Gaussian states as minimum uncertainty states |
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Institution: | 1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract: | In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) 40]. This characterization puts Gaussian states on a novel basis of physical significance. |
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Keywords: | Bosonic fields Gaussian states Uncertainty relation Minimum uncertainty states Wigner-Yanase skew information |
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