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Documents authored by Qian, Luowen

Document
DOI: 10.4230/LIPIcs.ITCS.2026.24
Unitary Complexity and the Uhlmann Transformation Problem

Authors: John Bostanci, Yuval Efron, Tony Metger, Alexander Poremba, Luowen Qian, and Henry Yuen

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
State transformation problems such as compressing quantum information or breaking quantum commitments are fundamental quantum tasks. However, their computational difficulty cannot easily be characterized using traditional complexity theory, which focuses on tasks with classical inputs and outputs. To study the complexity of such state transformation tasks, we introduce a framework for unitary synthesis problems, including notions of reductions and unitary complexity classes. We use this framework to study the complexity of transforming one entangled state into another via local operations. We formalize this as the Uhlmann Transformation Problem, an algorithmic version of Uhlmann’s theorem. Then, we prove structural results relating the complexity of the Uhlmann Transformation Problem, polynomial space quantum computation, and zero knowledge protocols. The Uhlmann Transformation Problem allows us to characterize the complexity of a variety of tasks in quantum information processing, including decoding noisy quantum channels, breaking falsifiable quantum cryptographic assumptions, implementing optimal prover strategies in quantum interactive proofs, and decoding the Hawking radiation of black holes. Our framework for unitary complexity thus provides new avenues for studying the computational complexity of many natural quantum information processing tasks.
Cite as

John Bostanci, Yuval Efron, Tony Metger, Alexander Poremba, Luowen Qian, and Henry Yuen. Unitary Complexity and the Uhlmann Transformation Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bostanci_et_al:LIPIcs.ITCS.2026.24,
  author =	{Bostanci, John and Efron, Yuval and Metger, Tony and Poremba, Alexander and Qian, Luowen and Yuen, Henry},
  title =	{{Unitary Complexity and the Uhlmann Transformation Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.24},
  URN =		{urn:nbn:de:0030-drops-253111},
  doi =		{10.4230/LIPIcs.ITCS.2026.24},
  annote =	{Keywords: Uhlmann’s theorem, unitary complexity theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.24
On the Computational Hardness Needed for Quantum Cryptography

Authors: Zvika Brakerski, Ran Canetti, and Luowen Qian

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
In the classical model of computation, it is well established that one-way functions (OWF) are minimal for computational cryptography: They are essential for almost any cryptographic application that cannot be realized with respect to computationally unbounded adversaries. In the quantum setting, however, OWFs appear not to be essential (Kretschmer 2021; Ananth et al., Morimae and Yamakawa 2022), and the question of whether such a minimal primitive exists remains open. We consider EFI pairs - efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states. Building on the work of Yan (2022), which shows equivalence between EFI pairs and statistical commitment schemes, we show that EFI pairs are necessary for a large class of quantum-cryptographic applications. Specifically, we construct EFI pairs from minimalistic versions of commitments schemes, oblivious transfer, and general secure multiparty computation, as well as from QCZK proofs from essentially any non-trivial language. We also construct quantum computational zero knowledge (QCZK) proofs for all of QIP from any EFI pair. This suggests that, for much of quantum cryptography, EFI pairs play a similar role to that played by OWFs in the classical setting: they are simple to describe, essential, and also serve as a linchpin for demonstrating equivalence between primitives.
Cite as

Zvika Brakerski, Ran Canetti, and Luowen Qian. On the Computational Hardness Needed for Quantum Cryptography. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brakerski_et_al:LIPIcs.ITCS.2023.24,
  author =	{Brakerski, Zvika and Canetti, Ran and Qian, Luowen},
  title =	{{On the Computational Hardness Needed for Quantum Cryptography}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{24:1--24:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.24},
  URN =		{urn:nbn:de:0030-drops-175278},
  doi =		{10.4230/LIPIcs.ITCS.2023.24},
  annote =	{Keywords: quantum cryptography, efi, commitment scheme, oblivious transfer, zero knowledge, secure multiparty computation}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.100
Beating Classical Impossibility of Position Verification

Authors: Jiahui Liu, Qipeng Liu, and Luowen Qian

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Chandran et al. (SIAM J. Comput. '14) formally introduced the cryptographic task of position verification, where they also showed that it cannot be achieved by classical protocols. In this work, we initiate the study of position verification protocols with classical verifiers. We identify that proofs of quantumness (and thus computational assumptions) are necessary for such position verification protocols. For the other direction, we adapt the proof of quantumness protocol by Brakerski et al. (FOCS '18) to instantiate such a position verification protocol. As a result, we achieve classically verifiable position verification assuming the quantum hardness of Learning with Errors. Along the way, we develop the notion of 1-of-2 non-local soundness for a natural non-local game for 1-of-2 puzzles, first introduced by Radian and Sattath (AFT '19), which can be viewed as a computational unclonability property. We show that 1-of-2 non-local soundness follows from the standard 2-of-2 soundness (and therefore the adaptive hardcore bit property), which could be of independent interest.
Cite as

Jiahui Liu, Qipeng Liu, and Luowen Qian. Beating Classical Impossibility of Position Verification. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 100:1-100:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liu_et_al:LIPIcs.ITCS.2022.100,
  author =	{Liu, Jiahui and Liu, Qipeng and Qian, Luowen},
  title =	{{Beating Classical Impossibility of Position Verification}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{100:1--100:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.100},
  URN =		{urn:nbn:de:0030-drops-156963},
  doi =		{10.4230/LIPIcs.ITCS.2022.100},
  annote =	{Keywords: cryptographic protocol, position verification, quantum cryptography, proof of quantumness, non-locality}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.8
Lower Bounds for Function Inversion with Quantum Advice

Authors: Kai-Min Chung, Tai-Ning Liao, and Luowen Qian

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
Function inversion is the problem that given a random function f: [M] → [N], we want to find pre-image of any image f^{-1}(y) in time T. In this work, we revisit this problem under the preprocessing model where we can compute some auxiliary information or advice of size S that only depends on f but not on y. It is a well-studied problem in the classical settings, however, it is not clear how quantum algorithms can solve this task any better besides invoking Grover’s algorithm [Grover, 1996], which does not leverage the power of preprocessing. Nayebi et al. [Nayebi et al., 2015] proved a lower bound ST² ≥ ̃Ω(N) for quantum algorithms inverting permutations, however, they only consider algorithms with classical advice. Hhan et al. [Minki Hhan et al., 2019] subsequently extended this lower bound to fully quantum algorithms for inverting permutations. In this work, we give the same asymptotic lower bound to fully quantum algorithms for inverting functions for fully quantum algorithms under the regime where M = O(N). In order to prove these bounds, we generalize the notion of quantum random access code, originally introduced by Ambainis et al. [Ambainis et al., 1999], to the setting where we are given a list of (not necessarily independent) random variables, and we wish to compress them into a variable-length encoding such that we can retrieve a random element just using the encoding with high probability. As our main technical contribution, we give a nearly tight lower bound (for a wide parameter range) for this generalized notion of quantum random access codes, which may be of independent interest.
Cite as

Kai-Min Chung, Tai-Ning Liao, and Luowen Qian. Lower Bounds for Function Inversion with Quantum Advice. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chung_et_al:LIPIcs.ITC.2020.8,
  author =	{Chung, Kai-Min and Liao, Tai-Ning and Qian, Luowen},
  title =	{{Lower Bounds for Function Inversion with Quantum Advice}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.8},
  URN =		{urn:nbn:de:0030-drops-121134},
  doi =		{10.4230/LIPIcs.ITC.2020.8},
  annote =	{Keywords: Cryptanalysis, Data Structures, Quantum Query Complexity}
}
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