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Coherence, detectability and correlation in the generalized Coleman–Hepp model

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Abstract

Coherence, detectability and correlation in a quantum measurement process are studied by means of the generalized Coleman–Hepp model, in which a spin of a propagating particle is measured and a detector system consists of a one-dimensional array of independent spin-1/2 particles. It is found that the coherence of the measured particle decreases in time, while the detectability of the particle spin by the whole detector system increases. The coherence and detectability satisfy a trade-off relation. The correlation between the particle spin and the whole detector system grows in time and its dependence on the interaction strength is clarified. On the other hand, after the correlation between the particle spin and the individual detector particle is created by the interaction, it decays in time due to the interaction with another detector particle. It is shown that the strong particle–detector interaction not only creates large correlation but also causes the rapid decay of the correlation. In the asymptotic limit, the entanglement between the particle spin and the individual detector particle becomes zero, while the quantum discord can take finite values. Furthermore, a numerical calculation reveals that the optimum measurement for detecting the particle spin is equal to that quantifying the classical correlation and the quantum discord.

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Acknowledgements

The authors thank Prof. S. Kitajima of Ochanomizu University for useful comments and encouragement.

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Authors and Affiliations

  1. Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Miku Ishizaki & Masashi Ban

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  1. Miku Ishizaki
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  2. Masashi Ban
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Correspondence to Masashi Ban.

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Ishizaki, M., Ban, M. Coherence, detectability and correlation in the generalized Coleman–Hepp model. Quantum Inf Process 17, 290 (2018). https://doi.org/10.1007/s11128-018-2065-9

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