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Chinese Physics B

Detection and quantification of entanglement with measurement-device-independent and universal entanglement witness*

Zhi‐Jin Ke, Yi‐Tao Wang, Shang Yu, Wei Liu, Yu Meng, Zhipeng Li, Hang Wang, Qiang Li, Jin‐Shi Xu, Ya Xiao, Jian‐Shun Tang, Chuan‐Feng Li, Guang‐Can Guo

Published May 13, 2020• 8 citations
Publisher

Abstract

Entanglement is the key resource in quantum information processing, and an entanglement witness (EW) is designed to detect whether a quantum system has any entanglement. However, prior knowledge of the target states should be known first to design a suitable EW, which weakens this method. Nevertheless, a recent theory shows that it is possible to design a universal entanglement witness (UEW) to detect negative-partial-transpose (NPT) entanglement in unknown bipartite states with measurement-device-independent (MDI) characteristic. The outcome of a UEW can also be upgraded to be an entanglement measure. In this study, we experimentally design and realize an MDI UEW for two-qubit entangled states. All of the tested states are well-detected without any prior knowledge. We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography. The relation between them is also revealed. The entire experimental framework ensures that the UEW is MDI.

DOI
10.1088/1674-1056/ab9288

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Entanglement is the key resource in quantum information processing, and an entanglement witness (EW) is designed to detect whether a quantum system has any entanglement. However, prior knowledge of the target states should be known first to design a suitable EW, which weakens this method. Nevertheless, a recent theory shows that it is possible to design a universal entanglement witness (UEW) to detect negative-partial-transpose (NPT) entanglement in unknown bipartite states with measurement-device-independent (MDI) characteristic. The outcome of a UEW can also be upgraded to be an entanglement measure. In this study, we experimentally design and realize an MDI UEW for two-qubit entangled states. All of the tested states are well-detected without any prior knowledge. We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography. The relation between them is also revealed. The entire experimental framework ensures that the UEW is MDI.
Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information processing. But such a detection should be made in a device-independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as an entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement-device-independent way [Phys. Rev. Lett. 110, 060405 (2013)] does require information about the state. Here, by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A 77, 030301 (2008)], we provide a universal entanglement detection scheme for two-qubit states in a measurement-device-independent way. We also provide a set of universal witness operators for detecting NPT-ness (negative under partial transpose) of two-qudit states in a measurement-device-independent way. We conjecture that no such universal entanglement witness scheme exists for PPT (positive under partial transpose) entangled states. We also analyze the robustness of some of the experimental schemes---for detecting entanglement in a measurement-device-independent way---under the influence of noise in the inputs (from the referee) as well as in the measurement operator.
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.
Entanglement, the essential resource in quantum information processing, should be witnessed in many tasks such as quantum computing and quantum communication. The conventional entanglement witness method, relying on an idealized implementation of measurements, could wrongly conclude a separable state to be entangled due to imperfect detections. Inspired by the idea of a time-shift attack, we construct an attack on the conventional entanglement witness process and demonstrate that a separable state can be falsely identified to be entangled. To close such detection loopholes, based on a recently proposed measurement-device-independent entanglement witness method, we design and experimentally demonstrate a measurement-device-independent entanglement witness for a variety of two-qubit states. By the new scheme, we show that an entanglement witness can be realized without detection loopholes.
Entanglement is one of the most puzzling features of quantum theory and of great importance for the new field of quantum information. The determination whether a given state is entangled or not is one of the most challenging open problems of the field. Here we report on the experimental demonstration of measurement-device-independent (MDI) entanglement detection using witness method for general two qubits photon polarization systems. In the MDI settings, there is no requirement to assume perfect implementations or neither to trust the measurement devices. This experimental demonstration can be generalized for the investigation of properties of quantum systems and for the realization of cryptography and communication protocols.
Abstract Entanglement witnesses (EWs) are one of the most effective methods to detect entanglement. It is known that nonlinear EW provide better entanglement detection than their linear counterparts, in that the former detect a strictly larger subset of entangled states than the latter. Whether linear or nonlinear, the method is measurement-device dependent, so that imperfect measurements may cause false certification of entanglement in a shared state. Measurement-device-independent EW provide an escape from such measurement dependence of the entanglement detection for linear EW. Here we present measurement-device-independent nonlinear EW for non-positive partial transpose entangled states as well as for bound entangled states with positive partial transpose. Although the witness considered herein does not detect a larger set of entangled states than other nonlinear EW, it is more efficient in that it never leads to a false detection corresponding to wrong measurements. The constructed measurement-device-independent nonlinear EW certify the entanglement of the same sets of entangled states as their device-dependent parents do, and therefore are better than the linear EW, device-independent or otherwise.
Entanglement, a critical resource for quantum information processing, needs to be witnessed in many practical scenarios. Theoretically, witnessing entanglement is by measuring a special Hermitian observable, called an entanglement witness (EW), which has non-negative expected outcomes for all separable states but can have negative expectations for certain entangled states. In practice, an EW implementation may suffer from two problems. The first one is reliability. Due to unreliable realization devices, a separable state could be falsely identified as an entangled one. The second problem relates to robustness. A witness may not be optimal for a target state and fail to identify its entanglement. To overcome the reliability problem, we employ a recently proposed measurement-device-independent entanglement witness scheme, in which the correctness of the conclusion is independent of the implemented measurement devices. In order to overcome the robustness problem, we optimize the EW to draw a better conclusion given certain experimental data. With the proposed EW scheme, where only data postprocessing needs to be modified compared to the original measurement-device-independent scheme, one can efficiently take advantage of the measurement results to maximally draw reliable conclusions.