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On the local unitary equivalence of states of multi-partite systems

Mario Ziman·Peter Stelmachovic·Vladimir Buzek
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Abstract

Two pure states of a multi-partite system are alway are related by a unitary transformation acting on the Hilbert space of the whole system. This transformation involves multi-partite transformations. On the other hand some quantum information protocols such as the quantum teleportation and quantum dense coding are based on equivalence of some classes of states of bi-partite systems under the action of local (one-particle) unitary operations. In this paper we address the question: ``Under what conditions are the two states states, $\varrho$ and $σ$, of a multi-partite system locally unitary equivalent?'' We present a set of conditions which have to be satisfied in order that the two states are locally unitary equivalent. In addition, we study whether it is possible to prepare a state of a multi-qudit system. which is divided into two parts A and B, by unitary operations acting only on the systems A and B, separately.

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Mario Ziman, Peter Stelmachovic, Vladimir Buzek. 2001-07-03. On the local unitary equivalence of states of multi-partite systems. https://doi.org/10.1002/1521-3978(200110)49%3A10%2F11%3C1123%3A%3Aaid-prop1123%3E3.0.co%3B2-q

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