Generalized Schmidt decomposition based on injective tensor norm

Details Generalized Schmidt decomposition based on injective tensor norm Generalized Schmidt decomposition based on injective tensor norm

2008-09-08

arxiv.org/abs/0809.1290v2

Physics

Quantum Physics

rewritten as a regular paper, necessary and sufficient conditions are derived for the existence of completely mixed subsystems

Scientific paper

We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm of the state. The largest coefficient quantifies the quantum correlation of the state. Other coefficients have a lot of information such as the unentangled particles as well as the particles whose reduced states are completely mixed. The decomposition clearly distinguishes the states entangled in inequivalent ways and have an information on the applicability to the teleportation and superdense coding when the given quantum state is used as a quantum channel.

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