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 entangled states satisfy the sufficient requirements for the full inseparability. The type of entangled states has especially potential application in quantum information with continuous quantum variables.
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.
We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$-partite correlations. We show that symmetric states with no $N$-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd nu…
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…
Following previous work, we distinguish between genuine $N$-partite entanglement and full $N$-partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous variable (position and momentum) measurements. Our criteria are similar but different to those based on the van Loock-Furusawa inequalities, which detect full $N$-partite inseparability. We explain how the criteria can be used to detect the genuine $N$-partite entanglement of continuous variable states generated from squeezed and vacuum state inputs, including the continuous variable Gr…
We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine $n$-partite entanglement which has previously not been identified. In addition, our criteria can be used in …
We construct tri-qubit genuinely entangled states which have positive partial transposes with respect to bi-partition of systems. These examples disprove a conjecture [L. Novo, T. Moroder and O. G\" uhne, Phys.Rev.A {88}, 012305 (2013)] which claims that PPT mixtures are necessary and sufficient for biseparability of three qubits.
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 derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.
The ability to deterministically generate genuine multi-partite entanglement is fundamental for the advancement of quantum information science. We show that the interaction between entangled twin beams of light and an atomic ensemble under conditions for electromagnetically induced transparency leads to the generation of genuine hybrid tri-partite entanglement between the two input fields and the atomic ensemble. In such a configuration, the system is driven through dissipation to a steady state given by the hybrid entangled state. To show the presence of the genuine hybrid entanglement, we in…
Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement measure, $3\leq k<m$. In addition, as a complement to the three-qubit concurrence triangle proposed in [Phys. Rev. Lett., 127, 040403], we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body quantum entanglement which is one of the focuses of current quantum information theory. We give several results on the necessary compatibility relations between a set of reduced density matrixes, including: (i) compatibility conditions for the one-party reduced density matrixes of any $N_A\times N_B$ dimensional bi-partite mixed quantum state, (ii) compatibi…
We investigate the concentration of multi-party entanglement by focusing on simple family of three-partite pure states, superpositions of Greenberger-Horne-Zeilinger states and singlets. Despite the simplicity of the states, we show that they cannot be reversibly concentrated by the standard entanglement concentration procedure, to which they seem ideally suited. Our results cast doubt on the idea that for each N there might be a finite set of N-party states into which any pure state can be reversibly transformed. We further relate our results to the concept of locking of entanglement of forma…
Non-classical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are $n$-particle states which do not exhibit $n$-partite correlations at all but still are genuinely $n$-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without $n$-partite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local reali…
We construct a method for verifying mode entanglement of N-mode W states. The ideal W state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-party entanglement with M<N, including mixtures of the latter. We specialize to the case N=4 for illustrative purposes. In the optical case, where excitations are photons, our method can be implemen…
With the complexity of information tasks, the bipartite and tripartite entanglement can no longer meet our needs, and we need more entangled particles to process relativistic quantum information. In this paper, we study the genuine N-partite entanglement and distributed relationships for Dirac fields in the background of dilaton black holes. We present the general analytical expression including all physically accessible and inaccessible entanglement in curved spacetime. We find that the accessible N-partite entanglement exhibits irreversible decoherence as the increase of black hole's dilaton…
We show that all multi-partite pure states can, under local operations, be transformed into bi-partite pairwise entangled states in a "lossless fashion": An arbitrary distinguished party will keep pairwise entanglement with all other parties after the asymptotic protocol - decorrelating all other parties from each other - in a way that the degree of entanglement of this party with respect to the rest will remain entirely unchanged. The set of possible entanglement distributions of bi-partite pairs is also classified. Finally, we point out several applications of this protocol as a useful primi…
We propose a new three-party quantum private comparison protocol using genuinely maximally entangled six-qubit states. In our protocol, three participants can determine whether their private information are equal or not without an external third party who helps compute the comparison result. At the same time the participants can preserve the privacy of their inputs, respectively. Our protocol does not need any unitary operations to encode information due to the excellent properties of genuinely maximally entangled six-qubit states. Additionally, the protocol uses one-step quantum transmission …
The variety of multi-partite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view classifications have been introduced. Accordingly, here we derive criteria and demonstrate how to experimentally discriminate an observed state against the ones of certain other classes of multi-partite entangled states. Our method, originating in Bell inequalities, adds an important tool for the characterization of multi-party entanglement.
In this paper, we mainly discuss the separability of $n$-partite quantum states from elements of density matrices. Practical separability criteria for different classes of $n$-qubit and $n$-qudit quantum states are obtained. Some of them are also sufficient conditions for genuine entanglement of $n$-partite quantum states. Moreover, one of the resulting criteria is also necessary and sufficient for a class of $n$-partite states.
We present an explicit protocol ${\cal E}_0$ for faithfully teleporting an arbitrary two-qubit state via a genunie four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party GHZ and W states. We also give a dense coding scheme ${\cal D}_0$ involving our state as a shared resource of entanglement. Both ${\cal D}_0$ and ${\cal E}_0$ indicate that our four-qubit state is a likely candidate for the genunine four-partite analogue to a Bell state.
We consider the problem of determining whether genuine multipartite entanglement was produced in an experiment, without relying on a characterization of the systems observed or of the measurements performed. We present an n-partite inequality that is satisfied by all correlations produced by measurements on biseparable quantum states, but which can be violated by n-partite entangled states, such as GHZ states. In contrast to traditional entanglement witnesses, the violation of this inequality implies that the state is not biseparable independently of the Hilbert space dimension and of the meas…
While Bell nonlocality of a bipartite system is counter-intuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrati…
We develop separability criteria to identify non-$k$-separability $(k = 2,3,\ldots,n)$ and genuine multipartite entanglement in different classes of mixed $n$-partite quantum states using elements of density matrices. With the help of these criteria, we detect non-$k$-separability in $n$-qudit GHZ and W states respectively added with white noise. We also discuss the experimental implementation of our criteria by means of local observables.
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 sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary multipartite systems.
The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong $N$-party correlations with $N$-party entanglement in an $N$-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest $N$-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest $N$-party correlations may be a tens…
We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria.
A renormalized version of the von Neumann quantum entropy (which is finite and continuous in general, infinite dimensional case) and which obeys several of the natural physical demands (as expected for a "good" measure of entanglement in the case of general quantum states describing bipartite and infinite-dimensional systems) is proposed. The renormalized quantum entropy is defined by the explicit use of the Fredholm determinants theory. To prove the main results on continuity and finiteness of the introduced renormalization the fundamental Grothendick approach, which is based on the infinite …
A classification of N-partite states, based on K-way negativities (K=2 to N), is proposed. The K-way partial transpose with respect to a subsystem is defined so as to shift the focus to K-way coherences instead of K subsystems of the composite system. For an N-partite system, the fraction of K-way negativity contributing to global negativity, is obtained. After minimizing K-way negativities through local unitary qubit rotations, a combined analysis of 2-way, 3-way and global negativities is shown to provide distinct measures of genuine tripartite, W-state like and bipartite entanglement, for t…
We study the relations between quantum coherence and quantum nonlocality, genuine quantum entanglement and genuine quantum nonlocality. We show that the coherence of a qubit state can be converted to the nonlocality of two-qubit states via incoherent operations. The results are also generalized to qudit case. Furthermore, rigorous relations between the quantum coherence of a single-partite state and the genuine multipartite quantum entanglement, as well as the genuine three-qubit quantum nonlocality are established.
The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an upper bound for maximally allowable entanglement is derived in terms of geometric measure of entanglement. This upper bound is characterized exclusively by the dimensions $d_1,\ldots, d_n$ of composite subsystems. Numerous examples demonstrate that the upper bound appears to be reasonably tight.
We develop the concept of genuine N-partite Einstein-Podolsky-Rosen (EPR) steering. This nonlocality is the natural multipartite extension of the original EPR paradox. Useful properties emerge that are not guaranteed for genuine multipartite entangled states. In particular, there is a close link with the task of one-sided device-independent quantum secret sharing. We derive inequalities to demonstrate multipartite EPR steering for Greenberger-Horne-Zeilinger (GHZ) and Gaussian continuous variable (CV) states in loophole-free scenarios.
We present a protocol for performing entanglement swapping with intense pulsed beams. In a first step, the generation of amplitude correlations between two systems that have never interacted directly is demonstrated. This is verified in direct detection with electronic modulation of the detected photocurrents. The measured correlations are better than expected from a classical reconstruction scheme. In the entanglement swapping process, a four--partite entangled state is generated. We prove experimentally that the amplitudes of the four optical modes are quantum correlated 3 dB below shot nois…
A set of multipartite orthogonal quantum states is strongly nonlocal if it is locally irreducible for every bipartition of the subsystems [Phys. Rev. Lett. 122, 040403 (2019)]. Although this property has been shown in three-, four- and five-partite systems, the existence of strongly nonlocal sets in $N$-partite systems remains unknown when $N\geq 6$. In this paper, we successfully show that a strongly nonlocal set of orthogonal entangled states exists in $(\mathbb{C}^d)^{\otimes N}$ for all $N\geq 3$ and $d\geq 2$, which for the first time reveals the strong quantum nonlocality in general $N$-…
The laws of quantum mechanics allow for the distribution of a secret random key between two parties. Here we analyse the security of a protocol for establishing a common secret key between N parties (i.e. a conference key), using resource states with genuine N-partite entanglement. We compare this protocol to conference key distribution via bipartite entanglement, regarding the required resources, achievable secret key rates and threshold qubit error rates. Furthermore we discuss quantum networks with bottlenecks for which our multipartite entanglement-based protocol can benefit from network c…
The last two decades have witnessed an increasing effort of the scientific community toward pursuing a better framework for quantum resource covariance, with the focus predominantly posed on quantum entanglement. In this work, we move the discussion one step further by analyzing the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts. Specifically, we conduct a case study for the problem of an electron-positron pair created in a superposed multipartite pure state. Our approach is different from the standard treatments also in that we consider all the c…
Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if $N$ players share an $N$-party genuine secret-sharing state, then arbitrary $M$ players out of the total players can share an $M$-party genuine secret-sharing state by means of local operations and classical communication on the state…
We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Zukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet-defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlyin…
We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely multi-partite entangled. We develop an entropic witness for tripartite entanglement, and show that the degree of violation of this witness places a lower limit on the tripartite entanglement of formation. We test our results in the three-qubit regime using the GHZ-Werner state and the W-Werner state, and in the high-dimensional pure-state regime using the tr…
We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication. This result affirms the comparability of multipartite pure entangled states.
We introduce a quantification of genuine three-party pure-state coherence for wave fields, classical and quantum, by borrowing concepts from classical optics. The tensor structure of a classical paraxial light beam composed of three principle degrees of freedom is shown to be equivalent to that of a three-qubit quantum state. The traditional basis-independent optical coherence quantity called degree of polarization is then determined to be the desired quantitative two-party coherence measure. When appropriately generalized, a set of fundamental constraint relations is derived among three two-p…
