Quantum Zeno Dynamics from General Quantum Operations

Daniel Burgarth1, Paolo Facchi2,3, Hiromichi Nakazato4, Saverio Pascazio2,3, and Kazuya Yuasa4

1Center for Engineered Quantum Systems, Dept. of Physics & Astronomy, Macquarie University, 2109 NSW, Australia
2Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
3INFN, Sezione di Bari, I-70126 Bari, Italy
4Department of Physics, Waseda University, Tokyo 169-8555, Japan

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We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.

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Cited by

[1] Tim Möbus and Michael M. Wolf, "Quantum Zeno effect generalized", Journal of Mathematical Physics 60 5, 052201 (2019).

[2] Norbert Barankai and Zoltán Zimborás, "Generalized quantum Zeno dynamics and ergodic means", arXiv:1811.02509.

[3] Daniel Burgarth, Paolo Facchi, Giovanni Gramegna, and Saverio Pascazio, "Generalized product formulas and quantum control", Journal of Physics A Mathematical General 52 43, 435301 (2019).

[4] Paolo Facchi and Saverio Pascazio, "Kick and fix: the roots of quantum control", arXiv:1902.01591.

[5] Simon Becker, Nilanjana Datta, and Robert Salzmann, "Quantum Zeno effect for open quantum systems", arXiv:2010.04121.

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