We study the three-parameter family of quantum conditional R\'enyi entropies $H_{\alpha,z}^\lambda$ introduced in \textit{Commun. Math. Phys.} 407, 180 (2026). We prove that the previously established data-processing region is sharp. We then characterize the club-sandwiched family through a classical coarse-graining principle: within the full data-processing region, universal monotonicity under deterministic coarse-graining of the classical conditioned register holds if and only if $z = \alpha$. Finally, we establish rigidity of entropic duality by showing that any universal duality relation for finite-dimensional tripartite pure states must satisfy the known parameter relations. Thus, the data-processing region, the club-sandwiched subfamily, and the duality transformation are each uniquely characterized by their respective universal properties.
Standard finite quantum de Finetti theorems approximate the $k$-system marginals of permutation-invariant states of $n$-systems by mixtures of independent and identically distributed (iid) states, usually in trace distance. We prove both standard and Renner's exponential de Finetti theorems in the stronger form of oper...
Extracting operationally meaningful quantities such as von Neumann entropy and mutual information is central to characterizing many-body quantum systems, yet experiments and numerics often provide direct access only to integer R\'enyi entropies. Whereas conventional extrapolation relies on a prescribed fitting ansatz,...
A. Raj, Akash Vijay, Hong-Chen Jiang et al.· 0 citations
Quantum conditional mutual information (QCMI) is a fundamental measure of conditional independence, with central applications throughout quantum information theory and many-body physics. Despite its importance, finding a fully quantum R\'enyi generalization that satisfies all desirable structural properties has remaine...
Roberto Rubboli, Amir Arqand, Mark M. Wilde· 0 citations
We investigate Strong Data-Processing Inequality (SDPI) constants for R\'enyi Divergences on finite spaces. We study their dependence on the R\'enyi order $\alpha$, proving that they are non-decreasing and that their scaling by $(\alpha-1)$ is convex for $\alpha\geq1$. We also identify several support restrictions on t...
Adrien Vandenbroucque, A. Esposito, Michael C. Gastpar· 1 citation· ⚡1
We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $\alpha$-$z$ conditional R\'enyi entropies with $z=\alpha/2\in[1/2,1]$. This contrasts with the sandwiched conditional R\'enyi entropies that typically govern strong converse e...
Mario Berta, Hao-Chung Cheng, Roberto Rubboli et al.· 2 citations· ⚡1
In odd local dimension $D$, complete Wigner positivity yields stochastic phase-space dynamics on Wigner-nonnegative states but does not control signed inputs, entanglement across channel uses, or collective decoding. Using a subsystem-resolved Weyl decomposition, we characterize the equality conditions of the tensor-st...
Se-Wan Ji· 0 citations
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