The Structure of Quantum States

Sergey Nikolaevich Mayburov

Zhihao Ma, Sen Zhu

Quantum states play a fundamental role in quantum physics; so it is necessary to study intrinsic structure of quantum states. In this paper, we study topological structure and measurable structure of state space of a quantum system, and find that almost all physical important properties on quantum states coincide.

Zhaoyang Wang, Ziyu Zhan, Anton N. Vetlugin +3 more

Control of structured light is of great importance to explore fundamental physical effects and extend practical scientific applications, which has been advanced by accepting methods of quantum optics - many classical analogies of exotic quantum states were designed using structured modes. However, the prevailing quantum-like structured modes are limited by discrete states where the mode index is analog to the photon number state. Yet, beyond discrete states, there is a broad range of quantum states to be explored in the field of structured light -- continuous-variable (CV) states. As a typical example of CV states, squeezed state plays a prominent role in high-sensitivity interferometry and gravitational wave detection. In this work, we bring together two seemingly disparate branches of physics, namely, classical structured light and quantum squeezed state. We propose the structured light analogy of squeezed state (SLASS), which can break the spatial limit following the process of surpassing the standard quantum limit (SQL) with quantum squeezed states. This work paves the way for adopting methods from CV quantum states into structured light, opening new research directions of CV entanglement, teleportation, classical and quantum informatics of structured light in the future.

L. A. Lugiato, A. Gatti, K.I. Petsas

L.A. Lugiato, A. Gatti, K.I. Petsas

Jincheng Zhang

This paper presents a novel approach to quantum state space representation based on dynamic topology. We introduce a new framework, Dynamic Topology Quantum State Space Structure (DTSSS), which leverages topological properties to model quantum state evolution. This model offers a fundamentally different perspective on quantum mechanics, enabling a deeper understanding of quantum states through their dynamic transformations. The core of DTSSS involves employing topological tools to optimize the structure of quantum states during evolution, thereby facilitating more accurate predictions of quantum state trajectories. This work addresses the limitations of traditional approaches by embracing the inherent dynamism of quantum systems. We demonstrate the effectiveness of DTSSS through a series of illustrative examples, showcasing its potential for advanced quantum simulation and analysis.