Degradability of Bosonic Gaussian channels

2006/03/31 by Filippo Caruso, Vittorio Giovannetti · 96 citations
Computer Science · Mathematics · Physics and Astronomy · #Additive function #Beam splitter #Combinatorics #Discrete mathematics #Equivalence (formal languages) #Gaussian #Laser #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Topology (electrical circuits) #Unitary state #cond-mat.other #physics.optics #quant-ph

paper · pdf · doi:10.1103/physreva.74.062307

published in Physical Review A 74(6) (American Physical Society) · 7 pages, 1 figure, 1 table (minor editing)

openalex publication_date 2006/12/13 · arxiv created 2007/02/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The notion of weak-degradability of quantum channels is introduced by generalizing the degradability definition given by Devetak and Shor. Exploiting the unitary equivalence with beam-splitter/amplifier channels we then prove that a large class of one-mode Bosonic Gaussian channels are either weakly degradable or anti-degradable. In the latter case this implies that their quantum capacity Q is null. In the former case instead, this allows us to establish the additivity of the coherent information for those maps which admit unitary representation with single-mode pure environment.

Citations

• Capacity of the noisy quantum channel
• Capacities of Quantum Erasure Channels
• A single quantum cannot be cloned
• Quantum information theory

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