Grunnleggende konsepter
Establishing optimal second-order rates for quantum information decoupling.
Sammendrag
The content delves into the analysis of optimal second-order rates for quantum information decoupling. It covers the standard quantum decoupling protocol, applications in entanglement distillation, and achievability bounds. The paper provides detailed proofs and comparisons with existing results.
Directory:
- Introduction
- Discusses the importance of quantum decoupling.
- Quantum Decoupling
- Defines the process and error criteria.
- Presents one-shot characterizations and asymptotic expansions.
- Proof of Achievability Bound
- Demonstrates lower bound proof using randomizing channels.
- Proof of Converse Bound
- Establishes upper bound proof based on trace distance estimates.
- Application: Entanglement Distillation
- Applies decoupling results to derive lower bounds for maximal distillable entanglement.
Statistikk
Due to the importance of quantum decoupling, there have been extensive studies on the one-shot characterizations for ℓε(A | E)ρ.
Tight one-shot and asymptotic characterizations have been obtained when purified distance [10] is used as the error criterion [11–14].
Our main result is a lower and upper bound of one-shot characterization of maximal remainder dimension: log ℓε(A | E)ρ ≈1/2 (log |A| + H1−ε±δ h (A | E)ρ).
In i.i.d. scenario, our result leads to optimal second-order asymptotic rate: log ℓε(An|En)ρ⊗n = n[1/2(log |A| + H(A|E)ρ)] + 1/2√nV (A|E)ρ Φ−1(ε) + O(log n).
Sitater
"Due to the importance of quantum decoupling, there have been extensive studies on the one-shot characterizations."
"Tight one-shot and asymptotic characterizations have been obtained when purified distance is used as the error criterion."
"Our main result is a lower and upper bound of one-shot characterization of maximal remainder dimension."