An application of a matrix inequality in quantum information theory

Details An application of a matrix inequality in quantum information theory An application of a matrix inequality in quantum information theory

2004-12-06

arxiv.org/abs/quant-ph/0412046v1

Physics

Quantum Physics

Presented at ICMP 2003, Lisbon, Portugal

Scientific paper

Quantum information theory has generated several interesting conjectures involving products of completely positive maps on matrix algebras, also known as quantum channels. In particular it is conjectured that the output state with maximal p-norm from a product channel is always a product state. It is shown here that the Lieb-Thirring inequality can be used to prove this conjecture for one special case, namely when one of the components of the product channel is of the type known as a diagonal channel, which acts on a state by taking the Hadamard product with a positive matrix.

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