On simultaneous min-entropy smoothing

Abstract

In the context of network information theory, one often needs a multiparty probability distribution to be typical in several ways simultaneously. When considering quantum states instead of classical ones, it is in general difficult to prove the existence of a state that is jointly typical. Such a difficulty was recently emphasized and conjectures on the existence of such states were formulated. In this paper, we consider a one-shot multiparty typicality conjecture. The question can then be stated easily: is it possible to smooth the largest eigenvalues of all the marginals of a multipartite state ρ simultaneously while staying close to ρ? We prove the answer is yes whenever the marginals of the state commute. In the general quantum case, we prove that simultaneous smoothing is possible if the number of parties is two or more generally if the marginals to optimize satisfy some non-overlap property.

5 pages

References in corpus (1)

• Multiparty quantum protocols for assisted entanglement distillation

Cited by in corpus (10)

• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Smooth Entropy Bounds on One-Shot Quantum State Redistribution
• Random tensor networks with nontrivial links
• A minimax approach to one-shot entropy inequalities
• On the near-optimality of one-shot classical communication over quantum channels
• Thermodynamic Implementations of Quantum Processes
• A Quantum Multiparty Packing Lemma and the Relay Channel
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• One-shot inner bounds for sending private classical information over a quantum MAC
• Tight relations and equivalences between smooth relative entropies