On distinguishability distillation and dilution exponents

Abstract

In this note, I define error exponents and strong converse exponents for the tasks of distinguishability distillation and dilution. These are counterparts to the one-shot distillable distinguishability and the one-shot distinguishability cost, as previously defined in the resource theory of asymmetric distinguishability. I show that they can be evaluated by semi-definite programming, establish a number of their properties, bound them using Renyi relative entropies, and relate them to each other.

v2: 29 pages, minor changes, published in Quantum Information Processing

References in corpus (4)

• The Quantum Chernoff Bound
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification
• Multiple Quantum Hypothesis Testing Expressions and Classical-Quantum Channel Converse Bounds