Abstract
A way of constructing special entangled basis with fixed Schmidt number 2 (SEB2) in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) is proposed, and the conditions mutually unbiased SEB2s (MUSEB2s) satisfy are discussed. In addition, a very easy way of constructing MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\) is presented. We first establish the concrete construction of SEB2 and MUSEB2s in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4}\) and \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{8}\), respectively, and then generalize them into \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k\in z^+,3\not \mid k)\) and display the condition that MUSEB2s satisfy; we also give general form of two MUSEB2s as examples in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}(k=2^l)\).
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This work is supported by Natural Science Foundation of China under Numbers 11361065, 11761073.
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Han, YF., Zhang, GJ., Yong, XL. et al. Mutually unbiased special entangled bases with Schmidt number 2 in \({\mathbb {C}}^3 \otimes {\mathbb {C}}^{4k}\). Quantum Inf Process 17, 58 (2018). https://doi.org/10.1007/s11128-018-1824-y
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DOI: https://doi.org/10.1007/s11128-018-1824-y