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.
Sharp estimates of quantum covering problems via a novel trace inequality
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abstract
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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Quantum relative entropy is the unique normalized, additive, Lorenz-continuous divergence monotone under binary guessing games.
Smoothing exponents of max-relative entropy and catalytic decoupling reliability exponents retain their finite-dimensional sandwiched-Rényi formulae on semifinite von Neumann algebras.
citing papers explorer
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Optimal Trace Inequalities for Single-Shot Quantum Information
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.
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Quantum Noncommutativity Uniquely Determines Relative Entropy
Quantum relative entropy is the unique normalized, additive, Lorenz-continuous divergence monotone under binary guessing games.
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Smoothing Exponents and Decoupling in Semifinite von Neumann Algebras
Smoothing exponents of max-relative entropy and catalytic decoupling reliability exponents retain their finite-dimensional sandwiched-Rényi formulae on semifinite von Neumann algebras.