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Existence of the Schmidt decomposition for tripartite systems

Arun K. Pati
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Abstract

For any bipartite quantum system the Schmidt decomposition allows us to express the state vector in terms of a single sum instead of double sums. We show the existence of the Schmidt decomposition for tripartite system under certain condition. If the partial inner product of a basis (belonging to a Hilbert space of smaller dimension) with the state of the composite system gives a disentangled basis, then the Schmidt decomposition for a tripartite system exists. In this case the reduced density matrix of each of the subsystem has equal spectrum in the Schmidt basis.

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Arun K. Pati. 2000-07-11. Existence of the Schmidt decomposition for tripartite systems. https://doi.org/10.1016/s0375-9601(00)00767-2

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