Optimal Temporal Hiding in Correlated Quantum Reference-Frame Processes
Abstract
A finite group-valued temporal reference frame defines a correlated random-unitary process rather than a list of independent channels. We identify a regime in which its complete trajectory law is an exact operational coordinate. If the carrier contains every irreducible representation of the finite group G, one ancilla-assisted input resolves all group elements, and for arbitrary laws μ,ν on Gn the strategy half-distance equals dTV(μ,ν). Optimal output-side causal post-processing likewise reduces to classical convolution on Gn. This converts temporal hiding into a q-ary coding problem. Uniform coset laws of an [n,k]q code are identical on every set of fewer than d(C⊥) slots and perfectly distinguishable globally. For M sectors with leakage at most η from t selected slots and global decoding error ε, we obtain (1−ε)log M ≤ (n−t)log q+η+h2(ε). For nested codes C⊂ D, the payload R=dim D−dim C, invisible depth t=drel(C⊥,D⊥)−1, and sector distance drel(D,C) obey R+t+drel(D,C)−1≤ n and R+t+2e+f≤ n, where e and f are adversarial errors and known erasures. Nested generalized Reed-Solomon codes attain the bounds in their existence range. We also give the exact projection-rank leakage profile and show that hiding arbitrary coherent superpositions from t slots is precisely quantum erasure correction, yielding logq K+2t≤ n. The results separate classical trajectory privacy from coherent temporal privacy and quantify the robust payload hidden from reduced process tomography.
Related
- Reference-Null Calibrated Thresholds for E-Processes with Applications to Conformal Martingales
- Independently Verified Causal Spatio-Temporal Covariance Under Correlated Amplitude and Pointing Noise in Fractional Nonlocal Photo-Thermoelastic Semiconductors
- Assessing Temporal Dispersion of Time-Varying Channel at 38 GHz for Different Reference Signals
- Mutual Information Optimal Density Control of Linear Systems and Generalized Schrödinger Bridges with Reference Refinement
- Rigidity of one-dimensional point processes via optimal transport
BibTeX
@misc{churilov2026optimal,
title = {{Optimal Temporal Hiding in Correlated Quantum Reference-Frame Processes}},
author = {Maxim V. Churilov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18948},
eprint = {2609.18948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18948},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Temporal Hiding in Correlated Quantum Reference-Frame Processes
AU - Maxim V. Churilov
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.18948
UR - https://arxiv.org/abs/2609.18948
AB - A finite group-valued temporal reference frame defines a correlated random-unitary process rather than a list of independent channels. We identify a regime in which its complete trajectory law is an exact operational coordinate. If the carrier contains every irreducible representation of the finite group G, one ancilla-assisted input resolves all group elements, and for arbitrary laws μ,ν on G^n the strategy half-distance equals d_TV(μ,ν). Optimal output-side causal post-processing likewise reduces to classical convolution on G^n. This converts temporal hiding into a q-ary coding problem. Uniform coset laws of an [n,k]_q code are identical on every set of fewer than d(C^⊥) slots and perfectly distinguishable globally. For M sectors with leakage at most η from t selected slots and global decoding error ε, we obtain (1−ε)log M ≤ (n−t)log q+η+h_2(ε). For nested codes C⊂ D, the payload R=dim D−dim C, invisible depth t=d_rel(C^⊥,D^⊥)−1, and sector distance d_rel(D,C) obey R+t+d_rel(D,C)−1≤ n and R+t+2e+f≤ n, where e and f are adversarial errors and known erasures. Nested generalized Reed-Solomon codes attain the bounds in their existence range. We also give the exact projection-rank leakage profile and show that hiding arbitrary coherent superpositions from t slots is precisely quantum erasure correction, yielding log_q K+2t≤ n. The results separate classical trajectory privacy from coherent temporal privacy and quantify the robust payload hidden from reduced process tomography.
ER -