What question did this study set out to answer?

To prove that N-qubit systems exhibit a palindromic symmetry in the Liouvillian spectrum under dephasing conditions.

March 25, 2026Open Access

Palindromic Liouvillian symmetry under dephasing: proof, hardware validation, and dephasing noise as information channel

Key Points

To prove that N-qubit systems exhibit a palindromic symmetry in the Liouvillian spectrum under dephasing conditions.
Analysis of N-qubit systems with various graph topologies under local single-axis dephasing
Verification through hardware testing on IBM Torino
Measurement of channel capacity and optimization strategies for quantum communication
Exact palindromic symmetry in Liouvillian spectrum for all tested topologies
Measured channel capacity of 15.5 bits at 1% noise
Achieved 100% accuracy in classifying spatial profiles with significant optimization

Abstract

We prove that for N-qubit systems with any Pauli-pair Hamiltonian on any graph topology, subject to local single-axis dephasing, the Liouvillian spectrum has an exact palindromic symmetry. The conjugation operator Π satisfies Π L Π¹ = −L − 2Σγ I. Key Results Palindromic proof: Verified through N=8 (65536×65536 Liouvillian, 54, 118 oscillatory eigenvalues, zero exceptions). All topologies: chain, star, ring, complete graph, binary tree. 36/36 resolution: All two-term Pauli-pair combinations explained. 20 via uniform Π (P1/P4 families), 3 via non-uniform alternating operators, 11 break structurally at N≥3, 2 via genuinely non-local (entangled) Π operators. Hardware validation: IBM Torino (ibmₜorino, Q80). Predicted crossing time 15. 01 μs, measured 15. 29 μs. Deviation: 1. 9%. Central New Result: Noise Is Signal The spatial dephasing profile across a spin chain is a readable information channel: 15. 5 bits channel capacity at 1% noise (of 16. 6 theoretical max) 5 independent SVD modes, each a spatial frequency 100% classification accuracy across 20 spatial profiles 21. 5× optimization via V-shape gradient, dynamic decoupling, time-resolved decoding +83% end-to-end MI with staged relay protocol (11-qubit chain) The palindromic spectral structure functions as the antenna. Additional Proven Results Qubit uniqueness: d²−2d=0 excludes all higher dimensions. Only qubits (d=2) carry a palindromic mirror. Incompleteness proof: Five internal noise candidates eliminated. Dephasing must originate from outside the framework. Universal lifetime: x³+x=½ gives t*/T₂ ≈ 0. 858 (platform-independent). Fold catastrophe: CΨ=¼ is structurally stable (Thom-Arnold classification), equivalent to the Mandelbrot cusp at c=¼. Experienced time: γ is necessary and sufficient for irreversibility. J provides content, γ provides the arrow. Engineering Six design rules for palindrome-aware quantum repeaters. Mediator bridge preserves palindrome (1024/1024 pairs). Quantum transistor mapping: gate=γ, threshold=¼. Repository 59 experiment documents, 7 formal proofs, 14 synthesis documents, and a complete mathematical reference (Tafelwerk). Every document has SEO keywords, abstract, and standard header. Quality-reviewed by independent AI pass (93 fixes across 37 files).

Palindromic Liouvillian symmetry under dephasing: proof, hardware validation, and dephasing noise as information channel

Key Points

Abstract

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