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تسجيل مستخدم جديدQuantum Zeno Dynamics from General Quantum Operations
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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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We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bo
unded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.
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A connection is estabilished between the non-Abelian phases obtained via adiabatic driving and those acquired via a quantum Zeno dynamics induced by repeated projective measurements. In comparison to the adiabatic case, the Zeno dynamics is shown to
be more flexible in tuning the system evolution, which paves the way to the implementation of unitary quantum gates and applications in quantum control.
We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${cal H}_0$ of the system, and targeting a unique dark state in ${cal H}_0$. We show
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because they are the first to have time-complexities that are comparable to the best known methods for simulating time-independent Hamiltonian evolution, given appropriate smoothness criteria on the Hamiltonian are satisfied. We provide a thorough cost analysis of these algorithms that considers discretizion errors in both the time and the representation of the Hamiltonian. In addition, we provide the first upper bounds for the error in Lie-Trotter-Suzuki approximations to unitary evolution operators, that use adaptively chosen time steps.
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