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arXiv:2106.05796 · Journal of Physics A Mathematical and Theoretical

Measurement-device-independent nonlinear entanglement witnesses

Kornikar Sen, Chirag Srivastava, Ujjwal Sen

Published Jul 5, 2023• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1751-8121/ace4a5

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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.
The concept of entanglement witnesses forms a useful technique to detect entanglement in realistic quantum devices. Measurement-device-independent nonlinear entanglement witnesses (MDI-NEWs) are a kind of entanglement witness that eliminates dependence on the correct alignments of measurement devices for guaranteeing the existence of entanglement and also detects more entangled states than its linear counterparts. While this method guarantees entanglement independent of measurement alignments, it is still prone to serving wrong results due to other loopholes. Here, we study the response of MDI-NEWs to two categories of faults occurring in experiments. In the first category, the detection loophole, characterized by lost and additional events of outcomes of measurements, is investigated, and bounds which guarantee entanglement are obtained in terms of the efficiency of measurement being performed. In the second category, we study noise associated with the sets of additional quantum inputs required in MDI-NEW scenarios. In this case, a type of noise is identified which still allows the MDI-NEWs to guarantee entanglement. We also show that MDI-NEWs are less or equally robust in comparison to their linear counterparts under the same noise in additional quantum inputs, although the former group detects a larger volume of entangled states in the noiseless scenario than their linear cousins.
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.
Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EWs) are used in order to prove the presence of entanglement in a quantum state. EWs can be constructed from available measurement results and do not require a reconstruction of the whole density matrix (full tomography), which is especially valuable for high-dimensional systems. We provide a method to construct accessible nonlinear EWs, which incorporate two important properties. First, they improve on linear EWs in the sense that each nonlinear EW detects more entangled states than its linear counterpart and therefore allows the verification of entanglement without critical dependence on having found the ``right'' linear witness. Second, they can be evaluated using exactly the same data as for the evaluation of the original linear witness. This allows a reanalysis of published experimental data to strengthen statements about entanglement verification without the requirement to perform additional measurements. These particular properties make the accessible nonlinear EWs attractive for the implementations in current experiments, for they can also enhance the statistical significance of the entanglement verification.
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.