Spin minimum uncertainty states for refined uncertainty relations

Abstract

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.

References in corpus (15)

• Quantum entanglement
• Quantum metrology
• Quantum metrology with nonclassical states of atomic ensembles
• Entropic Uncertainty Relations and their Applications
• The Einstein-Podolsky-Rosen paradox: from concepts to applications
• Entropic uncertainty relations - A survey
• Quantum root-mean-square error and measurement uncertainty relations
• Entropic uncertainty relation for mutually unbiased bases
• Quantum uncertainty relation using coherence
• Entropic uncertainty relations from quantum designs
• Uncertainty relations and approximate quantum error correction
• Uncertainty relations: An operational approach to the error-disturbance tradeoff
• Quantum Measurements in the Light of Quantum State Estimation
• Asymmetry and tighter uncertainty relations for Rényi entropies via quantum-classical decompositions of resource measures
• Standard symmetrized variance with applications to coherence, uncertainty and entanglement