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Quantum dynamics of simultaneously measured non-commuting observables

Shay Hacohen-Gourgy, Leigh S. Martin, Emmanuel Flurin +3 more

arXiv:1608.06652NatureOct 1, 2016156 citations

Noncommutativity of quantum observables

B. Rumbos

International Journal of Theoretical PhysicsAug 1, 19930 citations

Evolution Law of Quantum Observables from Classical Hamiltonian in Non-Commutative Phase Space

Daniela Dragoman

The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is quite general; it does not rely on any assumption on the operator nature of x and p and is independent of the quantum mechanical formalism.

arXiv:quant-ph/0604076Apr 11, 20061 citation

Further Aspects of Quantum Observables

Kevin Costello, Owen Gwilliam

Cambridge University Press eBooksSep 10, 20210 citations

Structural Asymmetry Between Configuration and Update as the Basis for Operator Non-Commutation

Gregory A. L. White

Project This project develops a structural interpretation of operator non-commutation in quantum mechanics. Rather than introducing non-commutation as a purely algebraic postulate, the framework presented here interprets it as arising from an asymmetry between configuration-local and update-local observables within an ordered evolution structure. In this view: Configuration observables act on a resolved state. Update observables act on the transition between successive states. Because these quantities are defined on structurally distinct layers of evolution, their operations are non-equivalent. The canonical commutator [ x̂ , p̂ ] = iℏ is preserved without modification, but is interpreted as the formal signature of this structural asymmetry rather than as an unexplained primitive feature. The framework does not modify the formal structure of quantum mechanics or relativity. Continuous time and relativistic covariance are recovered in the high-resolution limit. This project presents the structural interpretation and develops its implications in successive versions.Project This project develops a structural interpretation of operator non-commutation in quantum mechanics. Rather than introducing non-commutation as a purely algebraic postulate, the framework presented here interprets it as arising from an asymmetry between configuration-local and update-local observables within an ordered evolution structure. In this view: Configuration observables act on a resolved state. Update observables act on the transition between successive states. Because these quantities are defined on structurally distinct layers of evolution, their operations are non-equivalent. The canonical commutator [ x̂ , p̂ ] = iℏ is preserved without modification, but is interpreted as the formal signature of this structural asymmetry rather than as an unexplained primitive feature. The framework does not modify the formal structure of quantum mechanics or relativity. Continuous time and relativistic covariance are recovered in the high-resolution limit. This project presents the structural interpretation and develops its implications in successive versions.

Feb 24, 20260 citations

Extension of 9D-USTE Non-Commutative Geometry: Topological Coupling Law of Quantum Entanglement and Remote Regulation

Houlang Li

Based on the non-commutative geometry framework of the Nine-Dimensional Universal Unified Evolution Theory of Entropic Topology (9D-USTE), this paper reconstructs quantum entanglement as a non-commutative topological coupling effect on a 9-dimensional topological manifold. By introducing three core non-commutative observables—the non-commutative topological coupling tensor Θ_ij, entanglement entropy control parameter Σ, and topological causal connectivity κ* (the local operator form of the global κ* in previous cosmological works)—we derive the fundamental topological coupling conservation law: Θ_ij · Σ · κ* = Ĉ, where the non-commutative topological constant Ĉ ∝ θ / ℓ_P² (θ: non-commutative parameter, ℓ_P: Planck length). This law reveals that the nonlocal nature of quantum entanglement is a projection effect of 9D topological connectivity onto 4D spacetime. We further propose the critical conditions for remote regulation and a unique observable signature: a topological phase shift Δφ = π/2 · Θ_ij. This work provides a testable, geometrically complete foundation for quantum entanglement and topological quantum control, unifying quantum information with 9D-USTE cosmology.Based on the non-commutative geometry framework of the Nine-Dimensional Universal Unified Evolution Theory of Entropic Topology (9D-USTE), this paper reconstructs quantum entanglement as a non-commutative topological coupling effect on a 9-dimensional topological manifold. By introducing three core non-commutative observables—the non-commutative topological coupling tensor Θ_ij, entanglement entropy control parameter Σ, and topological causal connectivity κ* (the local operator form of the global κ* in previous cosmological works)—we derive the fundamental topological coupling conservation law: Θ_ij · Σ · κ* = Ĉ, where the non-commutative topological constant Ĉ ∝ θ / ℓ_P² (θ: non-commutative parameter, ℓ_P: Planck length). This law reveals that the nonlocal nature of quantum entanglement is a projection effect of 9D topological connectivity onto 4D spacetime. We further propose the critical conditions for remote regulation and a unique observable signature: a topological phase shift Δφ = π/2 · Θ_ij. This work provides a testable, geometrically complete foundation for quantum entanglement and topological quantum control, unifying quantum information with 9D-USTE cosmology.

Mar 31, 20260 citations

Evolution of quantum observables: from non-commutativity to commutativity

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