title: Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs.
abstract: Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore.
authors.forename: A
authors.initials: A
authors.lastname: Chia
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore.|Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Gwanak-gu, Seoul, Korea.
authors.forename: K C
authors.initials: KC
authors.lastname: Tan
authors.affiliation: Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Gliwice, Poland.
authors.forename: Ł
authors.initials: Ł
authors.lastname: Pawela
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore.|Faculty of Physics, Adam Mickiewicz University in Poznań, Poznań, Poland.
authors.forename: P
authors.initials: P
authors.lastname: Kurzyński
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore.|Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore.
authors.forename: T
authors.initials: T
authors.lastname: Paterek
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore.
authors.forename: D
authors.initials: D
authors.lastname: Kaszlikowski