Detecting non-Markovianity via quantified coherence: theory and experiments
Kang‐Da Wu, Zhibo Hou, Guo‐Yong Xiang, Chuan‐Feng Li, Guang‐Can Guo, Daoyi Dong, Franco Nori
Abstract
Abstract The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the quantum-incoherent relative entropy of coherence ( $${\mathcal{Q}}{\mathcal{I}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:math> REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the $${\mathcal{Q}}{\mathcal{I}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:math> REC. Also we implement an all-optical experiment to demonstrate that the behavior of the $${\mathcal{Q}}{\mathcal{I}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:math> REC is coincident with the entanglement shared between the system and the ancilla for both Markovian and non-Markovian evolution; while other coherence-based non-Markovian information carriers violate monotonicity, even in Markovian processes. Moreover, both theoretically and experimentally, we show that non-Markovianity enhances the ability of creating coherence on an ancilla. This is the first experimental study of the relation between dynamical behavior of the $${\mathcal{Q}}{\mathcal{I}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:math> REC and the phenomenon of information backflow. Our methods for detecting non-Markovianity are applicable to general quantum evolutions.