aiqbench analysis
This research establishes unbounded gaps in the Holevo additivity theorem within finite-dimensional quantum systems, demonstrating scenarios where classical capacity diverges despite vanishing single-use information. By constructing specific channels derived from mixed-unitary structures and free-probabilistic proofs, the study provides explicit bounds on input-qubit costs required to achieve these linear output-qubit gaps. These findings advance fundamental limits in quantum information theory regarding channel capacities and entropy gaps.
Unbounded Holevo additivity gaps in finite dimensions
arXiv:2609.18222v1 Announce Type: new Abstract: We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(\Theta_K(n^2))$, and \[ \chi(T_n^{\otimes2})-2\chi(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates
Abstract:We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(\Theta_K(n^2))$, and \[ \chi(T_n^{\otimes2})-2\chi(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates
Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph)
arXiv:2609.18222 [quant-ph]
(or arXiv:2609.18222v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.18222 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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