Decoherence of a two-level system in a coherent superposition of two dephasing environments
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Decoherence of a two-level system in a coherent superposition of two dephasing environments Masashi Ban1 Received: 6 April 2020 / Accepted: 20 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Decoherence of a two-level system is studied when it interacts with one of two environments via a dephasing coupling, where the environments are treated as classical and quantum systems. The situation is considered in which the environment that actually interacts with the two-level system is determined by a state of an ancillary two-level system. When information conveyed by the ancillary two-level system is discarded, the reduced dynamics of the relevant two-level system is described by a statistical mixture of two dephasing channels, which shows mixing-induced non-Markovianity. When projective measurement is performed on the ancillary two-level system to extract some information, the diagonal elements of the reduced state of the two-level system depend on time in spite of the dephasing process. Furthermore, it is found that the coherence of the two-level system can exceed its initial value. The parameter region is clarified in which the measurement on the ancillary two-level system can improve the coherence of the relevant two-level system. In particular, when the two environments are equivalent and the ancillary two-level system is in the maximally coherent state, the coherence of the two-level system can be always enhanced by measurement. Keywords Decoherence · Two-level system · Stochastic process · Spin-boson model · Superposition of environments
1 Introduction A physical system that obeys the quantum mechanical laws exhibits distinguished features, such as quantum coherence [1], entanglement [2] spatial and temporal non-local correlations [3–5], that cannot be explained by classical mechanics or its extension to local hidden variable theories [6,7]. These features stem from superposition of quan-
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Masashi Ban [email protected] Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan 0123456789().: V,-vol
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tum states and non-commutativity of observables. Quantum coherence and correlation are indispensable not only for understanding physical phenomena [1–5] but also novel information technology, called quantum information processing [8], including quantum cryptography [9,10], quantum communication [11,12] and quantum computation [13,14], which are impossible by the traditional information technology [15,16] based on devices which are subject to the laws of classical physics. Unfortunately, a physical system of interest in the real world is inevitably influenced by a surrounding environment [17–20]. As a result, a physical system undergoes irreversible time-evolution, during which the quantumness of the physical system is eventually destructed since quantum mechanical properties are very fragile. Hence, it is extremely important to protect the quantumness of an open system from a s
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