One-shot quantum state redistribution and quantum Markov chains
arXiv:2104.08753 · doi:10.1109/TIT.2023.3271316
Abstract
We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution.
arXiv commentv2: Exposition improved, references added, typos corrected. 32 pages, 2 figures. v1: 26 pages, 2 figures
References in corpus (31)
- On quantum Renyi entropies: a new generalization and some properties
- Distance measures to compare real and ideal quantum processes
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- Coding Theorem and Strong Converse for Quantum Channels
- Structure of states which satisfy strong subadditivity of quantum entropy with equality
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
- One-Shot Classical-Quantum Capacity and Hypothesis Testing
- A Fully Quantum Asymptotic Equipartition Property
- A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
- Duality Between Smooth Min- and Max-Entropies
- The quantum capacity of channels with arbitrarily correlated noise
- Second-order asymptotics for quantum hypothesis testing
- Embezzling Entangled Quantum States
- One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
- Robustness of quantum Markov chains
- Quantum message compression with applications
- Renyi generalizations of the conditional quantum mutual information
- Smooth Max-Information as One-Shot Generalization for Mutual Information
- Entanglement of the Antisymmetric State
- Sine distance for quantum states
- Lower bound on the relative error of mixed-state cloning and related operations
- Strong converse theorems using Rényi entropies
- Smooth Entropy Bounds on One-Shot Quantum State Redistribution
- Quantum state discrimination bounds for finite sample size
- Deconstruction and conditional erasure of quantum correlations
- Partially smoothed information measures
- A one-shot achievability result for quantum state redistribution
- Conditional Decoupling of Quantum Information
- Efficient methods for one-shot quantum communication
- What is Possible Without Disturbing Partially Known Quantum States?
- A unified approach to source and message compression