MFEF of any state is determined by a system of finite-order polynomial equations. Therefore, the MFEF can …
We study the conditions for obtaining maximally multipartite entangled states (MMES) as non-degenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMES as eigenstates.
Based upon standard angular momentum theory, we develop a framework to investigate polarization squeezing and multipartite entanglement of a quantum light field. Both mean polarization and variances of the Stokes parameters are obtained analytically, with which we study recent observation of triphoton states [L. K. Shalm {\it et al}, Nature \textbf{457}, 67 (2009)]. Our results show that the appearance of maximally entangled NOON states accompanies with a flip of mean polarization and can be well understood in terms of quantum Fisher information.
We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of mu…
We discuss and investigate the geometrical structure of general multipartite states. In particular, we show that a geometrical measure of entanglement for general multipartite states can be constructed by the complex projective varieties defined by quadratic polynomials.
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement res…
Two- and three-mode squeezing in a three-qubit entangled system
研究三量子比特纠缠系统中三模和三模压缩的现象及其实现。
In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.
We consider a resonant bichromatic excitation of N trapped ions that generates displacement and squeezing in their collective motion conditioned to their ionic internal state, producing eventually Scrhodinger cat states and entangled squeezing. Furthermore, we study the case of tetrachromatic illumination or producing the so called entangled coherent states in two motional normal modes.
The spectral decomposition of all (n,2,2) Bell operators ($2^{2^n}$ in number, $n \ge 2$), as introduced by Werner and Wolf, is done. Its implications on the characterization of Bell operators as probes of entanglement are considered in detail.
Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero entanglement resources to start with. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of a geometric measure of entanglement and a related quantity. The results are compared with those for the negativity and the relative entropy of entanglement.
We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition. MME states are a special kind of maximally entangled mixed state (MEMS) for which every pure decomposition state in all decompositions is maximally entangled. Thus, MME states have entanglement 1 by all valid unit-normalized entanglement measures, whereas general MEMS can have entanglement less than 1. Multipartite MME states likely have important applications such as remote state preparation, …
Multipartite Entanglement Measure : Genuine to Absolutely Maximally Entangled
本文提出GME-AME多体纠缠度量，非零值对应真正多体纠缠态，最大值仅由绝对最大纠缠态达到，并成功用于四体qutrit态的分类与纠缠结构研究。
"Quantum conversation" is a way in which two parties can communicate classical information with each other using entanglement as a shared resource. We present this scheme using a multipartite entangled state after describing its generation through appropriate circuit diagrams. We make use of a discrimination scheme which allows one to perform a measurement on the system without destroying its entanglement. We later prove that this scheme is secure in a noiseless and a lossless quantum channel.
We assess quantum non-locality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger (GHZ), W and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditio…
We propose two deterministic secure quantum communication (DSQC) protocols employing three-qubit GHZ-like states and five-qubit Brown states as quantum channels for secure transmission of information in units of two bits and three bits using multipartite teleportation schemes developed here. In these schemes, the sender's capability in selecting quantum channels and the measuring bases leads to improved qubit efficiency of the protocols.
Integrated photonic sources of frequency-bin-encoded multipartite entangled states
本研究提出在集成光子平台中通过频率箱编码生成真多体纠缠态，设计了四光子GHZ态与三光子W态源，预测毫瓦泵浦下硅微环源产生速率约10⁴ Hz，为高维大规模纠缠态生成提供了有前景的方案。
A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is …
Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces -- the class of subspaces consisting entirely of genuinely multipartite entangled pure states. In this paper we present several methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the correspondence betwe…
We show how defects in a spin chain described by the XXZ model may be used to generate entangled states, such as Bell and W states, and how to maintain them with high fidelity. In the presence of several excitations, we also discuss how the anisotropy of the system may be combined with defects to effectively assist in the creation of the desired states.
This thesis is an attempt to enhance understanding of the following questions A- Given a multipartite quantum state (possibly mixed), how to find out whether it is entangled or separable? (Detection of entanglement.) B- Given an entangled state, how to decide how much entangled it is? (Measure of entanglement.), in the context of multipartite quantum states. We have explored two approaches. In the first approach, we assign a weighted graph with multipartite quantum state and address the question of separability in terms of these graphs and various operations involving them. In the second appro…
Self-testing of genuine multipartite non-local and non-maximally entangled states
针对非最大纠缠但具有真正多体非局域性的态难以自测试的问题，本文提出适用于任意参与方数的类 Cabello 悖论，并在标准框架下实现此类态的识别与自测试。
We have studied the generation of multipartite entangled states for the superconducting phase qubits. The experiments performed in this direction have the capacity to generate several specific multipartite entangled states for three and four qubits. Our studies are also important as we have used a computable measure of genuine multipartite entanglement whereas all previous studies analyzed certain probability amplitudes. As a comparison, we have reviewed the generation of multipartite entangled states via von Neumann projective measurements.
The generation and the characterization of multipartite entangled light is an important and challenging task in quantum optics. In this paper the entanglement properties of the light emitted from a planar semiconductor microcavity are studied. The intracavity scattering dynamics leads to the emission of light that is described by a fourpartite W state. Its multipartite correlations are identified by using the method of entanglement witnesses. Entanglement conditions are derived, which are based on a general witness constructed from W states. The results can be used to detect entanglement of li…
We propose a entanglement generating set for a general multipartite state based on the of concurrence. In particular, we show that concurrence for general multipartite states can be constructed by different classes of local operators which are defined by complement of positive operator valued measure on quantum phases. The entanglement generating set consists of different classes of entanglement that are detected by these classes of operators and contributes to the degree of entanglement for a general multipartite state.
We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled …
All genuinely entangled stabilizer subspaces are multipartite fully nonlocal
针对源自稳定子形式的多体态系统，本文建立真正纠缠与真正非局域性的等价关系，证明真正纠缠稳定子子空间上的态为多体完全非局域，并推导任意多体态真正非局域性含量下界，为实验估计奠定基础。
We describe an entanglement purification protocol (EPP) for multipartite three-level atomic entangled pair using photonic Faraday rotation. In this EPP, the multipartite atomic entangled state can be purified with the help of some single photons. This protocol resorts to the photonic Faraday rotation to realize the function of the controlled-Not (CNOT) gate. The purified multipartite atomic entangled state can be retained and to be repeated to reach a higher fidelity.
Entanglement theory is formulated as a quantum resource theory in which the free operations are local operations and classical communication (LOCC). This defines a partial order among bipartite pure states that makes it possible to identify a maximally entangled state, which turns out to be the most relevant state in applications. However, the situation changes drastically in the multipartite regime. Not only do there exist inequivalent forms of entanglement forbidding the existence of a unique maximally entangled state, but recent results have shown that LOCC induces a trivial ordering: almos…
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…
Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The result…
We examine the perfect cloning of non-local, orthogonal states with only local operations and classical communication. We provide a complete characterisation of the states that can be cloned under these restrictions, and their relation to distinguishability. We also consider the case of catalytic cloning, which we show provides no enhancement to the set of clonable states.
We construct an explicit Wigner function for N-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the non-locality of multipartite entangled state by the violation of Zukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for such squeezed state violate these inequalities by an amount that grows with the number N.
Green-Horne-Zeilinger states are a typical type of multipartite entangled states, which plays a central role in quantum information processing. For the generation of multipartite entangled states, the single-step method is more preferable as the needed time will not increase with the increasing of the qubit number. However, this scenario has a strict requirement that all the two-qubit interaction strengths should be the same, or the generated state will be of low quality. Here, we propose a scheme for generating multipartite entangled states of superconducting qubits, from a coupled circuit ca…
In this work we provide a method for generating quantum circuits preparing maximally multipartite entangled states using genetic programming. The presented method is faster that known realisations thanks to the applied fitness function and several modifications to the genetic programming schema. Moreover, we enrich the described method by the unique possibility to define an arbitrary structure of a system. We use the developed method to find new quantum circuits, which are simpler from known results. We also analyse the efficiency of generating entanglement in the spin chain system and in the …
For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes... d_n$, $d_1\ge d_2\ge...\ge d_n$, is there an entangled state {\em maximum} in the sense that all other states in the system can be obtained from the state through local quantum operations and classical communications (LOCC)? When $d_1\geΠ_{i=2}^n d_i$, such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space $\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^4$ by merging two different systems of an existing $7$-qubit UPB of size $11$. Moreover, a new family of $7$-qubit positive-partial-transpose (PPT) entangled states of rank $2^7-11$ is constructed. We analytically derive a geometric measure of entanglement of a special PPT entangled states. Also an upper bound a…
We explicate conditions under which, the two magnon state becomes highly entangled and is useful for several quantum communication protocols. This state, which is experimentally realizable in quantum dots using Heisenberg exchange interaction, is found to be suitable for carrying out deterministic teleportation of an arbitrary two qubit composite system. Further, conditions for which the channel capacity reaches "Holevo bound", allowing maximal amount of classical information to be encoded, are derived. Later, an explicit protocol for the splitting and sharing of a two qubit entangled state am…
The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterisation of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterised beyond an assumption about the dimension of their Hilbert spaces. Our scheme can certify that an $n$-partite high-dimensional quantum state features genuine multipartite entanglement. Moreover, the scheme can certify that a joint measurement on $n$ subsystems is entang…
Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multi-photon non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing paramet…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product states components. We show that this convex decomposition can be achieved in practice with the help of an algorithm based on linear programming, which in the general case scales polynomially with the dimension of the multipartite system. Furthermore, we suggest methods for analyzing the multipartite entanglement content of the…
We have tried to gauge the utility of a recently introduced seven-qubit state by Xin-Wei Zha et al for quantum teleportation and quantum state sharing. It is shown that this state can be used for the teleportation of an arbitrary single, double and triple qubit systems. We have also come up with 3 proposals for Quantum State Sharing using the Xin-Wei Zha state.
Scalable and modular generation of multipartite entangled states through memory-enhanced fusion
针对大规模多体纠缠态生成的挑战，本文提出利用光子互连实现内存增强的纠缠态融合，通过异步制备和单光子干涉成功创建并验证了远程量子内存模块间的四体W态纠缠，为分布式量子信息处理铺路。
The ability to generate and verify multipartite entanglement is an important benchmark for near-term quantum devices devices. We develop a scalable entanglement metric based on multiple quantum coherences, and demonstrate experimentally on a 20-qubit superconducting device - the IBM Q System One. We report a state fidelity of 0.5165$\pm$0.0036 for an 18-qubit GHZ state, indicating multipartite entanglement across all 18 qubits. Our entanglement metric is robust to noise and only requires measuring the population in the ground state; it can be readily applied to other quantum devices to verify …
An integrated photonic approach for complex quantum state generation through dynamical Casimir effect (DCE) is demonstrated. This approach provides a scheme to realize multipartite high-dimensional entangled states in the microwave (MW) and terahertz (THz) regimes, through the modulation in a MW-resonator coupled to an optical microresonator supporting temporal optical solitons. The states at the MW-resonator evolve from the ground state, realizing real-photons from the virtual photons at the ground state. The periodic modulation of the MW-resonator through a Kerr-induced refractive index chan…
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with the entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states--i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this proto…
In analogy with the spin-squeezing inequality of Wang and Sanders [Physical Review A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields, and whose violation implies entanglement of the photons that make up the optical beam. We consider a realistic and exactly-solvable experimental scenario employing polarization- squeezed light from an optical parametric oscillator (OPO) and find that any two photons separated by less than the OPO coherence time are polarization entangled. The polarization entanglement is robust aga…
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death …
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