A continuous-time diffusion limit theorem for dynamical decoupling and intrinsic decoherence

Abstract

We discuss a few mathematical aspects of random dynamical decoupling, a key tool procedure in quantum information theory. In particular, we place it in the context of discrete stochastic processes, limit theorems and CPT semigroups on matrix algebras. We obtain precise analytical expressions for expectation and variance of the density matrix and fidelity over time in the continuum-time limit depending on the system Lindbladian, which then lead to rough short-time estimates depending only on certain coupling strengths. We prove that dynamical decoupling does not work in the case of intrinsic (i.e., not environment-induced) decoherence, and together with the above-mentioned estimates this yields a novel method of partially identifying intrinsic decoherence.

24 pages. Final published version

References in corpus (4)

• Dynamical Decoupling of Open Quantum Systems
• Random decoupling schemes for quantum dynamical control and error suppression
• Quantum error correction of coherent errors by randomization
• Dynamical control of qubit coherence: Random versus deterministic schemes

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