The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we introduce a quantifier of complexity of continuous-variable states, e.g. quantum optical states, based on the Husimi quasiprobability distribution. This quantity is built upon two functions of the state: the Wehrl entropy, capturing the spread of the distribution, and the Fisher information with respect to location parameters, which captures the opposite behavior, i.e. localization in phase space. We analyze the basic properties of the quantifier and illustrate its features by evaluating complexity of Gaussian states and some relevant non-Gaussian states. We further generalize the quantifier in terms of s-ordered phase-space distributions and illustrate its implications.

Publication:

QUANTUM SCIENCE AND TECHNOLOGY

http://dx.doi.org/10.1088/2058-9565/ae08df

Author:

Siting Tang

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

Dipartimento di Fisica, Universit`a di Milano, I-20133 Milano, Italy

Francesco Albarelli

Scuola Normale Superiore, I-56126 Pisa, Italy

Yue Zhang

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

Shunlong Luo

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

Matteo G A Paris

Dipartimento di Fisica, Universit`a di Milano, I-20133 Milano, Italy

Author to whom any correspondence should be addressed.

E-mail: matteo.paris@fisica.unimi.it