Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.
Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.
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 tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.
Monogamy inequalities for the way bipartite Einstein-Podolsky-Rosen (EPR) steering can be distributed among N systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalize to m settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to m, and takes a form similar to the Coffman-Kundu-Wootters relation for entanglement. The results enable characterization of the tripartite steering for CV Gaussian systems and qubit Greenberger-Horne-Zeilinger and W states.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
Quantum steering captures the ability of one party, through local measurements on a shared entangled state, to affect the conditional states held by distant parties in a way that admits no local explanation. Its device-independent (DI) quantification -- requiring no characterization of any state or measurement -- has been developed in the bipartite setting, notably through the framework of assemblage moment matrices (AMMs) [Phys. Rev. Lett. 116, 240401 (2016)], but has remained largely unexplored beyond it. Here, we extend the AMM framework to tripartite steering, covering both the scenario in which two parties jointly steer a third one (2-steer-1) and that in which a single party steers the remaining two (1-steer-2). For each scheme, we construct a semidefinite program that, from the observed correlations -- or merely from the violation of a Bell inequality -- yields lower bounds on the steering robustness of the underlying assemblage. As a by-product, our bounds also certify, in a DI manner, the incompatibility of the measurements performed by the steering parties.
It is a well-known fact that both quantum entanglement and nonlocality (implied by the violation of Bell inequalities) constitute quantum correlations that cannot be arbitrarily shared among subsystems. They are both monogamous, albeit in a different fashion. In the present contribution we focus on nonlocality monogamy relations such as the Toner-Verstraete, the Seevinck, and a derived monogamy inequality for three parties and compare them with multipartite nonlocality measures for the whole set of pure states distributed according to the Haar measure. In this numerical endeavor, we also see that, although monogamy relations for nonlocality cannot exist for more than three parties, in practice the exploration of the whole set of states for different numbers of qubits will return effective bounds on the maximum value of all bipartite Bell violations among subsystems. Hence, we shed light on the effective nonlocality monogamy bounds in the multiqubit case.