https://doi.org/10.1140/epjp/s13360-025-06592-7
Regular Article
Quantifying imaginarity via the quantum optimal transport cost
1
School of Mathematics and Computational Science, Xiangtan University, 411105, Xiangtan, China
2
School of Mathematical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
Received:
6
February
2025
Accepted:
25
June
2025
Published online:
17
July
2025
Imaginarity has been proven indispensable in quantum mechanics and plays a crucial role in various quantum information processing tasks. In this work, we introduce an imaginarity measure via the quantum optimal transport cost, and prove that it satisfies faithfulness, monotonicity, convexity, and subadditivity for product states. We further establish the relationship between this imaginarity measure and the geometric measure of imaginarity, providing an explicit expression of this measure for pure states. Additionally, we derive the structure of quantum states that maximize this imaginarity measure. Finally, we demonstrate that this imaginarity measure characterizes both the minimum time needed for a unitary evolution to convert the given pure state into a real state and the maximum probability for pure state transformations under real operations, which provide two operational interpretations of the imaginarity measure for pure states.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
