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=γgent−γg(1)−γg(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 geometric structure of a Hermitian two-level mixing Hamiltonian motivated by neutral meson oscillations and its connections with qubit, fermionic, and topological descriptions. Mapping the Hamiltonian to an effective qubit representation, we analyze the geometric phase associated with cyclic parameter evolution on the Bloch sphere. Without identifying the complex mixing phase with a physical CP-violation observable, we interpret it as a CP-like geometric parameter controlling the azimuthal orientation of the Hamiltonian vector and its reversal under phase conjugation. Third-order Bargmann invariants constructed from the eigenstates yield an associated discrete phase whose dependence on the mixing parameters is examined alongside the continuous geometric construction. The cyclic evolution is also represented as a single-qubit Rz phase operation and expressed through Majorana bilinears. Extending the construction to the momentum-dependent Bogoliubov-de Gennes Hamiltonian of the Kitaev chain, we relate momentum-space winding to the topological regimes and the quantized Berry (Zak) phase in the real-parameter model, while the corresponding Bargmann construction approaches the global phase in the continuum limit. Together, these results provide a geometric perspective connecting phase structure, qubit operations, fermionic representations, and momentum-space topology within related two-level Hamiltonians.
This work presents a model-independent analysis of gravity-mediated entanglement based on the geometric structure of interaction-induced phase evolution. Using a minimal two-body phase model inspired by recent gravity-mediated entanglement proposals, it is shown that quantum entanglement between initially separable systems arises if and only if the induced phase structure is non-factorable. The central result identifies a gauge-invariant plaquette phase as a necessary and sufficient operational condition for entanglement generation. When this plaquette invariant is nonzero, standard quantum information diagnostics—such as negativity, concurrence, and Bell–CHSH correlations—confirm the presence of entanglement. When the invariant is eliminated, entanglement vanishes identically, even when individual phase magnitudes remain nonzero. A comprehensive suite of falsification tests is applied, including local phase factorization, plaquette removal, deterministic and stochastic phase scrambling, permutation symmetry tests, LOCC protocols, causal reordering, and controlled noise injection. Across all tests, entanglement survives exclusively in the presence of non-factorable phase structure. Scaling analyses further demonstrate consistent dependencies on mass, interaction time, separation distance, and superposition size, yielding a distinctive interaction fingerprint incompatible with classical or semiclassical channels. The framework is fully operational and does not assume a specific theory of quantum gravity. Instead, it provides a concrete, experimentally accessible criterion for probing nonclassical aspects of gravity using near-term interferometric platforms. The results sharpen the interpretational foundations of gravity-mediated entanglement proposals by isolating the minimal structural feature responsible for entanglement generation.
The geometric phase is of fundamental interest and plays an important role in quantum information processing. However, the definition and calculation of this phase for open systems remain problematic due to the lack of agreement on generalizations of the parallel transport condition to mixed-state nonunity evolutions. Here we tackle this problem by associating the open-system geometric phase with the parallel transport of the joint system-reservoir state and find that the associated geometric phase can be calculated when the total Hamiltonian is time independent. Our approach not only provides a way around the nonunitary evolution obstacle, but also sheds light on the relation between the geometric phase and the system-reservoir entanglement. Based on this approach, we calculate the geometric phase of different quantum systems subject to energy decay, showing that it is robust against decoherence, which is in distinct contrast with previous results.
This paper establishes a geometric bridge between two operational results concerning gravity-mediated entanglement and phase-based field structure. First, prior work showed that entanglement in minimal gravity-mediated interferometric models arises if and only if the interaction phases contain a non-factorable plaquette invariant. This invariant represents an oriented loop phase that cannot be decomposed into local contributions and therefore serves as a necessary and sufficient condition for entanglement generation. Second, the Harmonic Code framework describes persistent physical effects as loop-structured phase geometry, in which closed phase loops encode enduring information about curvature and field structure. The present work unifies these viewpoints by demonstrating that the plaquette phase emerges naturally as a curvature-induced loop holonomy. An effective phase-gradient field is introduced, and the oriented loop phase is defined as Π = ∮ k · dℓ = ∬ (∇ × k) · dA, showing that the non-factorable phase invariant is directly generated by the curl of the phase-gradient field. A minimal rotational field model is used to derive the relation Π = 2εA, where A is the enclosed area and ε is the curl parameter. Numerical simulations verify the key geometric properties expected of a true holonomy: Linear scaling with enclosed area Shape independence at fixed area Sign reversal under orientation flip Convergence under discretization refinement The loop phase Π is then mapped to standard two-qubit entanglement measures. For the separable input state |++⟩, the concurrence and negativity are shown to depend only on Π: C(Π) = |sin(Π/2)| N(Π) = C/2 These results demonstrate that the non-factorable phase structure required for gravity-mediated entanglement has a direct geometric origin as a curvature-induced loop holonomy. The paper therefore provides a unified operational statement: Curvature generates loop phases, and those loop phases are exactly the structures responsible for gravity-mediated entanglement. This establishes a concrete geometric mechanism linking spacetime curvature, phase holonomy, and quantum entanglement, and offers a clear, experimentally testable framework for probing quantum aspects of gravity.
Besides Heisenberg uncertainty, entanglement is another mechanism that can enforce complementarity in multipartite quantum systems. Analysing its effects in a bipartite system of two qubits, M. Jakob and J. Bergou had shown that the usual wave-particle duality relation, in interferometric systems, regarding which-way information and interference visibility, should be extended to a ¿triality¿ relation containing, in addition, a quantitative entanglement measure. Employing a model for the neutral K-meson propagation in free space in which its weak decay products are included as a second party, we study its effect in the neutral kaon interferometry. We show that a new quantitative triality relation can also be established in this case. The state of the total system remains pure in the course of dynamics, so, we can use the von Neumann entropy of a reduced party as a quantitative measure of entanglement. The other two quantities in the triality relation are the distinguishability between the decay products states corresponding to the two distinct kaon propagation modes KS and KL, and the wave-like path interference between these states. These two distinct modes are the analogues to the two separated paths in usual interferometric devices. The inequality obtained here can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature. Moreover, it allows us to visualise through the K0 ¿ K0 oscillations the fundamental role of entanglement in quantum complementarity.
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the geometric phases appearing in the time evolution of mixed meson systems like Bs0−Bˉs0 and the K0−Kˉ0 are linked to the parameter z describing the CPT violation. A non zero phase difference between particle and antiparticle arises only in the presence of CPT symmetry breaking. Then the geometric phase can represent a completely new test for the CPT invariance. Moreover, we study the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution and propose the realization of interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature. We are glad to dedicate this paper to Professor Gaetano Vilasi in the occasion of his 70th birthday.