Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs

2005/11/30 by Tohya Hiroshima · 2 citations
Mathematics · Physics and Astronomy · #Additive function #Additive white Gaussian noise #Algorithm #Discrete mathematics #Entropy (arrow of time) #Gaussian #Gaussian noise #Majorization #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical physics #Statistics #Symplectic geometry #White noise #quant-ph

paper · pdf · doi:10.1103/physreva.73.012330

published as Phys. Rev. A 73, 012330 (2006) · 9 pages, no figures. Published Version

openalex publication_date 2006/01/23 · arxiv created 2006/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove multiplicativity of maximal output p norm of classical noise channels and thermal noise channels of arbitrary modes for all p>1 under the assumption that the input signal states are Gaussian states. As a direct consequence, we also show the additivity of the minimal output entropy and that of the energy-constrained Holevo capacity for those Gaussian channels under Gaussian inputs. To the best of our knowledge, newly discovered majorization relation on symplectic eigenvalues, which is also of independent interest, plays a central role in the proof.

Citations

• Strong superadditivity of the entanglement of formation follows from its additivity
• Additivity of the classical capacity of entanglement-breaking quantum channels
• Matrix Analysis

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