Quantum measurement and dynamical maps

Dynamic Topology Mapping (DTM) offers a novel approach to quantum entanglement measurement, leveraging the inherent topological properties of the entangled state. This paper explores the development of a quantum entanglement measurement protocol based on DTM, demonstrating significant improvements in measurement precision and robustness against environmental noise. We introduce a dynamic mapping technique that models the evolution of entangled states as a topological transformation, optimizing the measurement process through the self-similarity inherent in the topology. This method provides a fundamentally different perspective on entanglement measurement, addressing limitations of traditional approaches.Dynamic Topology Mapping (DTM) offers a novel approach to quantum entanglement measurement, leveraging the inherent topological properties of the entangled state. This paper explores the development of a quantum entanglement measurement protocol based on DTM, demonstrating significant improvements in measurement precision and robustness against environmental noise. We introduce a dynamic mapping technique that models the evolution of entangled states as a topological transformation, optimizing the measurement process through the self-similarity inherent in the topology. This method provides a fundamentally different perspective on entanglement measurement, addressing limitations of traditional approaches.

Aug 31, 20260 citations

Dynamical Model of Quantum Measurement

Jose L. Balduz

Jan 1, 19951 citation

Understanding quantum measurement from the solution of dynamical models

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

arXiv:1107.2138Physics ReportsNov 14, 2012239 citations

Singularity of dynamical maps

S. C. Hou, X. X. Yi, Sixia Yu +1 more

For a dynamical map $\ensuremath{\Lambda}(t,0)$, which sends a state $\ensuremath{\rho}(0)$ of a quantum open system to a state $\ensuremath{\rho}(t)=\ensuremath{\Lambda}(t,0)\ensuremath{\rho}(0)$, the decomposition law $\ensuremath{\Lambda}(t,0)=\ensuremath{\Lambda}(t,{t}_{c})\ensuremath{\Lambda}({t}_{c},0)$ may break down at a specific time ${t}_{c}$ . In this paper, we present a method to find the singular points ${t}_{c}$ and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, and the measure of singularity for these singular points is calculated and discussed. An extension to a high-dimensional system is presented.For a dynamical map $\ensuremath{\Lambda}(t,0)$, which sends a state $\ensuremath{\rho}(0)$ of a quantum open system to a state $\ensuremath{\rho}(t)=\ensuremath{\Lambda}(t,0)\ensuremath{\rho}(0)$, the decomposition law $\ensuremath{\Lambda}(t,0)=\ensuremath{\Lambda}(t,{t}_{c})\ensuremath{\Lambda}({t}_{c},0)$ may break down at a specific time ${t}_{c}$. In this paper, we present a method to find the singular points ${t}_{c}$ and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, and the measure of singularity for these singular points is calculated and discussed. An extension to a high-dimensional system is presented.

arXiv:1203.0053Physical Review AJul 5, 201226 citations

Characterizing entanglement dynamics in QED scattering processes

Massimo Blasone, Silvio De Siena, Gaetano Lambiase +2 more

We study entanglement dynamics among helicity degrees of freedom in quantum electrodynamics (QED) scattering processes. For generic initial states, we consider scattering at fixed momentum, corresponding to a generalized measurement described by a positive operator-valued measure, resulting in a post-measurement state. Such processes are modeled in terms of quantum maps, whose spectral structure fully determines the associated entanglement dynamics. For scattering involving fermions only, maximal entanglement present in the initial state is always preserved. Moreover, iterating the corresponding quantum maps on arbitrary initial states, we obtain the fixed points of the maps, which, in the largest number of cases, are asymptotic (pure) maximally entangled states. The structure of the maps also accounts for the entanglement dynamics in processes involving both fermions and photons. The defining properties of these maps originate from discrete symmetries of the QED interaction.We study entanglement dynamics among helicity degrees of freedom in quantum electrodynamics (QED) scattering processes. For generic initial states, we consider scattering at fixed momentum, corresponding to a generalized measurement described by a positive operator-valued measure, resulting in a post-measurement state. Such processes are modeled in terms of quantum maps, whose spectral structure fully determines the associated entanglement dynamics. For scattering involving fermions only, maximal entanglement present in the initial state is always preserved. Moreover, iterating the corresponding quantum maps on arbitrary initial states, we obtain the fixed points of the maps, which, in the largest number of cases, are asymptotic (pure) maximally entangled states. The structure of the maps also accounts for the entanglement dynamics in processes involving both fermions and photons. The defining properties of these maps originate from discrete symmetries of the QED interaction.

quant-pharXiv:2604.10136Physical review. D/Physical review. D.Apr 14, 20260 citations

{t}_{c}

. In this paper, we present a method to find the singular points

{t}_{c}

and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, and the measure of singularity for these singular points is calculated and discussed. An extension to a high-dimensional system is presented.