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Information-Mirror Interpretation of Coherence Recovery in Structured Qubit

Humberto Arrabal

Published Apr 27, 2026• 0 citations
Publisher

Abstract

For a qubit undergoing pure dephasing, the trace distance between a natural pair of phase-oppositestates equals the ℓ1 coherence of the qubit. This identity provides a simple way to interpret distinguishabilitybackflow as single-qubit coherence recovery. Using this observation, we motivate aninformation-mirror interpretation of coherence revivals in structured environments: environmentaldegrees of freedom may temporarily store phase information and later make part of it locally visibleagain in the qubit. We define a cycle-resolved reflection coefficient, R = B/L, where L is the coherencelost during a decay segment and B is the coherence recovered during the following revival. Fora recovery cycle referenced to its preceding coherence maximum, ordinary partial recovery satisfies0 ≤ R ≤ 1, with R = 1 corresponding to complete return to the previous maximum. This coefficientdoes not replace standard non-Markovianity measures, but provides a compact diagnostic of howstrongly a structured environment returns previously lost coherence.

DOI
10.6084/m9.figshare.32102143

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For a qubit undergoing pure dephasing, the trace distance between a natural pair of phase-oppositestates equals the ℓ1 coherence of the qubit. This identity provides a simple way to interpret distinguishabilitybackflow as single-qubit coherence recovery. Using this observation, we motivate aninformation-mirror interpretation of coherence revivals in structured environments: environmentaldegrees of freedom may temporarily store phase information and later make part of it locally visibleagain in the qubit. We define a cycle-resolved reflection coefficient, R = B/L, where L is the coherencelost during a decay segment and B is the coherence recovered during the following revival. Fora recovery cycle referenced to its preceding coherence maximum, ordinary partial recovery satisfies0 ≤ R ≤ 1, with R = 1 corresponding to complete return to the previous maximum. This coefficientdoes not replace standard non-Markovianity measures, but provides a compact diagnostic of howstrongly a structured environment returns previously lost coherence.
We consider a single qubit undergoing pure dephasing with fixed populations and show that, fora natural pair of phase-opposite states, the trace distance coincides exactly with the ℓ1-norm ofcoherence. This allows the Breuer–Laine–Piilo (BLP) non-Markovianity indicator to be expresseddirectly in terms of single-qubit coherence dynamics within this setting, avoiding the usual optimizationover initial states. We also derive a simple relation between the entropy rate and coherence,showing that coherence revivals necessarily correspond to intervals of decreasing von Neumann entropy.Together, these results provide a transparent way to connect coherence, distinguishability,and information flow in dephasing qubits.
We derive a closed-form relation between the von Neumann entropy rate and the coherence dynamicsof a qubit undergoing pure dephasing without assuming Markovianity. For fixed populations,the entropy rate is expressed solely in terms of the ℓ1-coherence and its time derivative. The Markovianexponential decay is recovered as a limiting case. In non-Markovian regimes, the relationpredicts intervals of negative entropy production associated with coherence revivals. In realisticquantum devices, deviations from the ideal relation provide a direct diagnostic of non-ideal dephasing,enabling detection and mitigation of noise and relaxation effects from coherence measurementsalone.
We derive an analytical relation between the von Neumann entropy rate and the coherence dynamicsof a qubit undergoing pure dephasing without assuming Markovianity. The result expresses˙S(t) solely in terms of the ℓ1-coherence C(t) and its time derivative ˙C (t), for fixed populations. TheMarkovian exponential decay is recovered as a special case. In non-Markovian regimes, the formulapredicts intervals of negative entropy rate associated with coherence revivals, providing a compactlink between information backflow and entropy dynamics.
A single-qubit Ramsey or T2 measurement reports how much interference survives on a qubit, but not why the rest is missing. Phase information lost to an unobserved environment and phase information coherently redistributed into neighbouring qubits produce the same local signature, although only the second can be recovered. We study the interference that a target qubit regains when a controller measures a chosen set of helper systems and applies an outcome-dependent phase correction. For a fixed interference basis and any helper subset T, we prove that the maximum average l1 coherence recoverable this way equals 2‖C_T‖₁, twice the trace norm of the off-diagonal block of the reduced state, and that a projective measurement on T attains it. Imposing a budget on the number of helpers gives a monotone hierarchy I(0) ≤ I(1) ≤ … ≤ I(m) from local coherence to full assistance, from which we derive an access order d_η (the fewest helpers that recover a fraction η of the accessible interference) and an unlocking spectrum π_r. Exact examples show that states with identical local and fully assisted coherence can have opposite access structure, and that coherent leakage and dephasing with the same Ramsey visibility separate at the first helper layer. Exact state-vector calculations on eight qubits show the access order rising from 0.90 for depth-2 local circuits to 3.25 at depth 8 and 4.10 for Haar-random states. Applied retrospectively to published Bell-state tomography from the ibm_brisbane processor, the first layer shows that 91–96% of the accessible interference is invisible in the target marginal. We outline uses in hardware diagnostics: separating redistribution from decoherence, pairwise leakage maps from two-qubit tomography, and sizing mid-circuit readout for feed-forward. Files: the paper (PDF) and CRIA_code.zip, a Python package that regenerates every figure, table and number in the paper and numerically verifies its analytic results (run: python interference_accessibility_reproducibility.py --verify).
Directed Recoherence in Structured Non-Markovian Environments presents a rigorously defined operating regime of open quantum system dynamics in which environmental memory leads not to oscillatory revivals, but to directed, monotonic recoherence toward a long-lived metastable coherence plateau. The work introduces a minimal and physically standard two-bath pure-dephasing model composed of a broadband Markovian noise bath and a narrowband non-Markovian reference bath. Within this framework, a dimensionless recoherence parameter R = λ_R² / [ γ_N Γ (1 + (δ/Γ)² ) ] is shown to govern a sharp transition between ordinary decoherence and a directed recoherence regime. When R exceeds a threshold of order unity, the system exhibits a single coherence minimum followed by monotonic recoherence and a metastable phase-locked plateau over experimentally relevant timescales. Exact closed-form solutions for the coherence dynamics are derived, alongside falsifiable predictions including bounded phase deviation relative to the reference bath. Numerical simulations confirm the existence of a critical threshold and distinguish this regime from known non-Markovian revivals, decoherence-free subspaces, driven steady states, and many-body prethermalization. The manuscript reframes Self-Initiated Phase Re-Coherence (SIPR) not as a new physical principle, but as a previously under-characterized regime within standard quantum open-system theory. Potential experimental realizations are discussed for superconducting qubits with Purcell-filtered environments and trapped ions with engineered sidebands. A companion conceptual document explores the epistemic and interpretational implications of measurement, observation, and environmental structure without modifying the physical results presented here.