Minimum Uncertainty States

Shuangshuang Fu, Shunlong Luo, Yue Zhang

Hao Dai, Yue Zhang

Minimum uncertainty states of the conventional Heisenberg uncertainty relation have been extensively studied and are often regarded as the most classical quantum states from the perspective of uncertainty, providing valuable insight into the nature of quantumness and its potential applications. In this work, we investigate the minimum uncertainty states associated with an information-theoretic refinement of the Heisenberg uncertainty relation in general spin systems. Using two different approaches, the matrix formulation and the Wick symbol representation, we derive explicit expressions for the states that saturate the uncertainty bound. We show that spin coherent states indeed achieve minimum uncertainty, consistent with their conventional identification as the classical states of spin systems. Moreover, we also identify additional classes of minimum uncertainty states beyond the coherent family. Finally, we compare the spin-system results with the previously studied bosonic case and elucidate the origin of the differences between the two settings.

Ravinder Rupchand Puri, G. S. Agarwal

The notion of the minimum uncertainty states (MUS) of a Lie algebra is discussed. That is used to obtain the MUS of SU(1, 1) algebra. Those states fall in two classes. One is the class of the states obtained by the SU(1, 1) group transformation on the MUS of the pair of its noncompact hermitian generators and the other is obtained by that on the MUS of the pair of a compact and a noncomp]act generator.

Huangjun Zhu

The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a quantum memory entangled with the system. Minimum uncertainty states are peculiar quantum states that can eliminate uncertainties of incompatible von Neumann observables once assisted by suitable measurements on the memory. Here we determine all minimum uncertainty states of any given set of observables and determine the minimum entanglement required. It turns out all minimum uncertainty states are maximally entangled in a generic case, and vice versa, even if these observables are only weakly incompatible. Our work establishes a precise connection between minimum uncertainty and maximum entanglement, which is of interest to foundational studies and practical applications, including quantum certification and verification.

Stephanie McBride, Catherine A. Fitzgerald, Brian Hand +2 more