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Documents authored by Chen, Kean

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Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.58
Quantum Multi-Level Estimation of Functionals of Discrete Distributions

Authors: Kean Chen, Minbo Gao, Tongyang Li, Qisheng Wang, and Xinzhao Wang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We propose a quantum multi-level estimation framework for a functional ∑_{i=1}^n f(p_i) of a discrete distribution (p_i)_{i=1}^n. We partition the values p_i into logarithmically many intervals whose length decays exponentially. For each interval, we perform non-destructive singular value discrimination to isolate the relevant p_i, enabling adaptive estimation of the partial sum over this interval. Unlike previous variable-time approaches, our method avoids high control overhead and requires only constant extra ancilla qubits. As an application, we present efficient quantum estimators for the q-Tsallis entropy of discrete distributions. Specifically, - For q > 1, we obtain a near-optimal quantum algorithm with query complexity Θ̃(1/ε^{max{1/(2(q-1)), 1}}), improving the prior best O(1/ε^{1+1/(q-1)}) due to Liu and Wang (SODA 2025; IEEE Trans. Inf. Theory 2026). - For 0 < q < 1, we obtain a quantum algorithm with query complexity Õ(n^{1/q-1/2}/ε^{1/q}), exhibiting a quantum speedup over the near-optimal classical estimators due to Jiao, Venkat, Han, and Weissman (IEEE Trans. Inf. Theory 2017). Our results achieve, to our knowledge, the first near-optimal quantum estimators for parameterized q-entropy for non-integer q.
Cite as

Kean Chen, Minbo Gao, Tongyang Li, Qisheng Wang, and Xinzhao Wang. Quantum Multi-Level Estimation of Functionals of Discrete Distributions. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 58:1-58:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2026.58,
  author =	{Chen, Kean and Gao, Minbo and Li, Tongyang and Wang, Qisheng and Wang, Xinzhao},
  title =	{{Quantum Multi-Level Estimation of Functionals of Discrete Distributions}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{58:1--58:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.58},
  URN =		{urn:nbn:de:0030-drops-264473},
  doi =		{10.4230/LIPIcs.ICALP.2026.58},
  annote =	{Keywords: Quantum algorithms, functional estimation, entropy estimation, query complexity, Tsallis entropy}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.59
Strict Hierarchy for Quantum Channel Certification to Unitary

Authors: Kean Chen, Qisheng Wang, and Zhicheng Zhang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We consider the problem of quantum channel certification to unitary, where one is given access to an unknown d-dimensional channel ℰ, and wants to test whether ℰ is equal to a target unitary channel or is ε-far from it in the diamond norm. We present optimal quantum algorithms for this problem, settling the query complexities in three access models with increasing power. Specifically, we show that: 1) Θ(d/ε²) queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). 2) Θ(d/ε) queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). 3) Θ(√d/ε) queries suffice for source-code access model, matching the lower bound due to Jeon and Oh (npj Quantum Inf. 2026). This demonstrates a strict hierarchy of complexities for quantum channel certification to unitary across various access models.
Cite as

Kean Chen, Qisheng Wang, and Zhicheng Zhang. Strict Hierarchy for Quantum Channel Certification to Unitary. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2026.59,
  author =	{Chen, Kean and Wang, Qisheng and Zhang, Zhicheng},
  title =	{{Strict Hierarchy for Quantum Channel Certification to Unitary}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{59:1--59:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.59},
  URN =		{urn:nbn:de:0030-drops-264480},
  doi =		{10.4230/LIPIcs.ICALP.2026.59},
  annote =	{Keywords: Quantum algorithms, quantum channels, quantum certification, query complexity, entanglement fidelity}
}
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