Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems

Abstract

We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from subsequent iterations of the noise. We also demonstrate that in the case of unital noise operations one can identify a subset of all correctable subsystems -- those that can be corrected by a single unitary operation -- as the noiseless subsystems for the composition of the noise operation with its dual. Using the recently developed structure theory for noiseless subsystems, the identification of such unitarily correctable subsystems is reduced to an algebraic exercise.

Physical Review A, to appear, 8 pages

References in corpus (16)

• Mixed State Entanglement and Quantum Error Correction
• Decoherence Free Subspaces for Quantum Computation
• Noiseless Quantum Codes
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Computers and Dissipation
• A Theory of Quantum Error-Correcting Codes
• Preserving coherence in quantum computation by pairing quantum bits
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Stabilizer Formalism for Operator Quantum Error Correction
• A Unified and Generalized Approach to Quantum Error Correction
• Stabilizing Quantum Information
• Information-theoretic approach to quantum error correction and reversible measurement
• Quantum Error Correcting Codes From The Compression Formalism
• Constructing Qubits in Physical Systems
• A method to find quantum noiseless subsystems

Cited by in corpus (28)

• General entanglement-assisted quantum error-correcting codes
• Information preserving structures: A general framework for quantum zero-error information
• The structure of preserved information in quantum processes
• Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics
• Experimentally scalable protocol for identification of correctable codes
• Robust Quantum Error Correction via Convex Optimization
• Classical Enhancement of Quantum Error-Correcting Codes
• Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
• Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
• Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries
• The multiplicative domain in quantum error correction
• Multiplicative Properties of Quantum Channels
• Quantum error correction on infinite-dimensional Hilbert spaces
• Operator quantum error correction for continuous dynamics
• Entanglement-assisted Coding Theory
• Norms and Cones in the Theory of Quantum Entanglement
• Spectral Properties of Tensor Products of Channels
• Open-System Quantum Error Correction
• Optical implementation of a unitarily correctable code
• Protecting Quantum Information with Entanglement and Noisy Optical Modes
• Robustness of the concatenated quantum error-correction protocol against noise for channels affected by fluctuation
• Automated searching for quantum subsystem codes
• Generality of the concatenated five-qubit code
• Information flow at the quantum-classical boundary
• On time-reversal and space-time harmonic processes for Markovian quantum channels
• Quantum Complementarity and Operator Structures
• Structure Theorem for Quantum Replacer Codes
• Entropy of a quantum error correction code