See related work by Ya-Li Mao et al. (arXiv:2201.12753). 12 pages (7 of appendices), 5 figures (2 in appendices). H.C., M-O.R. and C.Z contributed equally to this work
Quantum theory predicts the existence of genuinely tripartite-entangled states, which cannot be obtained from local operations over any bipartite entangled states and unlimited shared randomness. Some of us recently proved that this feature is a fundamental signature of quantum theory. The state $\left|{GHZ}_3\right\rangle=(\left|000\right\rangle+\left|111\right\rangle)/\sqrt{2}$ gives rise to tripartite quantum correlations which cannot be explained by any causal theory limited to bipartite nonclassical common causes of any kind (generalising entanglement) assisted with unlimited shared randomness. Hence, any conceivable physical theory which would reproduce quantum predictions will necessarily include genuinely tripartite resources.
In this work, we verify that such tripartite correlations are experimentally achievable. We derive a new device-independent witness capable of falsifying causal theories wherein nonclassical resources are merely bipartite. Using a high-performance photonic $\left|{GHZ}_3\right\rangle$ states with fidelities of $ 0.9741\pm0.002$, we provide a clear experimental violation of that witness by more than $26.3$ standard deviation, under the locality and fair sampling assumption. We generalise our work to the $\left|{GHZ}_4\right\rangle$ state, obtaining correlations which cannot be explained by any causal theory limited to tripartite nonclassical common causes assisted with unlimited shared randomness.
Nonlocal correlations as revealed by the violations to Bell inequalities are incompatible with local models without any nonlocal correlations. However some tripartite entangled states, e.g., symmetric pure states, exhibit a stronger nonlocality even incompatible with hybrid local/nonlocal models allowing nonlocal correlations between any two parties. Here we propose a three-particle Hardy-type test without inequality, as illustrated by a gedanken experiment, that is failed by all non-signaling local models while is passed by all tripartite entangled asymmetric pure states. Our result implies t…
From an operational criterion of physical reality, a quantifier of realism-based nonlocality was recently introduced for two-part quantum states. This measure has shown to capture aspects that are rather different from Bell nonlocality. Here we take a step further and introduce a tripartite realism-based nonlocality quantifier. We show that this measure reduces to genuine tripartite entanglement for a certain class of pure tripartite states and manifests itself in correlated mixed states even in the absence of quantum correlations. A case study for noisy GHZ and W states points out the existen…
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 …
Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevan…
The upper bound of the fine-grained uncertainty relation is different for classical physics, quantum physics and no-signaling theories with maximal nonlocality (supper quantum correlation), as was shown in the case of bipartite systems [J. Oppenheim and S. Wehner, Science 330, 1072 (2010)]. Here, we extend the fine-grained uncertainty relation to the case of tripartite systems. We show that the fine-grained uncertainty relation determines the nonlocality of tripartite systems as manifested by the Svetlichny inequality, discriminating between classical physics, quantum physics and super quantum…
Quantum nonlocality is a kind of significant quantum correlation that is stronger than quantum entanglement and EPR steering. The standard tripartite nonlocality can be detected by the violation of the Mermin inequality. By using local filtering operations, we give a tight upper bound on the maximal expected value of the Mermin operators. By detailed examples we show that the hidden standard nonlocality can be revealed by local filtering which can enhance the robustness of the noised entangled states.
Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts three-party correlations that admit no such simulation, suggesting there are versions of nonlocality in nature transcending the phenomenon of bipartite nonsignaling nonlocality. This paper introduces a rigorous framework for analyzing tripartite correlations that can be simulated by bipartite-only networks. We confirm that expected properties of so…
In the nonsignaling framework, nonclassicality in correlation arising from two spatially separated input-output devices gets manifested, solely, through its \emph{nonlocal} behavior. Study of correlations based on this said feature is commonly known as local-nonlocal paradigm. While in two-party scenario correlations can be of only two types either local or nonlocal, the situation gets more involved for multi-party scenario, \emph{e.g.,} for tripartite scenario, correlations can be of three types: fully local, two-way local, and genuinely nonlocal. Nonsignaling correlations having quantum real…
We experimentally demonstrate the nonclassical photon number correlations expected in tripartite continuous variable states obtained by parametric processes. Our scheme involves a single nonlinear crystal, where two interlinked parametric interactions take place simultaneously, and represents a bright and compact source of a sub-shot-noise tripartite light field. We analyze the effects of the pump intensities on the numbers of detected photons and on the amount of noise reduction in some details, thus demonstrating a good agreement between the experimental data and a single-mode theoretical de…
Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions
College of Computer Science and Engineering, Shandong University of Science and Technology（山东科技大学计算机科学与工程学院）；College of Mathematics and Systems Science, Shandong University of Science and Technology（山东科技大学数学与系统科学学院）；College of Cyberspace Science and Technology, Beijing University of Technology（北京工业大学网络空间科学技术学院）
Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell's theorem imply new and sometimes stronger forms of nonclassicality. Due to a number of practical difficulties, however, the experimental implementation of such networks remains far less explored. Going beyond what has been previously tested, here we verify the nonlocality of an experimental tr…
Phase-controlled bipartite and tripartite entanglement and Bell nonlocality in a closed-loop optomechanical system
Beijing Institute of Radio Metrology and Measurement（北京无线电计量测试研究所）；Science and Technology on Metrology and Calibration Laboratory, Beijing Institute of Radio Metrology and Measurement（北京无线电计量测试研究所计量与校准重点实验室）
We show that some tripartite quantum correlations are inexplicable by any causal theory involving bipartite nonclassical common causes and unlimited shared randomness. This constitutes a device-independent proof that Nature's nonlocality is fundamentally at least tripartite in every conceivable physical theory - no matter how exotic. To formalize this claim we are compelled to substitute Svetlichny's historical definition of genuine tripartite nonlocality with a novel theory-agnostic definition tied to the framework of Local Operations and Shared Randomness (LOSR). A companion article [PRA. 10…
A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode position correlation and relative momentum correlation between the sender and the receiver and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28dB and 3.18dB respectively. If the mean …
We report an experimental implementation of tripartite controlled quantum teleportation on the quantum optical devices. The protocol is performed through bi- and tripartite entangled channels of discrete variables and qubits encoded in polarization of individual photons. The experimental results demonstrate successful controlled quantum teleportation with a fidelity around $83\%$, well above the classical limit. By realizing the controlled quantum teleportation through biseparable state, we show that tripartite entangled is not a necessary resource for controlled quantum teleportation and the …
In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality un…
We propose an experimentally feasible scheme to demonstrate quantum nonlocality, using Greenberger-Horne-Zeilinger (GHZ) and $W$ entanglement between atomic ensembles generated by a new developed method based on laser manipulation and{} single-photon detection.
We study the principle of information causality for the set of extremal correlations in the tripartite scenario. We show that all but one nonlocal extremal correlations in this scenario violate information causality. This undetected correlation is shown to satisfy any bipartite physical principle.
Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartit…
We show a transitivity property of nonlocal correlations: There exist tripartite nonsignaling correlations of which the bipartite marginals between A and B as well as B and C are nonlocal and any tripartite nonsignaling system between A, B, and C consistent with them must be such that the bipartite marginal between A and C is also nonlocal. This property represents a step towards ruling out certain alternative models for the explanation of quantum correlations such as hidden communication at finite speed. Whereas it is not possible to rule out this model experimentally, it is the goal of our a…
The equivalence of tripartite pure states under local unitary transformations is investigated. The nonlocal properties for a class of tripartite quantum states in $\Cb^K \otimes \Cb^M \otimes \Cb^N$ composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.
We present a device independent analysis of controlled quantum teleportation where the receiver is not trusted. We show that the notion of genuine tripartite nonlocality allows us to certify control power in such a scenario. By considering a specific adversarial attack strategy on a device characterized by depolarizing noise, we find that control power is a monotonically increasing function of genuine tripartite nonlocality. These results are relevant for building practical quantum communication networks and also shed light on the role of nonlocality in multipartite quantum information process…
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…
Experimental free-will or measurement independence is one of the crucial assumptions in derivation of any nonlocal theorem. Any nonlocal correlation obtained in quantum world can have a local deterministic explanation if there is no experimental free-will in choosing the measurement settings. Recently, in [Phys. Rev. Lett. {\bf105}, 250404 (2010)] it has been shown that to obtain a local deterministic description for singlet state correlation one does not need to give up measurement independence completely, but a partial measurement dependence suffices. In three party scenario considering GHZ …
The Einstein-Podolsky-Rosen (EPR) paradox established a link between entanglement and nonlocality in quantum mechanics. EPR steering is the nonlocality associated with the EPR paradox and has traditionally only been investigated between two parties. Here, we present the first experimental observations of multipartite EPR steering, and of the genuine tripartite continuous variable entanglement of three mesoscopic optical systems. We explore different linear optics networks - each one with optimised asymmetries - that create multipartite steerable states containing different numbers of quantised…
We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems $\mathcal{C}^{d}\otimes\mathcal{C}^{d}\otimes\mathcal{C}^{d}~(d\geq3)$ and $\mathcal{C}^d\otimes \mathcal{C}^{d+1}\otimes \mathcal{C}^{d+2}~(d\geq 3)$. Then for general tripartite quantum system $\mathcal{C}^{n_{1}}\otimes\mathcal{C}^{n_{2}}\otimes\mathcal{C}^{n_{3}}$ $(3\leq n_{1}\leq n_{2}\leq n_{3})$, we obtain $2(n_{2}+n_{3}-1)-n_{1…
The fine-grained uncertainty relation can be used to discriminate among classical, quantum and super-quantum correlations based on their strength of nonlocality, as has been shown for bipartite and tripartite systems with unbiased measurement settings. Here we consider the situation when two and three parties, respectively, choose settings with bias for playing certain non-local games. We show analytically that while the fine-grained uncertainty principle is still able to distinguish classical, quantum and super-quantum correlations for biased settings corresponding to certain ranges of the bi…
Usually, the three-tangle of a tripartite pure state of qubits can be directly measured with the simultaneous preparation of a not-less-than-four-fold copy of the state. We show that the exact genuine tripartite entanglement for ($2\otimes2\otimes n$)-dimensional pure quantum states can be measured in a similar manner, provided that only two simultaneous copies of the state are available. Lower bounds are also proposed for more convenient experimental operations. As an example, a comprehensive demonstration of the scheme is provided for the three-tangle of a three-qubit state.
The multipartite setting offers much more complexity of nonlocality than the bipartite one. We analyze the structure of tripartite nonlocal correlations by proposing inequalities satisfied by each type: bilocal, broadcasting and quantum, but violated by the other two. One of the inequalities satisfied by broadcasting correlations is generalized for multipartite systems. The study of its quantum mechanical violation reveals that Greenberger-Horne-Zeilinger-like states exhibit new, powerful correlations.
In the present work, we study tripartite quantum steering of quantum correlations arising from two local dichotomic measurements on each side in the two types of partially device-independent scenarios: $1$-sided device-independent scenario where one of the parties performs untrusted measurements while the other two parties perform trusted measurements and $2$-sided device-independent scenario where one of the parties performs trusted measurements while the other two parties perform untrusted measurements. We demonstrate that tripartite steering in the $2$-sided device-independent scenario is w…
It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a non-separable, tripartite GHZ-like state of path, polarization and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by…
In this paper, we investigate the construction of orthogonal product states with strong nonlocality in multiparty quantum systems. Firstly, we focus on the tripartite system and propose a general set of orthogonal product states exhibiting strong nonlocality in $d\otimes d\otimes d$ quantum system, which contains $6{{\left( d-1 \right)}^{2}}$ states. Secondly, we find that the number of the sets constructed in this way could be further reduced. Then using $4\otimes 4\otimes 4$ and $5\otimes 5\otimes 5$ quantum systems as examples, it can be seen that when d increases, the reduced quantum state…
Quantum correlation between nodes in a network which consist of several independent sources of entanglement and in multipartite entanglement systems are important for general understanding of the nature of nonlocality, quantum information processing and communication. In previous years, demonstrations of network nonlocality for bilocal scenarios have been in the focus. Yet, it has been found that the seminal protocols do not certify entanglement between end nodes, which otherwise require all sources in the network to be of nonlocal nature. This has motivated for development of even stronger co…
An experiment demonstrating nonlocality at detection is proposed. A single-photon Michelson-Morley experiment could be performed under exactly the same conditions as well. Hence, the two experiments are "loophole free" to the same extent. It is argued that both quantum theory and relativity share the same experimental basis and derive from the same principles. Relativity and the quantum are two aspects of one and the same physical description of the world.
We experimentally demonstrate the nonlocal reversal of a partial-collapse quantum measurement on two-photon entangled state. Both the partial measurement and the reversal operation are implemented in linear optics with two displaced Sagnac interferometers, which are characterized by single qubit quantum process tomography. The recovered state is measured by quantum state tomography and its nonlocality is characterized by testing the Bell inequality. Our result will be helpful in quantum communication and quantum error correction.
Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, we investigate the correlations of the tripartite W-type states based on bipartite quantum resources. The interrelations among the degree of coherence, concurrence, Bell nonlocality and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser-Horne-Shimony-Holt inequality) states for the two-qubit subsystems derived from the…
Recently, Gallego et.al. [Phys. Rev. Lett 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and post-quantum correlation must be intrinsically multipartite in nature. We establish similar result by using device independent success probability of Hardy's nonlocality argument for tripartite quantum system. We construct an example of a tri-partite Hardy correlation which is post-quantum but satisfies not only all bipartite information principle but also the GYNI inequality.
The characterization of quantum correlations in terms of information-theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource. While bipartite entanglement and Bell inequality violation in this setting have been extensively studied, relatively little is known about their multipartite counterpart. In this paper, we apply and adapt the recently proposed definitions of multipartite nonlocality [Phys. Rev. A 88, 014102] to the three- and four-partite scenario to gain new insight on the resource aspect of multipartite nonlocal quantum correlation…
The future progress of semi-device independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite dimensional quantum resources. In this work, we characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations. In the bipartite case, we find that the first level of the hierarchy returns non-trivial bounds in all cases considered, allowing to study nonlocality scenarios with four measurement settings on one side and twelve (12) on the other in a…
Localizability of entanglement in fully inseparable states is a key ingredient of assisted quantum information protocols as well as measurement-based models of quantum computing. We investigate the existence of fully inseparable states with nonlocalizable entanglement, that is, with entanglement which cannot be localized between any pair of subsystems by any measurement on the remaining part of the system. It is shown, that the nonlocalizable entanglement occurs already in suitable mixtures of a three-qubit GHZ state and white noise. Further, we generalize this set of states to a two-parametri…
Reproducing with elementary resources the correlations that arise when a quantum system is measured (quantum state simulation), allows one to get insight on the operational and computational power of quantum correlations. We propose a family of models that can simulate von Neumann measurements in the x-y plane of the Bloch sphere on n-partite GHZ states using only bipartite nonlocal boxes. For the tripartite and fourpartite states, the models use only bipartite nonlocal boxes; they can be translated into classical communication schemes with finite average communication cost.
Franson-type nonlocal quantum correlation based on the particle nature of quantum mechanics has been intensively studied for both fundamental physics and potential applications of quantum key distribution between remotely separated parties over the last several decades. Recently, a coherence theory of deterministic quantum features has been applied for Franson-type nonlocal correlation [arXiv:2102.06463] to understand its quantumness in a purely classical manner, where the resulting features are deterministic and macroscopic. Here, nearly sub-Poisson distributed coherent photon pairs obtained …
The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question: how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce a n…
Quantum nonlocality stands as a resource for Device Independent Quantum Information Processing (DIQIP), as, for instance, Device Independent Quantum Key Distribution. We investigate experimentally the assumption of limited Measurement Dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particle and/or by an adversary. Using a recently derived Bell-like inequality [Phys. Rev. Lett. 113 190402] and a 99% fidelity source of partially entangled polarization photonic qubits, we obtain a clear violation of the ine…
In this letter we experimentally implement a single photon Bell test based on the ideas of S. Tan et al. [Phys. Rev. Lett., vol. 66, 252 (1991)] and L. Hardy [Phys. Rev. Lett.,vol. 73, 2279 (1994)]. A double heterodyne measurement is used to measure correlations in the Fock space spanned by zero and one photons. Local oscillators used in the correlation measurement are distributed to two observers by co-propagating it in an orthogonal polarization mode. This method eliminates the need for interferometrical stability in the setup, consequently making it a robust and scalable method.
Experimental demonstration of entanglement needs to have a precise control of experimentalist over the system on which the measurements are performed as prescribed by an appropriate entanglement witness. To avoid such trust problem, recently device-independent entanglement witnesses (\emph{DIEW}s) for genuine tripartite entanglement have been proposed where witnesses are capable of testing genuine entanglement without precise description of Hilbert space dimension and measured operators i.e apparatus are treated as black boxes. Here we design a protocol for enhancing the possibility of identif…
A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition. Most known constructions of strongly nonlocal orthogonal product set (OPS) are limited to tripartite systems, and they are lack of intuitive structures. In this work, based on the decomposition for the outermost layer of an $n$-dimensional hypercube for $n= 3,4,5$, we successfully construct strongly nonlocal OPSs in any possible three, four and five-partite systems, which answers an open question given by Halder et al. [Phys. Rev. Lett.122, 040403 (2019)] and Yuan et al. [Phy…
We study a generalization of nonlocal games---which we call extended nonlocal games---in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski, and Wehner, which they also generalize. We prove that a natur…
