2001/05/13 by Jim Harrington, John Preskill · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Code (set theory) #Computer science #Gaussian #Hilbert space #Lattice (music) #Mathematics #Phase space #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum capacity #Quantum channel #Quantum information #Quantum mechanics #Quantum network #Quantum-Dot Cellular Automata #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.64.062301
published as Phys. Rev. A 64, 062301 (2001) · 12 pages, 4 eps figures, REVTeX
arxiv created 2001/05/13 · openalex publication_date 2001/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.