The Communication Value of a Quantum Channel
From MaRDI portal
Publication:6194003
DOI10.1109/TIT.2022.3218540arXiv2109.11144MaRDI QIDQ6194003
Author name not available (Why is that?), Eric Chitambar, Marius Junge, Author name not available (Why is that?)
Publication date: 19 March 2024
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional min-entropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.
Full work available at URL: https://arxiv.org/abs/2109.11144
Related Items (1)
This page was built for publication: The Communication Value of a Quantum Channel
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6194003)
