Decoding general error correcting codes and the role of complementarity
arXiv:2210.06661 · doi:10.1038/s41534-024-00951-5
Abstract
Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper, we show that a decoding circuit for Calderbank-Shor-Steane (CSS) codes can be straightforwardly extended to handle general QECCs. The key to the extension lies in the use of a pair of classical-quantum (CQ) codes associated with the QECC to be decoded. The decoding error of the proposed decoding circuit depends on the classical decoding errors of the CQ codes and their degree of complementarity. We demonstrate the power of the decoding circuit in a toy model of the black hole information paradox, improving decoding errors compared to previous results. In addition, we reveal that black hole dynamics may optimally encode quantum information but poorly encode classical information.
Ver.1: 20 pages, 3 figures. Ver.2: 20 pages, 3 figures, an unnecessary assumption, which rarely holds, was removed. Theorem 1 was slightly improved. Ver.3: 20 pages, 3 figures, abstract and introduction are improved. Ver. 4: 25 pages, 5 figures, major update. Ver. 5 published version
References in corpus (36)
- Measurement-based quantum computation with cluster states
- Black holes as mirrors: quantum information in random subsystems
- Fast Scramblers
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Chaos in quantum channels
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Chaos and complexity by design
- Towards the fast scrambling conjecture
- The Ryu-Takayanagi Formula from Quantum Error Correction
- Structure of states which satisfy strong subadditivity of quantum entropy with equality
- Aspects of generic entanglement
- Verified Quantum Information Scrambling
- Randomizing quantum states: Constructions and applications
- The Gravity Dual of Renyi Entropy
- Quantum conditional mutual information and approximate Markov chains
- Superdense coding of quantum states
- Theory of quantum system certification: a tutorial
- One-shot decoupling
- Relating quantum privacy and quantum coherence: an operational approach
- Decoupling with random quantum circuits
- Quantum algorithm for Petz recovery channels and pretty good measurements
- Decoupling with unitary approximate two-designs
- Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates
- Relative Thermalization
- Decoding quantum information via the Petz recovery map
- Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry
- One-shot quantum error correction of classical and quantum information
- Uncertainty relations and approximate quantum error correction
- One-Shot Randomized and Nonrandomized Partial Decoupling
- Decoupling with random diagonal unitaries
- Optimal State Merging Without Decoupling
- Low-depth random Clifford circuits for quantum coding against Pauli noise using a tensor-network decoder
- Hayden-Preskill Recovery in Hamiltonian Systems
- One-Shot Triple-Resource Trade-Off in Quantum Channel Coding