Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
arXiv:2304.12114 · doi:10.1007/s00220-024-05156-7
Abstract
We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old [Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)] and new methods [Dupuis, arXiv:2105.05342], we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of Rényi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, that is for only partially known i.i.d. source or channel, which are furthermore optimal for entanglement of assistance and state merging.
This second version includes new results on the achievable rates of multi-party assisted entanglement distillation and entanglement of assistance in the compound setting, as well as further comments and corrections. The idea of the telescoping trick has independently and concurrently been discovered for multipartite decoupling by Hao-Chung Cheng, Li Gao and Mario Berta. 39 pages, 6 figures
References in corpus (30)
- On quantum Renyi entropies: a new generalization and some properties
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Quantum information can be negative
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Holographic duality from random tensor networks
- Randomizing quantum states: Constructions and applications
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
- Quantum state merging and negative information
- The mother of all protocols: Restructuring quantum information's family tree
- Sandwiched Rényi Divergence Satisfies Data Processing Inequality
- Quantum Reverse Shannon Theorem
- Monotonicity of a relative Rényi entropy
- The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
- Entanglement of assistance and multipartite state distillation
- One-shot decoupling
- Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
- Relating different quantum generalizations of the conditional Renyi entropy
- Single-shot Quantum State Merging
- Playing Games with Multiple Access Channels
- A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
- Classical communication over a quantum interference channel
- "Pretty strong" converse for the quantum capacity of degradable channels
- Random tensor networks with nontrivial links
- Quantum to Classical Randomness Extractors
- Coding theorems for compound problems via quantum Rényi divergences
- On simultaneous min-entropy smoothing
- Distributed Private Randomness Distillation
- Decoupling with random diagonal unitaries
- Novel one-shot inner bounds for unassisted fully quantum channels via rate splitting
- One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC