Schmidt number of bipartite and multipartite states under local projections |
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Authors: | Lin Chen Yu Yang Wai-Shing Tang |
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Affiliation: | 1.School of Mathematics and Systems Science,Beihang University,Beijing,China;2.International Research Institute for Multidisciplinary Science,Beihang University,Beijing,China;3.Department of Mathematics,National University of Singapore,Singapore,Republic of Singapore |
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Abstract: | The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and local projections are fundamental operations in quantum physics. We investigate the relation between the Schmidt numbers of bipartite states and their projected states. We show that there exist bipartite positive partial transpose entangled states of any given Schmidt number. We further construct the notion of joint Schmidt number for multipartite states and explore its relation with the Schmidt number of bipartite reduced density operators. |
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