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arXiv:2011.01705 · International Journal of Theoretical Physics

Entanglement Witnesses Based on Symmetric Informationally Complete Measurements

Tao Li, Le-Min Lai, Deng-Feng Liang, Shao-Ming Fei, Zhi-Xi Wang

Published Oct 23, 2020• 13 citations
arXivHTMLPDF
DOI
10.1007/s10773-020-04615-w

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In this work, we show that measurement in quantum 2-design, such as mutually unbiased bases (MUBs) or symmetric, informationally complete states (SICs), improves the capability of detecting entangled states both theoretically and experimentally. On the theoretical side, we show that measurement in quantum 2-design can detect entangled states twice compared to entanglement witnesses. On the implementation side, we present the scheme of entanglement detection with two detectors only of a Hong-Ou-Mandel interferometer. The experimental scheme applies single-copy level measurement followed by post-processing of measurement outcomes, which is feasible with current technologies.
Abstract The connection between uncertainty and entanglement is a prevalent topic in quantum information processing. Based on a broad class of informationally complete symmetric measurements, which can be viewed as a common generalization of symmetric, informationally complete positive operator-valued measures and mutually unbiased bases, a conical 2-design is calculated. This design plays a crucial role in quantum measurement theory. Subsequently, the relation between the uncertainty and the entanglement for a set of measurements is portrayed using conditional collision entropy. Furthermore, a tighter lower bound of the uncertainty relation is discussed according to the characterization of the entropic bound. Finally, the relation is applied to entanglement witnesses. It is demonstrated that the present results are unified and comprehensive.