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Register a new userAll-versus-nothing proof of tripartite quantum steering and genuine entanglement certification in the two-sided device-independent scenario
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We consider the task of certification of genuine entanglement of tripartite states. We first present an all-versus-nothing proof of tripartite Einstein-Podolsky-Rosen (EPR) steering by demonstrating the non-existence of a local hidden state (LHS) model in the tripartite network as a motivation to our main result. A full logical contradiction of the predictions of the LHS model with quantum mechanical outcome statistics for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states and pure W-class states is shown, using which, one can distinguish between the GGHZ and W-class states in the two-sided device-independent (2SDI) steering scenario. We next formulate a 2SDI fine-grained steering inequality for the tripartite scenario. We show that the maximum quantum violation of this FGI can be used to certify genuine entanglement of three-qubit pure states.
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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 in the experiment, namely, device-independently (DI). However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty to identify optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this work, we explore a general and robust DI method which can be applied to various realistic multipartite quantum state in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly-entangled GHZ states, thus showing that the method applies equally well to less standard states.
In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities both theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions.
We show that genuine multipartite entanglement of all multipartite pure states in arbitrary finite dimension can be detected in a device-independent way by employing bipartite Bell inequalities on states that are deterministically generated from the initial state via local operations. This leads to an efficient scheme for large classes of multipartite states that are relevant in quantum computation or condensed-matter physics, including cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model. For cluster states the detection of genuine multipartite entanglement involves only measurements on a constant number of systems with an overhead that scales linear with the system size, while for the AKLT model the overhead is polynomial. In all cases our approach shows robustness against experimental imperfections.
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 measured operators. Violation of this inequality does not imply, however, genuine multipartite non-locality. We show more generically how the problem of identifying genuine tripartite entanglement in a device-independent way can be addressed through semidefinite programming.
Recently [Cavalcanti textit{et al.} Nat Commun textbf{6}, 7941 (2015)] proposed a method to certify the presence of entanglement in asymmetric networks, where some users do not have control over the measurements they are performing. Such asymmetry naturally emerges in realistic situtations, such as in cryptographic protocols over quantum networks. Here we implement such semi-device independent techniques to experimentally witness all types of entanglement on a three-qubit photonic W state. Furthermore we analise the amount of genuine randomness that can be certified in this scenario from any bipartition of the three-qubit W state.
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