TY - JOUR

T1 - Unification of random dynamical decoupling and the quantum Zeno effect

AU - Hahn, Alexander

AU - Burgarth, Daniel

AU - Yuasa, Kazuya

N1 - Funding Information: AH would like to thank Mattias Johnsson for useful advice on numerics. In addition, AH acknowledges support by Leibniz Universität Hannover and in particular by Tobias Osborne, who provided the mandatory infrastructure and was always available for helpful discussions. AH was supported by the Sydney Quantum Academy. DB acknowledges funding by the Australian Research Council (Project numbers FT190100106, DP210101367, CE170100009). This work was supported in part by the Top Global University Project from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. KY was supported by the Grants-in-Aid for Scientific Research (C) (No. 18K03470) and for Fostering Joint International Research (B) (No. 18KK0073) both from the Japan Society for the Promotion of Science (JSPS).

PY - 2022/6/1

Y1 - 2022/6/1

N2 - Periodic deterministic bang-bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang-bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.

AB - Periodic deterministic bang-bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang-bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.

KW - open quantum systems

KW - pure Choi-Jamiolkowski state

KW - quantum control theory

KW - quantum Zeno effect

KW - random dynamical decoupling

KW - reduced dynamics

KW - unitary time evolution

UR - http://www.scopus.com/inward/record.url?scp=85134728924&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2112.04242

DO - 10.48550/arXiv.2112.04242

M3 - Article

AN - SCOPUS:85134728924

VL - 24

JO - New journal of physics

JF - New journal of physics

SN - 1367-2630

IS - 6

M1 - 063027

ER -