Existence of the Schmidt decomposition for tripartite systems

Details Existence of the Schmidt decomposition for tripartite systems Existence of the Schmidt decomposition for tripartite systems

1999-11-16

arxiv.org/abs/quant-ph/9911073v2

Physics

Quantum Physics

Latex prerpint style, 7 pages

Scientific paper

10.1016/S0375-9601(00)00767-2

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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