Strong Converse Exponent of Quantum State Merging

arXiv (Cornell University)

Abstract

We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $α$-$z$ conditional Rényi entropies with $z=α/2\in[1/2,1]$. This contrasts with the sandwiched conditional Rényi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.

Authors 4

1. Mario Berta Aachen Institute for Quantum Information

   Imperial College London · RWTH Aachen University

   Affiliation as printed

   Department of Computing , Imperial College London , United Kingdom

   Institute for Quantum Information , RWTH Aachen University , Germany

2. Hao-Chung Cheng
3. Roberto Rubboli

   University of Copenhagen

   Affiliation as printed

   Department of Mathematical Sciences , University of Copenhagen , Universitetsparken 5 , 2100 Denmark

4. Marco Tomamichel

   Centre for Quantum Technologies · National University of Singapore

   Affiliation as printed

   Centre for Quantum Technologies , National University of Singapore , Singapore 117543 , Singapore

   Department of Electrical and Computer Engineering , National University of Singapore , Singapore 117583 , Singapore