The structure of preserved information in quantum processes

Abstract

We introduce a general operational characterization of information-preserving structures (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every IPS is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrodinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.

References in corpus (21)

• Mixed State Entanglement and Quantum Error Correction
• Decoherence, einselection, and the quantum origins of the classical
• Decoherence Free Subspaces for Quantum Computation
• Noiseless Quantum Codes
• Quantum Computers and Dissipation
• A Theory of Quantum Error-Correcting Codes
• Experimental Quantum Error Correction
• Preserving coherence in quantum computation by pairing quantum bits
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• A Unified and Generalized Approach to Quantum Error Correction
• Reversing quantum dynamics with near-optimal quantum and classical fidelity
• Implementation of the Five Qubit Error Correction Benchmark
• Stabilizing Quantum Information
• Robustness of Decoherence-Free Subspaces for Quantum Computation
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Implementation of Universal Control on a Decoherence-Free Qubit
• Generalization of Quantum Error Correction via the Heisenberg Picture
• A method to find quantum noiseless subsystems
• On Protected Realizations of Quantum Information
• Experimental Implementation of a Concatenated Quantum Error-Correcting Code
• Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems

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