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Phase Coherence as a Control Axis in Bipartite Quantum Correlations: A Gate-Formalism Perspective on Entanglement Visibility (Paper I/VII)

Fabio Luigi Zander

Published Apr 15, 2026• 0 citations
Publisher

Abstract

Systematic analysis of a parametrized two-qubit system demonstrating that phase coherence functions as a physical resource governing entanglement visibility. The differential correlation Δ⟨σx⊗σx⟩ oscillates with relative phase φ, while Wootters concurrence C = |sin 2γ| remains phase-invariant. Results are framed within the Δ-Gate Formalism, where each measurement constitutes a coherence-dependent transition operator. The parametrization maps directly onto tt̄ spin correlations at the LHC, yielding three falsifiable predictions testable with ATLAS/CMS Run 3 data. Paper I of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).

DOI
10.5281/zenodo.19592029

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Systematic analysis of a parametrized two-qubit system demonstrating that phase coherence functions as a physical resource governing entanglement visibility. The differential correlation Δ⟨σx⊗σx⟩ oscillates with relative phase φ, while Wootters concurrence C = |sin 2γ| remains phase-invariant. Results are framed within the Δ-Gate Formalism, where each measurement constitutes a coherence-dependent transition operator. The parametrization maps directly onto tt̄ spin correlations at the LHC, yielding three falsifiable predictions testable with ATLAS/CMS Run 3 data. Paper I of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
Closed-form derivation of the coincidence tunneling probability for spin-entangled particle pairs traversing spin-dependent barriers. The central result P_coinc(φ,γ) decomposes into incoherent background plus coherent interference modulated by cos(φ + 2Δθ), where Δθ is the differential tunneling phase — a barrier property invisible to single-particle measurements but directly observable through entanglement. Numerical predictions for Co/Al₂O₃/Co magnetic tunnel junctions yield coincidence visibility >90% and modulation ratio R > 10⁴. Three experimental proposals: magnetic tunnel junctions with Cooper pair splitting, frustrated total internal reflection with photon pairs, and cold atoms in optical lattices. Paper IV of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765). , , , , , , ,
Introduces the coherence-time density operator ρ_K(t) as a spatially integrated, time-resolved threshold observable for quantum gate stability. Central result: a Δ-Gate remains active iff ρ_K(t) ≥ ρ_K,min. Proves Lindblad dephasing recovery in the spatially uniform limit (Proposition 2). Derives explicit collapse threshold for distance-d repetition codes (Proposition 3). Embeds all five companion papers (phase coherence, entangled tunneling, gate channel, Heisenberg-Gate, Omega operator) as projections or limits. Relativistic extension: gate lifetime dilates under Lorentz boosts with frame-invariant threshold condition. Seven falsifiable predictions proposed. Paper VI of VII — theoretical capstone of the Δ-Gate series. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
The second-order intensity correlation of entangled photons has been intensively studied for decades, particularly for the Hong-Ou-Mandel (HOM) effect and nonlocal correlation -- key quantum phenomena that have no classical counterparts. Recently, a path-entangled two-photon state has been experimentally demonstrated for both bosonic (symmetric) and fermionic (anti-symmetric) HOM effects by manipulating the photon phase at one input port. Entanglement represents a quantum superposition of path- or energy-correlated two-photon states with a relative phase. According to the conventional quantum mechanics, this phase is not an individual property but collective attribute of interacting photons. Here, the wave nature of photons is employed to coherently analyze the phase-controlled HOM effects recently observed in npj Quantum Info. 5, 43 (2019). A pure coherence approach is applied to derive a general solution for these phase-controlled HOM effects. Consequently, the quantum mystery of HOM effects, traditionally interpreted through the particle nature of quantum mechanics, is revealed as a coherent phenomenon between entangled photons via a selective choice of correlated photons.
This paper presents an intuitive, mechanistic explanation of quantum entanglement using standard physics language while incorporating deeper insights aligned with the MID/QC framework. Entanglement is typically described as a correlation between two particles that persists across distance, but standard quantum mechanics does not provide a physical mechanism for how this correlation is maintained. In this interpretation, entanglement arises when two quantum systems interact closely enough for the underlying medium to form a single coherent oscillation pattern spanning both. After separation, each system remains a boundary expression of this shared structure. Measurement does not transmit information; it reveals the state of the pre existing coherence pattern. This approach preserves all quantum predictions while offering a clear physical mechanism for entanglement, correlation, and decoherence.
We introduce a one-parameter quantum channel — the gate channel — that continuously interpolates between unitary evolution (K=0) and projective measurement (K=1) via K(t) = 1 − exp(−Γt). Proof that the continuum limit recovers the GKSL/Lindblad master equation for dephasing exactly. Extensions to pipeline structure, general Kraus operators, and multi-environment coupling. Three falsifiable experimental protocols proposed: double-slit interferometry, NMR spin-echo decay, and polarization-state degradation. Paper II of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
The perspective-neutral formulation of quantum reference frames (QRFs) treats observers as quantum systems and describes physics relationally from within the composite system. While frame-change maps and frame-invariant resource sums are theoretically understood, their impact on circuit-based quantum information processing has largely remained unexplored. We formulate QRF transformations as circuit compilation rules and, for systems with finite Abelian symmetry described by the regular representation, derive a gate-level dictionary that maps local operations in one frame to their images in another. This yields a group-theoretic classification of gates where symmetry-commuting operators remain local, up to frame-dependent phases, while generic gates are promoted to controlled entangling operations in which the original frame acts as a control register. The resulting frame-dependence entangling-gate count defines a relational circuit complexity where the cost of a computation depends on the internal reference frame of the observer. We instantiate the framework in a three-qubit model and show that the QRF unitary acts as a lossless converter between a purity-based local coherence and concurrence, preserving their invariant sum and giving a concrete realization of the relativity of entanglement. We implement the corresponding circuits on an IBM Quantum superconducting platform, using full state tomography to reconstruct the redistribution of resources between internal frames. The hardware data reproduce the predicted conversion of local coherence into entanglement, and the observed deviations from exact conservation quantify the effect of realistic device noise on relational quantum protocols.