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arXiv:2608.27202

Strong Converse Exponent of Quantum State Merging

Mario Berta, Hao-Chung Cheng, Roberto Rubboli, Marco Tomamichel

quant-phcs.ITSubmitted Aug 27, 2026• Announced Aug 28, 2026• 0 citations
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Abstract

We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $α$-$z$ conditional Rényi entropies with $z=α/2\in[1/2,1]$. This contrasts with the sandwiched conditional Rényi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.

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We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized ααα-zzz conditional Rényi entropies with z=α/2∈[1/2,1]z=α/2\in[1/2,1]z=α/2∈[1/2,1]. This contrasts with the sandwiched conditional Rényi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.
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Partially smoothed information measures are fundamental tools in one-shot quantum information theory. In this work, we determine the exact strong converse exponents of these measures for both pure quantum states and classical states. Notably, we find that the strong converse exponents based on trace distance takes different forms between pure and classical states, indicating that they are not uniform across all quantum states. Leveraging these findings, we derive the strong converse exponents for quantum data compression, intrinsic randomness extraction, and classical state splitting. A key technical step in our analysis is the determination of the strong converse exponent for classical privacy amplification, which is of independent interest.