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Thakuria, Dimpi; Srivastav, Abhay; Mohan, Brij; Kumari, Asmita; Pati, Arun Kumar

Generalised quantum speed limit for arbitrary time-continuous evolution. (English) Zbl 1536.81022

J. Phys. A, Math. Theor. 57, No. 2, Article ID 025302, 18 p. (2024).
Summary: The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e. the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.
{© 2023 IOP Publishing Ltd}

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
47D06 One-parameter semigroups and linear evolution equations
81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
81Q93 Quantum control
58J47 Propagation of singularities; initial value problems on manifolds
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
22D10 Unitary representations of locally compact groups

Keywords:

quantum speed limits; quantum information theory; non-Hermitian physics; quantum dynamics; quantum control; geometry of quantum evolution
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References:

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