An application of a matrix inequality in quantum information theory

Abstract

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.

Presented at ICMP 2003, Lisbon, Portugal

References in corpus (3)

• Additivity for a class of unital qubit channels
• On some additivity problems in quantum information theory
• Maximization of capacity and p-norms for some product channels

Cited by in corpus (5)

• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• On complementary channels and the additivity problem
• Simplification of additivity conjecture in quantum information theory
• Quantum Entanglement Capacity with Classical Feedback
• Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity