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Physical Review Letters

Measurement-Device-Independent Entanglement Witness of Tripartite Entangled States and Its Applications

Zheng-Da Li, Qi Zhao, Rui Zhang, Li-Zheng Liu, Xu-Fei Yin, Xingjian Zhang, Yue-Yang Fei, Kai Chen, Nai-Le Liu, Feihu Xu, Yu-Ao Chen, Li Li, Jian-Wei Pan

Published Apr 24, 2020• 23 citations
Publisher

Abstract

Entanglement witness is of great importance in characterizing quantum systems. The imperfections in conventional entanglement witness schemes could lead to the misidentification of a separated state as an entangled state. Measurement-device-independent entanglement witness (MDIEW) has been proposed and demonstrated to resolve the imperfect measurement devices. So far, however, the MDIEW has been restricted to a two-party qubit entangled state. Here, for the first time, we demonstrate MDIEW for multipartite entangled states. We experimentally detect the genuine entanglement and the entanglement structure of a tripartite entangled state based on an eight-photon interferometry. Furthermore, with the verified multipartite entangled state, we demonstrate quantum randomness generation and open-destination quantum key distribution in an measurement-device-independent manner. Our research presents an important step toward building a robust and secure quantum network.

DOI
10.1103/physrevlett.124.160503

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Entanglement witness is of great importance in characterizing quantum systems. The imperfections in conventional entanglement witness schemes could lead to the misidentification of a separated state as an entangled state. Measurement-device-independent entanglement witness (MDIEW) has been proposed and demonstrated to resolve the imperfect measurement devices. So far, however, the MDIEW has been restricted to a two-party qubit entangled state. Here, for the first time, we demonstrate MDIEW for multipartite entangled states. We experimentally detect the genuine entanglement and the entanglement structure of a tripartite entangled state based on an eight-photon interferometry. Furthermore, with the verified multipartite entangled state, we demonstrate quantum randomness generation and open-destination quantum key distribution in an measurement-device-independent manner. Our research presents an important step toward building a robust and secure quantum network.
The robust estimation of entanglement is key to the validation of implementations of quantum systems. On the one hand, the evaluation of standard entanglement measures, either using quantum tomography or using quantitative entanglement witnesses, requires perfect implementation of measurements. On the other hand, measurement-device-independent entanglement witnesses (MDIEWs) can certify entanglement of all entangled states using untrusted measurement devices. We show that MDIEWs can be used as well to quantify entanglement according to standard entanglement measures, and we present a practical method to derive such witnesses using experimental data only.
Imperfections in experimental measurement schemes can lead to falsely identifying, or over estimating, entanglement in a quantum system. A recent solution to this is to define schemes that are robust to measurement imperfections-measurement-device-independent entanglement witness (MDI-EW). This approach can be adapted to witness all entangled qubit states for a wide range of physical systems and does not depend on detection efficiencies or classical communication between devices. Here we extend the theory to remove the necessity of prior knowledge about the two-qubit states to be witnessed. Moreover, we tested this model via a novel experimental implementation for MDI-EW that significantly reduces the experimental complexity. By applying it to a bipartite Werner state, we demonstrate the robustness of this approach against noise by witnessing entanglement down to an entangled state fraction close to 0.4.
The reliable detection of entanglement plays a crucial role in the construction of quantum networks. The conventional entanglement witness (EW) method has high requirements for measurement device and relies on reliable implementation of the measurement. With unreliable measurement device, EW process can be easily attacked by eavesdroppers, which can lead to incorrect entanglement detection results. Therefore, a feasible and secure measurement device independent entanglement witness (MDIEW) method is desired for constructing quantum networks. Here, we detect the continuous variable entanglement by a MDIEW in a quantum network. It is demonstrated that the conventional EW method can be affected when the local oscillator intensity is changed, while the MDIEW method can detect entanglement between users without being affected. Our results provide a trustworthy method to detect entanglement, which is an important step for constructing secure quantum networks.
We experimentally demonstrated a protocol for measurement device independent entanglement witness (MDI-EW) presented in [1]. A measurement device independent (MDI) protocol will allow two parties (Alice and Bob) to verify that they share an entangled state via the help of trusted input states without making any assumption on the measurement device using only the statistics of the output of the measurement device. Verification of entanglement between states is important as entangled states are a commonly used resource in several aspects of quantum information science such as quantum key distribution. Experimental implementation of MDI-EW in discrete variables have previously been demonstrated in [2], [3].
Witnessing entanglement is crucial in quantum information processing. With properly preparing ancillary states, it has been shown previously that genuine entanglement can be witnessed without trusting measurement devices. In this work we generalize the scenario and show that generic multipartite entanglement structures, including entanglement of subsystems and entanglement depth, can be witnessed via measurement-device-independent means. As the original measurement-device-independent entanglement witness scheme exploits only one out of four Bell measurement outcomes for each party, a direct generalization to multipartite quantum states will inevitably cause inefficiency in entanglement detection after taking account of statistical fluctuations. To resolve this problem, we also present a way to utilize all the measurement outcomes. The scheme is efficient for multipartite entanglement detection and can be realized with state-of-the-art technologies.
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 identifying genuine tripartite entanglement in a device independent manner. We consider three mixed tripartite quantum states none of whose genuine entanglement can be detected by applying standard \emph{DIEW}s, but their genuine tripartite entanglement can be detected by applying the same when distributed in some suitable entanglement swapping network.