Geometry of quantum state space and quantum correlations

Yaokun Wang, Teng Ma, Heng Fan +2 more

Marek Kuś

Zhikuan Zhao, Robert Pisarczyk, Jayne E. Thompson +3 more

The traditional formalism of nonrelativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial and temporal quantum correlations. Here we unify the geometrical description of two-point quantum correlations in space-time. Our study presents the geometry of correlations between two sequential Pauli measurements on a single qubit undergoing an arbitrary quantum channel evolution together with two-qubit spatial correlations under a common framework. We establish a symmetric structure between quantum correlations in space and time. This symmetry is broken in the presence of nonunital channels, which further reveals a set of temporal correlations that are indistinguishable from correlations found in bipartite entangled states.

Prasenjit Deb, Pratapaditya Bej

Jincheng Zhang

This paper introduces the concept of Quantum Correlation Propagation Geometry (QCPG), a novel framework for understanding and manipulating quantum entanglement beyond traditional spacetime constraints. QCPG postulates the existence of a distinct geometric structure – denoted as [G_Q] – that governs the propagation of quantum correlations. Unlike conventional geometry, QCPG operates within this inherent space, offering a potential pathway to fundamentally different quantum information processing architectures. The core idea revolves around defining and utilizing a quantum correlation space, which allows for the description and manipulation of entangled states based on geometric relationships. This framework aims to provide a more intuitive and potentially experimentally feasible approach to harnessing quantum correlations for applications like quantum networking and advanced quantum computation. The presented model is conceptually rich and possesses significant potential for future research and development, potentially aligning with the goals of the Nobel Prize in Physics.

Christopher Woodyard

This presents a geometric formulation of Dynamic Location Theory (DLT), proposing that temporal experience and weak inter-configuration correlations in quantum systems emerge naturally from the intrinsic curvature of quantum state space. By treating projective Hilbert spaces as Riemannian manifolds endowed with the Fubini–Study metric, I derive a scalar coupling γ as a geometric invariant rather than a phenomenological parameter.