Proof of the Gaussian maximizers conjecture for the communication capacity of noisy heterodyne measurements
arXiv:2206.02133 · doi:10.1007/s11005-023-01634-6
Abstract
Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for a long-standing conjecture on optimality of Gaussian encondings for the ultimate communication rate of generalized heterodyne receivers under the oscillator energy constraint. Our results generalize previous ones (obtained under the assumption of validity of the energy threshold condition) and show a drastic difference in the structure of the optimal encoding within and beyond this condition. The core of the proof in the case beyond the threshold is a new log-Sobolev type inequality, which relates the generalized Wehrl entropy with the wavefunction gradient.
arXiv comment18 pages
References in corpus (17)
- General Entanglement Breaking Channels
- Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
- A solution of the Gaussian optimizer conjecture
- Quantum state majorization at the output of bosonic Gaussian channels
- Information capacity of quantum observable
- Capacity of optical communication in loss and noise with general Gaussian receivers
- Majorization and additivity for multimode bosonic Gaussian channels
- The Holevo capacity of infinite dimensional channels and the additivity problem
- Equivalence Relations for the Classical Capacity of Single-Mode Gaussian Quantum channels
- Information capacity of continuous variable measurement channel
- Gaussian benchmark for optical communication aiming towards ultimate capacity
- Gaussian maximizers for quantum Gaussian observables and ensembles
- On the classical capacity of quantum Gaussian measurement
- On the constrained classical capacity of infinite-dimensional covariant quantum channels
- Accessible information of a general quantum Gaussian ensemble
- The structure of general quantum Gaussian observable
- Uncertainty relations with quantum memory for the Wehrl entropy