Single-shot entanglement manipulation of states and channels revisited
arXiv:2312.17088 · doi:10.1109/TIT.2025.3570770
Abstract
We study entanglement distillation and dilution of states and channels in the single-shot regime. With the help of a recently introduced conversion distance, we provide compact closed-form expressions for the dilution and distillation of pure states and show how this can be used to efficiently calculate these quantities on multiple copies of pure states. These closed-form expressions also allow us to obtain second-order asymptotics. We then prove that the epsilon-single-shot entanglement cost of mixed states is given exactly in terms of an expression containing a suitably smoothed version of the conditional max-entropy. For pure states, this expression reduces to the smoothed max-entropy of the reduced state. Based on these results, we bound the single-shot entanglement cost of channels. We then turn to the one-way entanglement distillation of states and channels and provide bounds in terms of a quantity we denote coherent information of entanglement.
10+33 pages, comments welcome!
References in corpus (19)
- Distillation of secret key and entanglement from quantum states
- Quantum information can be negative
- Post-selection technique for quantum channels with applications to quantum cryptography
- Transforming quantum operations: quantum supermaps
- A Sharp Fannes-type Inequality for the von Neumann Entropy
- Necessary and Sufficient Conditions for the Trumping Relation
- Catalytic Conversion Probabilities for Bipartite Pure States
- Distilling entanglement from arbitrary resources
- Dynamical Entanglement
- Fundamental limitations on distillation of quantum channel resources
- Catalysis of entanglement and other quantum resources
- No-go theorems for quantum resource purification II: new approach and channel theory
- One-Shot Manipulation of Dynamical Quantum Resources
- Optimal Extensions of Resource Measures and their Applications
- One-Shot Yield-Cost Relations in General Quantum Resource Theories
- One-shot manipulation of entanglement for quantum channels
- Entanglement resource theory of quantum channel
- Complete Characterization of Entanglement Embezzlement
- One-Shot Static Entanglement Cost of Bipartite Quantum Channels