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arXiv:1911.00599 · Physical Review A

Improved entanglement detection with subspace witnesses

Won Kyu Calvin Sun, Alexandre Cooper, Paola Cappellaro

Published Jan 13, 2020• 12 citations
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Abstract

A ``subspace'' witness of entanglement, more robust than a typical state fidelity-based witness, is introduced and experimentally tested with a hybrid two-qubit system composed of electronic spins in diamond. Its straightforward implementation offers improved detection of specific genuine multipartite entangled states in noisy, intermediate-scale quantum processors.

DOI
10.1103/physreva.101.012319

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A ``subspace'' witness of entanglement, more robust than a typical state fidelity-based witness, is introduced and experimentally tested with a hybrid two-qubit system composed of electronic spins in diamond. Its straightforward implementation offers improved detection of specific genuine multipartite entangled states in noisy, intermediate-scale quantum processors.
Abstract Genuine multipartite entanglement (GME) is arguably the most valuable form of entanglement in the multipartite case with application for instance in quantum metrology. In order to detect that form of entanglement in multipartite quantum states, one typically uses entanglement witnesses. The aim of this paper is to generalize the results of Tóth and Gühne (2005 Phys. Rev. A 72 022340) in order to provide a construction of witnesses of GME tailored to entangled subspaces originating from the multi-qudit stabilizer formalism—a framework well known for its role in quantum error correction, which also provides a very convenient description of a broad class of entangled multipartite states (both pure and mixed). Our construction includes graph states of arbitrary local dimension. We then show that in certain situations, the obtained witnesses detecting GME in quantum systems of higher local dimension are superior in terms of noise robustness to those derived for multiqubit states.
We present entanglement witness operators for detecting genuine multipartite entanglement. These witnesses are robust against noise and require only two local measurement settings when used in an experiment, independent of the number of qubits. This allows detection of entanglement for an increasing number of parties without a corresponding increase in effort. The witnesses presented detect states close to Greenberger-Horne-Zeilinger, cluster, and graph states. Connections to Bell inequalities are also discussed.
Hybrid encoding of quantum information is a promising approach towards the realization of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable resource for quantum information protocols. In this work we present a hybrid entanglement witness that can be implemented on available experiments and is robust to noise currently observed in quantum optical setups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterized with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables.
Standard procedures for entanglement detection assume that experimenters can exactly implement specific quantum measurements. Here, we depart from such idealizations and investigate, in both theory and experiment, the detection of genuine multipartite entanglement when measurements are subject to small imperfections. For arbitrary qubits number n, we construct multipartite entanglement witnesses where the detrimental influence of the imperfection is independent of n. In a tabletop four-partite photonic experiment, we demonstrate first how a small amount of alignment error can undermine the conclusions drawn from standard entanglement witnesses and then perform the correction analysis. Furthermore, since we consider quantum devices that are trusted but not perfectly controlled, we showcase advantages in terms of noise resilience as compared to device-independent models.
Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be elusive as a result of experimental imperfections. Here, we introduce and demonstrate a novel procedure for entanglement detection which simply and seamlessly improves any standard witnessing procedure by using additional available information to tighten the witnessing bounds. Moreover, by relaxing the requirements on the witness operators, our method removes the general need for the difficult task of witness decomposition into local observables. We experimentally demonstrate entanglement detection with our approach using a separable test operator and a simple fixed measurement device for each agent. Finally, we show that the method can be generalized to higher-dimensional and multipartite cases with a complexity that scales linearly with the number of parties.