Information-theoretic interpretation of quantum error-correcting codes

Abstract

Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that "redundant" information can be distributed over quantum bits even though this does not violate the quantum "no-cloning" theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analogue of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.

14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev. A

References in corpus (2)

• Codes for the Quantum Erasure Channel
• Quantum Stabilizer Codes and Classical Linear Codes

Cited by in corpus (19)

• Information-theoretic approach to the study of control systems
• Entanglement-Assisted Quantum Communication Beating the Quantum Singleton Bound
• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• Experimental Realization of A Two Bit Phase Damping Quantum Code
• Constructing optimal quantum error correcting codes from absolute maximally entangled states
• $k$-Uniform states and quantum information masking
• Quantum secret sharing for general access structures
• Crystalline Quantum Circuits
• A degeneracy bound for homogeneous topological order
• Entropic bounds on coding for noisy quantum channels
• Nonlocal quantum information in bipartite quantum error correction
• Probing Quantum Telecloning on Superconducting Quantum Processors
• Reducing circuit depth with qubitwise diagonalization
• Semidefinite programming bounds on the size of entanglement-assisted codeword stabilized quantum codes
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• A scheme to protect against multiple quantum erasures
• Absolutely maximally entangled pure states of multipartite quantum systems
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Multiqubit monogamy relations beyond shadow inequalities