Information Rates Achievable with Algebraic Codes on Quantum Discrete Memoryless Channels
arXiv:quant-ph/0207113
Abstract
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension, and the codes that are proven to have the desired performance are symplectic stabilizer codes. On the depolarizing channel, this work's bound is actually the highest possible rate at which symplectic stabilizer codes work reliably.
25 pages, no figure. Ver.2: slight typographical errors and the inexact statement of a known result (Lemma 1) with a premise missing were corrected. Ver.3: Correction: In Lemma 3, `whose range is' should read `such that the ranges of rho and the adjoint of rho are'
References in corpus (9)
- Mixed State Entanglement and Quantum Error Correction
- Encoding a qubit in an oscillator
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- Quantum Error Correction and Orthogonal Geometry
- Information transmission through a noisy quantum channel
- Quantum Channel Capacity of Very Noisy Channels
- Achievable rates for the Gaussian quantum channel
- The quantum capacity is properly defined without encodings
- Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels