Quantum Rényi Divergences and the Strong Converse Exponent of State Discrimination in Operator Algebras

Strong converse exponent for classical-quantum channel coding

Milán Mosonyi 2, 3, ∗ and Tomohiro Ogawa † Institute for Advanced Studies, Technische Universität München, Lichtenbergstraße 2a, 85748 Garching, Germany Zentrum Mathematik, M5, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany Mathematical Institute, Budapest University of Technology and Economics, Egry József u 1., Budapest, 1111 Hungary. Graduate School of Information...

Strong converse theorems using Rényi entropies

A strong converse for the quantum state merging protocol

The Polyanskiy-Verdú paradigm provides an elegant way of using generalizeddivergences to obtain strong converses and thus far has remained confined to protocols involving channels (classical or quantum). In this paper, drawing inspirations from it, we provide strong converses for protocols involving LOCC (local operations and classical communication). The key quantity that we work with is the R...

Strong Converse Inequality for a Spherical Operator

In the paper titled as “Jackson-type inequality on the sphere” 2004 , Ditzian introduced a spherical nonconvolution operator Ot,r , which played an important role in the proof of the wellknown Jackson inequality for spherical harmonics. In this paper, we give the lower bound of approximation by this operator. Namely, we prove that there are constants C1 and C2 such that C1ω2r f, t p ≤ ‖Ot,rf − ...

Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication

We study the difficulty of discriminating between an arbitrary quantum channel and a “replacer” channel that discards its input and replaces it with a fixed state.1 The results obtained here generalize those known in the theory of quantum hypothesis testing for binary state discrimination. We show that, in this particular setting, the most general adaptive discrimination strategies provide no a...