We investigate the phase structure associated with correlated evolution in entangled neutral meson systems. Working within a rephasing-invariant interferometric framework, we construct the time-dependent interferometric geometric phase associated with the antisymmetric entangled neutral meson state undergoing nonunitary evolution. Exploiting the natural factorization of the overlap amplitude into global propagation and interference contributions, we derive an explicit expression for the phase in terms of the mass and decay-width differences that govern neutral meson mixing. To place the entangled phase in context, we derive the corresponding interferometric geometric phases accumulated by independently evolving neutral mesons within the same framework. This comparison naturally leads to the introduction of a correlation-induced interferometric geometric phase difference, $Δγ=γ_{\rm g}^{\rm{ent}}-γ_{\rm g}^{(1)}-γ_{\rm g}^{(2)}$ , defined as the deviation of the entangled interferometric geometric phase from the sum of the associated single-meson phases. We show that this quantity characterizes the nonadditive phase structure generated by correlated meson evolution and originates from interference between propagation pathways that have no analogue in isolated meson dynamics. The resulting phases depend solely on the eigenvalue differences governing neutral meson oscillations and decay. The system-dependent behavior of the interferometric geometric phases and the correlation-induced phase difference is analyzed across different neutral meson families, illustrating how the underlying mixing dynamics shape the resulting phase correlations. Our results provide an interferometric characterization of entangled neutral meson evolution and highlight the role of entanglement in generating nonadditive phase structures associated with correlated meson dynamics.We investigate the phase structure associated with correlated evolution in entangled neutral meson systems. Working within a rephasing-invariant interferometric framework, we construct the time-dependent interferometric geometric phase associated with the antisymmetric entangled neutral meson state undergoing nonunitary evolution. Exploiting the natural factorization of the overlap amplitude into global propagation and interference contributions, we derive an explicit expression for the phase in terms of the mass and decay-width differences that govern neutral meson mixing. To place the entangled phase in context, we derive the corresponding interferometric geometric phases accumulated by independently evolving neutral mesons within the same framework. This comparison naturally leads to the introduction of a correlation-induced interferometric geometric phase difference, $Δγ=γ_{\rm g}^{\rm{ent}}-γ_{\rm g}^{(1)}-γ_{\rm g}^{(2)}$, defined as the deviation of the entangled interferometric geometric phase from the sum of the associated single-meson phases. We show that this quantity characterizes the nonadditive phase structure generated by correlated meson evolution and originates from interference between propagation pathways that have no analogue in isolated meson dynamics. The resulting phases depend solely on the eigenvalue differences governing neutral meson oscillations and decay. The system-dependent behavior of the interferometric geometric phases and the correlation-induced phase difference is analyzed across different neutral meson families, illustrating how the underlying mixing dynamics shape the resulting phase correlations. Our results provide an interferometric characterization of entangled neutral meson evolution and highlight the role of entanglement in generating nonadditive phase structures associated with correlated meson dynamics.

arXiv:2602.23684Feb 27, 20260 citations

Maximum Speed of Quantum Evolution

M. Andrecut, Mazhar Ali

International Journal of Theoretical PhysicsApr 1, 200410 citations

Quantum mechanical evolution of relativistic particles

Philippe Droz-Vincent

Foundations of PhysicsJan 1, 19953 citations

Unitarity and real properties of the neutral meson complex

K. Urbanowski, J. Jankiewicz

The proof of the Khalfin Theorem for the neutral meson complex is analyzed.It is shown that the unitarity of the time evolution operator for the total system under considerations assures that the Khalfin's Theorem holds.The consequences of this Theorem for the neutral mesons system are discussed: it is shown that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex cannot be equal if CPT symmetry holds and CP symmetry is violated.The properties of time evolution governed by a time-independent effective Hamiltonian acting in the neutral mesons subspace of states are considered.Using the Khalfin's Theorem it is shown that if such Hamiltonian is time-independent then the evolution operator for the total a system containing the neutral meson complex cannot be a unitary operator.It is shown graphically for a given specific model how the Khalfin's Theorem works.It is also shown for this model how the difference of the mentioned diagonal matrix elements of the effective Hamiltonian varies in time.The proof of the Khalfin Theorem for the neutral meson complex is analyzed.It is shown that the unitarity of the time evolution operator for the total system under considerations assures that the Khalfin's Theorem holds.The consequences of this Theorem for the neutral mesons system are discussed: it is shown that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex cannot be equal if CPT symmetry holds and CP symmetry is violated.The properties of time evolution governed by a time-independent effective Hamiltonian acting in the neutral mesons subspace of states are considered.Using the Khalfin's Theorem it is shown that if such Hamiltonian is time-independent then the evolution operator for the total a system containing the neutral meson complex cannot be a unitary operator.It is shown graphically for a given specific model how the Khalfin's Theorem works.It is also shown for this model how the difference of the mentioned diagonal matrix elements of the effective Hamiltonian varies in time.

arXiv:0707.3219Journal of Physical StudiesJan 1, 20110 citations

Evolution of the Quantum Theory

E. U. Condon

Springer eBooksJan 1, 19912 citations

Δγ=γ_{\rm g}^{\rm{ent}}-γ_{\rm g}^{(1)}-γ_{\rm g}^{(2)}

, defined as the deviation of the entangled interferometric geometric phase from the sum of the associated single-meson phases. We show that this quantity characterizes the nonadditive phase structure generated by correlated meson evolution and originates from interference between propagation pathways that have no analogue in isolated meson dynamics. The resulting phases depend solely on the eigenvalue differences governing neutral meson oscillations and decay. The system-dependent behavior of the interferometric geometric phases and the correlation-induced phase difference is analyzed across different neutral meson families, illustrating how the underlying mixing dynamics shape the resulting phase correlations. Our results provide an interferometric characterization of entangled neutral meson evolution and highlight the role of entanglement in generating nonadditive phase structures associated with correlated meson dynamics.