On distinguishability distillation and dilution exponents
arXiv:2202.12433 · doi:10.1007/s11128-022-03735-y
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.
arXiv commentv2: 29 pages, minor changes, published in Quantum Information Processing
References in corpus (23)
- On quantum Renyi entropies: a new generalization and some properties
- Distance measures to compare real and ideal quantum processes
- The Quantum Chernoff Bound
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- One-Shot Classical-Quantum Capacity and Hypothesis Testing
- Sandwiched Rényi Divergence Satisfies Data Processing Inequality
- Monotonicity of a relative Rényi entropy
- Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- The quantum capacity of channels with arbitrarily correlated noise
- Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
- Resource theory of asymmetric distinguishability for quantum channels
- Relative submajorization and its use in quantum resource theories
- Resource theory of asymmetric distinguishability
- Generalized Entropies
- Optimized quantum f-divergences and data processing
- Applications of position-based coding to classical communication over quantum channels
- Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
- Lower bound on the relative error of mixed-state cloning and related operations
- An information-theoretic treatment of quantum dichotomies
- 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