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Schmidt number of bipartite and multipartite states under local projections

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Lin Chen at Beihang University
Lin Chen
Yu Yang
Yu Yang
Yu Yang
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Wai-shing Tang
Wai-shing Tang
Wai-shing Tang
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Abstract

The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation 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 (PPT) entangled states of any given Schmidt number. We further construct the notion of joint Schmidt number for multipartite states, and its relation with the Schmidt number of bipartite reduced density operators.
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Quantum Inf Process (2017) 16:75
DOI 10.1007/s11128-016-1501-y
Schmidt number of bipartite and multipartite states
under local projections
Lin Chen1,2·Yu Yang3·Wai-Shing Tang3
Received: 4 October 2016 / Accepted: 15 December 2016 / Published online: 2 February 2017
© Springer Science+Business Media New York 2017
Abstract The Schmidt number is a fundamental parameter characterizing the prop-
erties 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.
Keywords Quantum states ·Local projections ·PPT entangled states ·
Schmidt number ·Joint Schmidt number ·Reduced density operators
1 Introduction
The Schmidt number is a parameter characterizing quantum states. A quantum state is
entangled if and only if its Schmidt number is greater than one. Entangled states play the
BYu Yang
a0086285@u.nus.edu.sg
Lin Chen
linchen@buaa.edu.cn
Wai-Shing Tang
mattws@nus.edu.sg
1School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
2International Research Institute for Multidisciplinary Science, Beihang University,
Beijing 100191, China
3Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road,
Singapore 119076, Republic of Singapore
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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