Approximate quantum error correction for generalized amplitude damping errors
arXiv:1308.4582 · doi:10.1103/PhysRevA.89.022316
Abstract
We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the non-zero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analogue of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error correction framework for the GAD error model. We also analytically recover and/or clarify some previously known numerical results in the limiting case of vanishing temperature of the environment, the well-known traditional amplitude damping channel. In addition, our study suggests that degenerate stabilizer codes and self-complementary nonadditive codes are especially suitable for the error correction of the GAD noise model. Finally, comparing the properly normalized entanglement fidelities of the best performant stabilizer and nonadditive codes characterized by the same length, we show that nonadditive codes outperform stabilizer codes not only in terms of encoded dimension but also in terms of entanglement fidelity.
44 pages, 8 figures, improved v2
References in corpus (22)
- Multi-party entanglement in graph states
- An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
- Strong Resilience of Topological Codes to Depolarization
- Degenerate Quantum Codes for Pauli Channels
- Codeword Stabilized Quantum Codes
- The squeezed generalized amplitude damping channel
- Quantum Error Correcting Codes Using Qudit Graph States
- Optimum Quantum Error Recovery using Semidefinite Programming
- Structured Near-Optimal Channel-Adapted Quantum Error Correction
- Geometric Phase of a qubit interacting with a squeezed-thermal bath
- Nonadditive quantum error-correcting code
- A simple family of nonadditive quantum codes
- Quantum error correction may delay, but also cause, entanglement sudden death
- Quantum Stabilizer Codes Embedding Qubits Into Qudits
- Encoding One Logical Qubit Into Six Physical Qubits
- Towards a Unified Framework for Approximate Quantum Error Correction
- Entanglement properties of optical coherent states under amplitude damping
- Nonadditive quantum error correcting codes adapted to the ampltitude damping channel
- Channel-Adapted Quantum Error Correction
- Quantum error correction and detection: quantitative analysis of a coherent-state amplitude damping code
- Two infinite families of nonadditive quantum error-correcting codes
- Assessing quantum error correction: fidelity and entanglement measures with application to photonic codes
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