A scheme to distinguish entangled two-photon-polarization states (ETP) from two independent entangled one-photon-polarization states (EOP) is proposed. Using this scheme, the experimental generation of ETP by parametric down-conversion is confirmed through the anti-correlations between three orthogonal two-photon-polarization states. The estimated fraction of ETP among the correlated photon pairs is 37% in the present experimental setup.
We demonstrate that one maximally entangled state is sufficient and necessary to distinguish a complete basis of maximally entangled states by local operation and classical communication.
We propose an optical scheme to generate genuine entangled states of four atomic qubits in optical cavities using a single-photon source, beam splitters and single photon detectors. We show how to generate deterministically sixteen orthonormal and independent genuine entangled states of four atomic qubits. It is found that the sixteen genuine entangled states form a new type of representation of the four-atomic-qubit system, i.e., the genuine entangled-state representation. This representation brings new interesting insight onto better understanding multipartite entanglement.
It is an interesting problem to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. We consider the case that the states are two-qubit Werner states, we construct the interval of parameter of Werner states such that the tripartite state is genuine entangled. Further, we present the way of detecting the tripartite genuine entanglement using current techniques in experiments. We also investigate the lower bound of genuine multipartite entanglement concurrence.
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 …
In a recent paper, a genuine four-partite entangled state is proposed [Y. Yeo and W. K. Chua, Phys. Rev. Lett. 96, 060502 (2006)], which has been found to have many interesting entanglement properties. We show this state is locally equivalent to some graph states.
Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit entangled state is presented. We find a seven-qubit state whose marginal density matrices for subsystems of 1,2- qubits are all completely mixed and for subsystems of 3-qubits is almost completely mixed.
We discuss (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancila under local operation and classical communication. Whereas any two orthogonal GHZ states taken from the canonical GHZ basis, can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as blank copy.
We experimentally prepare a new type of continuous variable genuine four-partite entangled states, the quantum correlation property of which is different from that of the four-mode GHZ and cluster states, and which has not any qubit counterpart to be proposed at present. In the criterion inequalities for the full inseparability of the genuine four-partite entangled states, the amplitude and phase quadrature correlation variances totally consisting of three-party combination from the four entangled modes are involved. The measured correlation variances among the quadratures of the prepared enta…
The usefulness of the genuinely entangled six qubit state that was recently introduced by Borras et al. is investigated for the quantum teleportation of an arbitrary three qubit state and for quantum state sharing (QSTS) of an arbitrary two qubit state. For QSTS, we explicitly devise two protocols and construct sixteen orthogonal measurement basis which can lock an arbitrary two qubit information between two parties.
We investigate the usefulness of different classes of genuine quadripartite entangled states as quantum resources for teleportation and superdense coding. We examine the possibility of teleporting unknown one, two and three qubit states. We show that one can use the teleportation protocol to send any general one and two qubit states. A restricted class of three qubit states can also be faithfully teleported. We also explore superdense coding protocol in single-receiver and multi-receiver scenarios. We show that there exist genuine quadripartite entangled states that can be used to transmit fou…
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subspaces. We further investigate the tripartite state when one of the two bipartite states has rank two. Our results provide the latest progress on a conjecture proposed in the paper [Yi Shen $\textit{et al}$, J. Phys. A 53, 125302 (2020)]. We apply our …
We present a family of three-qubit quantum states with a basic local hidden variable model. Any von Neumann measurement can be described by a local model for these states. We show that some of these states are genuine three-partite entangled and also distillable. The generalization for larger dimensions or higher number of parties is also discussed. As a byproduct, we present symmetric extensions of two-qubit Werner states.
We propose a scheme for generating a genuine $χ$-type four-particle entangled state of superconducting artificial atoms with broken symmetry by using one-dimensional transmission line resonator as a data bus. The $Δ$-type three-level artificial atom we use in the scheme is different from natural atom and has cyclic transitions. After suitable interaction time and simple operations, the desired entangled state can be obtained. Since artificial atomic excited states and photonic states are adiabatically eliminated, our scheme is robust against the spontaneous emissions of artificial atoms and th…
We study the dynamics of genuine multipartite entanglement for quantum systems upto four qubits interacting with general collective dephasing process. Using a computable entanglement monotone for multipartite systems, we observe the feature of freezing dynamics of genuine entanglement for three and four qubits entangled states. We compare the dynamics with that of random states and find that most states exibit this feature. We then study the effects of collective dephasing on genuine nonlocality and find out that although quantum states remain genuinely entangled yet their genuine nonlocality …
Recently, Paolo Facchi et al. [Phys. Rev. A. 77, 060304 (R) (2008)] introduced the notion of maximally multipartite entangled states of n qubits. Here, we give a criterion for faithful controlled teleportation of an arbitrary two-qubit state via a five-qubit entangled state and obtain the general relation between the genuine five-qubit entangled state and controlled teleportation. This criterion can be extended to teleportation of an arbitrary N-qubit state using 2N+1-qubit entangled state. Furthermore, we study the optimal match of measuring basis and quantum channel.
Self-testing is a procedure for characterizing quantum resources with the minimal level of trust. Up to now it has been used as a device-independent certification tool for particular quantum measurements, channels, and pure entangled states. In this work we introduce the concept of self-testing more general entanglement structures. More precisely, we present the first self-tests of an entangled subspace - the five-qubit code and the toric code. We show that all quantum states maximally violating a suitably chosen Bell inequality must belong to the corresponding code subspace, which remarkably …
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 show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the more complicated tests are strictly stronger. The new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs. We successfully applied the results to many low-dimensional states from the literature where the PPT test fails. As a byproduct of the criteria, we prov…
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.
Herein, we present a feasible, general protocol for quantum communication within a network via generalized remote preparation of an arbitrary $m$-qubit entangled state designed with genuine tripartite Greenberger--Horne--Zeilinger-type entangled resources. During the implementations, we construct novel collective unitary operations; these operations are tasked with performing the necessary phase transfers during remote state preparations. We have distilled our implementation methods into a five-step procedure, which can be used to faithfully recover the desired state during transfer. Compared …
We present a practical entanglement distillation protocol (EDP) with linear optics for a genuine mixed state. Each components of the genuine mixed state is a pure less-entangled state. After successfully performing this EDP, we can obtain a high quality entangled mixed state. Our EDP can work for both ideal entanglement sources and current available spontaneous parametric down-conversion (SPDC) sources, which makes it feasible in current experimental technology. Moreover, by using the SPDC source, we can obtain a higher fidelity. This protocol can also be used to distill the multi-partite enta…
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite e…
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of bi-separable states, but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitl…
We propose genuine ($k$, $m$)-threshold controlling schemes for controlled teleportation via multi-particle entangled states, where the teleportation of a quantum state from a sender (Alice) to a receiver (Bob) is under the control of $m$ supervisors such that $k$ ($k\leq m$) or more of these supervisors can help Bob recover the transferred state. By construction, anyone of our quantum channels is a genuine multipartite entangled state of which any two parts are inseparable. Their properties are compared and contrasted with those of the well-known Greenberger-Horne-Zeilinger, W, and linear clu…
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.
Testing Genuine Multipartite Nonlocality via an Inflated Network with Multi-copy Entangled States
International Quantum Academy（国际量子科学院）；Southern University of Science and Technology（南方科技大学）；School of Information Science and Technology, Southwest Jiaotong University（西南交通大学信息科学与技术学院）；Hefei National Laboratory（合肥国家实验室）；School of Physics, Nankai University（南开大学物理学院）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）；Max-Planck-Institute for Mathematics in the Sciences（马克斯·普朗克科学研究所）
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of entangled systems compared with quantum multisource networks. We prove that any symmetric entangled pure state shows stronger nonlocality than the genuinely multipartite nonlocality in the biseparable model. Similar results hold for other entangled pure states with local dimensions no larger than $3$. We further provide computational conditions for witnessing …
We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a witness operator to detect genuinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.
The interaction between a superconducting phase qubit and the two-level systems locating inside the Josephson tunnel barrier is shown to be described by the XY model, which is naturally used to implement the iSWAP gate. With this gate, we propose a scheme to efficiently generate genuine multi-qubit entangled states of such two-level systems, including multipartite W state and cluster states. In particularly, we show that, with the help of the phase qubit, the entanglement witness can be used to efficiently detect the produced genuine multi-qubit entangled states. Furthermore, we analyze that t…
We propose a criterion for the detection of genuine entanglement of pure multiqubit states. To this aim, we define an operator called the losing one qubit operator, which is different from the reduced density operator. The states obtained from a multiqubit state by applying the losing one qubit operator are referred to as its projected states. We show that all of the projected states of a pure product n-qubit state are pure product states provided that it cannot be written as a product of a single qubit state and a genuinely entangled (n-1)-qubit state. We also show that a pure n-qubit state i…
Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states
International Institute of Information Technology Hyderabad（海德拉巴国际信息技术学院）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；VIT-AP University（维特-AP大学）
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely projective measurements. Here we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements (POVMs), and show that the states violate a Bell inequality after local filtering. Hence there exist entangled states, the nonl…
Recently the authors in [Phys. Rev. Lett. 125, 090401 (2020)] considered the following scenario: Alice and Bob each have half of a pair of entangled qubit state. Bob measures his half and then passes his part to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality with the single Alice. By taking the maximally entangled pure two-qubit state as an example, it has been constructively proved that arbitrarily many independent Bobs can share the nonlocality with the single Alice.…
Nonlocal correlations arising from measurements on tripartite entangled states can be classified into two groups, one genuinely $3-$way nonlocal and other local with respect to some bipartition. Still, whether a genuinely tripartite entangled quantum state can exhibit genuine $3-$way nonlocality, remains a challenging problem so far as measurement context is concerned. Here we introduce a novel approach in this regard. We consider three tripartite quantum states none of which is genuinely $3-$way nonlocal in a specific Bell scenario (three parties, two measurements per party, two outcomes per …
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.
In this work we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the $W$ states. With explicit examples we show that our measure results in distinct entanglement orderings from other measures, and can detect differences in certain types of genuine…
We generate and characterise entangled states of a register of 20 individually controlled qubits, where each qubit is encoded into the electronic state of a trapped atomic ion. Entanglement is generated amongst the qubits during the out-of-equilibrium dynamics of an Ising-type Hamiltonian, engineered via laser fields. Since the qubit-qubit interactions decay with distance, entanglement is generated at early times predominantly between neighbouring groups of qubits. We characterise entanglement between these groups by designing and applying witnesses for genuine multipartite entanglement. Our r…
A genuinely $N$-partite entangled state may display vanishing $N$-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd $N$ is to design an `anti-state' in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its anti-state then produces a mixed state with no $N$-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of `entan…
According to the studies of genuine tripartite nonlocality in discrete variable quantum systems conducted so far, Svetlichny inequality is considered as the best Bell-type inequality to detect genuine (three way) nonlocality of pure tripartite genuine entangled states. In the present work, we have considered another Bell-type inequality (which has been reported as the $99$-th facet of $NS_2$ local polytope in (J.-D. Bancal, et.al.,Phys. Rev.A \textbf{88}, 014102 (2013)), to reveal genuine tripartite nonlocality of generalized GHZ(Greenberger-Horne-Zeilinger) class and a subclass of extended GH…
For every possible spectrum of $2^N$-dimensional density operators, we construct an $N$-qubit X-state of same spectrum and maximal genuine multipartite (GM-) concurrence, hence characterizing a global unitary transformation that --- constrained to output X-states --- maximizes the GM-concurrence of an arbitrary input mixed state of $N$ qubits. We also apply semidefinite programming methods to obtain $N$-qubit X-states with maximal GM-concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the role, the so-called X-MEMS…
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected i…
We investigate the properties of different levels of entanglement in graph states which correspond to connected graphs. Combining the operational definition of graph states and the postulates of entanglement measures, we prove that in connected graph states of N>3 qubits there is no genuine three-qubit entanglement. For certain classes of graph states, all genuine k-qubit entanglement, 2\leq k\leq N-1, among every k qubits vanishes. These results about connected graph states naturally lead to the definition of fully multi-qubit entangled states. We also find that the connected graph states of …
In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show that the classification of all multipartite systems featuring those and only those two classes of genuine entanglement can be deduced from earlier work of algebraic geometers. This classification corresponds in fact to classification of fundamental subadjoint varieties and establish a connection between those systems, well known in Quantum Information Theory and fundamental s…
