arXiv subjects

Chuhan Lu

Publications and source records attributed to Chuhan Lu.

3 recordsLinked to original sources

arXiv2026

Complexity Theory for Quantum Promise Problems

We begin by establishing structural results for several fundamental quantum complexity classes: p/mBQP, p/mQ(C)MA, $\text{p/mQSZK}_{\text{hv}}$, p/mQIP, p/mBQP/qpoly, p/mBQP/poly, and p/mPSPACE. This includes identifying complete problems, as well as proving containment and separation results among these classes. Here, p/mC denotes the corresponding quantum promise complexity class with pure (p) or mixed (m) quantum input states for any classical complexity class C. Surprisingly, our findings uncover relationships that diverge from their classical analogues -- specifically, we show unconditionally that p/mQIP$\neq$p/mPSPACE and p/mBQP/qpoly$\neq$p/mBQP/poly. This starkly contrasts the classical setting, where QIP$=$PSPACE and separations such as BQP/qpoly$\neq$BQP/poly are only known relative to oracles. More interestingly, these separation results further connected to the topic of for both quantum property testing and unitary synthesis. This new framework has numerous applications in quantum cryptography, particularly in the contexts of Microcrypt. We provide a better characterization of its primitives; for example, we show that OWSG and PRS can be broken by a p/mQCMA oracle, leading to a natural quantum analogue of Impagliazzo's five worlds by substituting the classical complexity classes in Pessiland, Heuristica, and Algorithmica with mBQP and mQCMA. Moreover, we establish the relativization barrier for proving the existence of EFI, noting that no such barrier currently exists within traditional complexity theory.

quant-ph↗

arXiv2026

Parallel Kac's Walk Generates PRU

Ma and Huang recently proved that the PFC construction, introduced by Metger, Poremba, Sinha and Yuen [MPSY24], gives an adaptive-secure pseudorandom unitary family PRU. Their proof developed a new path recording technique [MH25]. In this work, we show that a linear number of sequential repetitions of the parallel Kac's Walk, introduced by Lu, Qin, Song, Yao and Zhao [LQS+26], also forms an adaptive-secure PRU, confirming a conjecture therein. Moreover, it additionally satisfies strong security against adversaries making inverse queries. This gives an alternative PRU construction, and provides another instance demonstrating the power of the path recording technique. We also discuss some further simplifications and implications.

quant-ph↗

arXiv2024

Quantum Pseudorandom Scramblers

Quantum pseudorandom state generators (PRSGs) have stimulated exciting developments in recent years. A PRSG, on a fixed initial (e.g., all-zero) state, produces an output state that is computationally indistinguishable from a Haar random state. However, pseudorandomness of the output state is not guaranteed on other initial states. In fact, known PRSG constructions provably fail on some initial states. In this work, we propose and construct quantum Pseudorandom State Scramblers (PRSSs), which can produce a pseudorandom state on an arbitrary initial state. In the information-theoretical setting, we obtain a scrambler which maps an arbitrary initial state to a distribution of quantum states that is close to Haar random in total variation distance. As a result, our scrambler exhibits a dispersing property. Loosely, it can span an $ε$-net of the state space. This significantly strengthens what standard PRSGs can induce, as they may only concentrate on a small region of the state space provided that average output state approximates a Haar random state. Our PRSS construction develops a parallel extension of the famous Kac's walk, and we show that it mixes exponentially faster than the standard Kac's walk. This constitutes the core of our proof. We also describe a few applications of PRSSs. While our PRSS construction assumes a post-quantum one-way function, PRSSs are potentially a weaker primitive and can be separated from one-way functions in a relativized world similar to standard PRSGs.

quant-ph↗