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Sharp estimates of quantum covering problems via a novel trace inequality

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arxiv 2507.07961 v1 pith:O2KFT37Q submitted 2025-07-10 quant-ph cs.ITmath.FAmath.ITmath.OA

Sharp estimates of quantum covering problems via a novel trace inequality

classification quant-ph cs.ITmath.FAmath.ITmath.OA
keywords quantumcoveringinequalitynovelone-shotoperatorproblemstrace
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this paper, we prove a novel trace inequality involving two operators. As applications, we sharpen the one-shot achievability bound on the relative entropy error in a wealth of quantum covering-type problems, such as soft covering, privacy amplification, convex splitting, quantum information decoupling, and quantum channel simulation by removing some dimension-dependent factors. Moreover, the established one-shot bounds extend to infinite-dimensional separable Hilbert spaces as well. The proof techniques are based on the recently developed operator layer cake theorem and an operator change-of-variable argument, which are of independent interest.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Optimal Trace Inequalities for Single-Shot Quantum Information

    quant-ph 2026-04 unverdicted novelty 8.0

    Optimal trace inequalities are derived for single-shot quantum information, replacing prior constants with a smaller Lambert-W prefactor for logarithmic traces and providing optimal two-sided collision-divergence bounds.

  2. Quantum Noncommutativity Uniquely Determines Relative Entropy

    quant-ph 2026-07 unverdicted novelty 7.0

    Quantum noncommutativity uniquely selects the Umegaki relative entropy as the only additive measure compatible with single-shot optimal discrimination in binary guessing games.

  3. Optimal Trace Inequalities for Single-Shot Quantum Information

    quant-ph 2026-04 unverdicted novelty 7.0

    The paper proves an optimal logarithmic trace inequality for positive operators using constant G_s from the scalar bound log(1+r) ≤ G_s r^s, lifted via iterative integration-by-parts, with optimality established for t...

  4. Smoothing Exponents and Decoupling in Semifinite von Neumann Algebras

    cs.IT 2026-07 accept novelty 6.5

    Smoothing exponents of max-relative entropy and catalytic decoupling reliability exponents retain their finite-dimensional sandwiched-Rényi formulae on semifinite von Neumann algebras.