Conditional Error Exponents of Probabilistic Quantum Resource Distillation
Abstract
Quantum resource distillation converts imperfect resource states into highly resourceful targets and is a central task in quantum information processing. When distillation is probabilistic, unfavorable outcomes may be discarded and the quality of the output is evaluated conditioned on success, leading to a notion of reliability that differs from the deterministic setting. Here we study the conditional error exponents of probabilistic quantum resource distillation under approximately resource-nongenerating instruments and derive its general connection to the postselected composite quantum hypothesis testing against the corresponding set of free states. This reduction leads naturally to scale-invariant projective distinguishability measures and provides finite-blocklength bounds for a broad class of resource theories. We apply the framework to entanglement, coherence, and magic. For entanglement and magic, we obtain exact zero-rate asymptotic characterizations of the conditional error exponent in terms of regularized projective distinguishability, while for coherence we derive general finite-blocklength and asymptotic bounds. For representative entangled and magic states, the resulting quantities can be evaluated analytically and reveal regimes in which postselection yields a strictly larger conditional error exponent than deterministic distillation. Furthermore, we also show that the conditional error exponents for probabilistic entanglement distillation under a strictly positive success probability constraint are smaller than those with no constraints on the success probability.
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BibTeX
@misc{shi2026conditional,
title = {{Conditional Error Exponents of Probabilistic Quantum Resource Distillation}},
author = {Xian Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.06688},
eprint = {2609.06688},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06688},
note = {CC0},
}
RIS
TY - UNPB
TI - Conditional Error Exponents of Probabilistic Quantum Resource Distillation
AU - Xian Shi
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2609.06688
UR - https://arxiv.org/abs/2609.06688
AB - Quantum resource distillation converts imperfect resource states into highly resourceful targets and is a central task in quantum information processing. When distillation is probabilistic, unfavorable outcomes may be discarded and the quality of the output is evaluated conditioned on success, leading to a notion of reliability that differs from the deterministic setting. Here we study the conditional error exponents of probabilistic quantum resource distillation under approximately resource-nongenerating instruments and derive its general connection to the postselected composite quantum hypothesis testing against the corresponding set of free states. This reduction leads naturally to scale-invariant projective distinguishability measures and provides finite-blocklength bounds for a broad class of resource theories. We apply the framework to entanglement, coherence, and magic. For entanglement and magic, we obtain exact zero-rate asymptotic characterizations of the conditional error exponent in terms of regularized projective distinguishability, while for coherence we derive general finite-blocklength and asymptotic bounds. For representative entangled and magic states, the resulting quantities can be evaluated analytically and reveal regimes in which postselection yields a strictly larger conditional error exponent than deterministic distillation. Furthermore, we also show that the conditional error exponents for probabilistic entanglement distillation under a strictly positive success probability constraint are smaller than those with no constraints on the success probability.
ER -