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arXiv:quant-ph/0608168 · Physical Review A

Single-experiment-detectable multipartite entanglement witness for ensemble quantum computing

Robabeh Rahimi, Akira SaiToh, Mikio Nakahara, Masahiro Kitagawa

Published Mar 12, 2007• 9 citations
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Abstract

In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of the entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single-qubit measurements are performed simultaneously; hence complete detection of entanglement is performed in a single-run experiment. In this sense, our scheme is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state for detection of entanglement.

DOI
10.1103/physreva.75.032317

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In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of the entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single-qubit measurements are performed simultaneously; hence complete detection of entanglement is performed in a single-run experiment. In this sense, our scheme is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state for detection of entanglement.
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.
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.
Recent progress in theories of quantum information has determined nonclassical correlation defined differently from the widely used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasible for implementation in bulk-ensemble systems.
How can a multipartite single-photon path-entangled state be certified efficiently by means of local measurements? We address this question by constructing an entanglement witness based on local photon detections preceded by displacement operations to reveal genuine multipartite entanglement. Our witness is defined as a sum of three observables that can be measured locally and assessed with two measurement settings for any number of parties N . For any bipartition, the maximum mean value of the witness observable over biseparable states is bounded by the maximum eigenvalue of an N×N matrix, which can be computed efficiently. We demonstrate the applicability of our scheme by experimentally testing the witness for heralded 4- and 8-partite single-photon path-entangled states. Our implementation shows the scalability of our witness and opens the door for distributing photonic multipartite entanglement in quantum networks at high rates.