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Quantumness of Bosonic Field States

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Abstract

In bosonic fields, coherent states are widely regraded as the most classical (the least quantum) states for several operational and physical reasons. In this context, a natural question arises: How classical/quantum is a state? This fundamental issue has been pursued from various perspectives, and many significant measures of quantumness (nonclassicality) have been proposed, each with its own unique merit and usage. However, there is no universal measure of quantumness, and it is desirable to characterize quantumness from different angles. In this work, by exploiting the Wigner-Yanase skew information and the resolution of identity induced by coherent states of bosonic fields, we introduce a measure of quantumness which possesses several remarkable properties: Easy computation, information-theoretic meaning, physical relevance. We reveal its connection with Renyi 2-entropy of Husimi distributions of square root of quantum states, illustrate its significance in capturing quantumness through prototypical examples, and show that it is indeed a bona fide measure of quantumness.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China, Grant Nos. 11875317, the National Center for Mathematics and Interdisciplinary Sciences, CAS, Grant No. Y029152K51.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Shunlong Luo & Yue Zhang

  2. School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, 100049, China

    Shunlong Luo & Yue Zhang

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  1. Shunlong Luo
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  2. Yue Zhang
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Correspondence to Shunlong Luo.

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Luo, S., Zhang, Y. Quantumness of Bosonic Field States. Int J Theor Phys 59, 206–217 (2020). https://doi.org/10.1007/s10773-019-04313-2

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