In Closing

Jennifer Maier

Haibin Li, Yang Yang, Pei Wang +1 more

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems.

Ziao Liu, Jixi Lu, Xiaoyu Li +3 more

The bandwidth and dynamic range of spin-exchange relaxation-free (SERF) atomic magnetometers (AMs) are effectively broadened by introducing magnetic field closed-loop control, rendering it a focal point in AM research. However, there is a deviation between the commonly used closed-loop AM model and the single-beam closed-loop AM experimentally constructed. In this study, we comprehensively analyzed each component in the actual system and proposed a closed-loop model of the single-beam SERF AM. The accuracy of the proposed model was varied through a comparative experiment with different control parameters. Based on comparative experiments, a tenfold reduction was verified in the mean square error of the proposed model compared with the commonly used closed-loop model. As an accurate model is essential for effective closed-loop control, the proposed closed-loop single-beam SERF AM model provides a theoretical foundation for the research and application of closed-loop AMs.

Marc Henneaux A

Cécile Grèzes

Peter Selinger

Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name “strongly compact closed categories”, as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch a proof of its completeness for equational reasoning. We give a general construction, the CPM construction, which associates to each dagger compact closed category its “category of completely positive maps”, and we show that the resulting category is again dagger compact closed. We apply these ideas to Abramsky and Coecke's interpretation of quantum protocols, and to D'Hondt and Panangaden's predicate transformer semantics.