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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[1] Vladislav Popkov and Carlo Presilla, "Full Spectrum of the Liouvillian of Open Dissipative Quantum Systems in the Zeno Limit", Physical Review Letters 126 19, 190402 (2021).

[2] Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, and Kazuya Yuasa, "Eternal adiabaticity in quantum evolution", Physical Review A 103 3, 032214 (2021).

[3] Simon Milz and Kavan Modi, "Quantum Stochastic Processes and Quantum non-Markovian Phenomena", PRX Quantum 2 3, 030201 (2021).

[4] Lester Ingber, "Forecasting with Importance-Sampling and Path-Integrals: Applications to COVID-19", SSRN Electronic Journal (2020).

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

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

[7] 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).

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

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

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-19 21:47:36) and SAO/NASA ADS (last updated successfully 2021-10-19 21:47:38). The list may be incomplete as not all publishers provide suitable and complete citation data.