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arXiv · 1805.12274

Necessary and sufficient condition for the existence of Schmidt decomposition in multipartite Hilbert spaces

Spandan Das·Goutam Paul
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Abstract

Pati (Physics Letters A, 2000) derived a sufficient condition for the existence of Schmidt decomposition in tripartite Hilbert spaces. In this paper, we show that the condition is erroneous by demonstrating some counter-examples. Moreover, we suitably modify the condition and provide a correctness proof. We also show for the first time how this can be generalized to $n$-partite Hilbert spaces for any $n\geq 2$. Finally, we prove that this condition is also a necessary condition.

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Spandan Das, Goutam Paul. 2018-05-31. Necessary and sufficient condition for the existence of Schmidt decomposition in multipartite Hilbert spaces. https://arxiv.org/abs/1805.12274

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