arXiv subjects

Minglong Qin

Publications and source records attributed to Minglong Qin.

8 recordsLinked to original sources

arXiv2026

Rank and Range Criteria for Mixed-State Determination from Local Marginals

Determining whether a mixed quantum state is uniquely determined among all states by its k-body marginals (k-UDA) is a fundamental problem in quantum system certification. We develop a range-based approach to this problem by analyzing the structure of the range of the global state. For three-qubit states, we show that states with GHZ-SLOCC-free ranges are 2-UDA at ranks one, three, and four. We derive a necessary and sufficient range criterion for rank-two 2-UDA states and reduce it to a finite quadratic-form test. To cover the remaining range configurations, we formulate an exact range-restricted semidefinite programming criterion and extend it to arbitrary finite-dimensional tripartite states. We also show that every three-qubit state of rank at least five is not 2-UDA, and further extend high-rank obstructions to multipartite systems. For a channel-based multipartite family, we characterize exactly when a state is $(n-1)$-UDA and show that lower-order marginals never suffice. Finally, we apply these results to the certification of genuine multipartite entanglement.

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arXiv2025

Nonlocal Games in the High-Noise Regime: Optimal Quantum Values and Rigidity

Motivated by the limitations of near-term quantum devices, we study nonlocal games in the high-noise regime, where the two players may share arbitrarily many copies of a noisy entangled state. In this regime, existing rigidity theorems are unable to certify any nontrivial quantum structure. We first characterize the maximal quantum winning probabilities of the CHSH game [Clauser et al. '69], the Magic Square game [Mermin '90], and their 2-out-of-n variants [Chao et al. '18] as explicit functions of the noise rate. These characterizations enable the construction of device-independent protocols for estimating the underlying noise level. Building on these results, we prove noise-robust rigidity theorems showing that these games certify one, two, and n pairs of anticommuting Pauli observables, respectively. To our knowledge, these are the first rigidity results of Pauli measurements that remain sound in the high-noise regime, which has applications in Measurement-Device-Independent (MDI) cryptography and studying the computational power of Multi-prover Interactive Proof System with entanglement and a vanishing completeness-soundness gap ($\text{MIP}^*_0$). Our proofs rely on Sum-of-Squares decompositions and Pauli analysis techniques originating from quantum proof systems and quantum learning theory, respectively.

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arXiv2025

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.

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arXiv2025

Consecutive Measurement Tradeoffs in Quantum Cryptography

Measuring a quantum system can reveal information while disturbing its state. Consequently, the probabilities of obtaining desired outcomes in individual measurements constrain the probability of obtaining them in sequence. This interplay arises naturally in mistrustful quantum cryptography, where a dishonest participant may perform sequential measurements to extract more information than the protocol allows. We develop consecutive measurement theorems (CMTs) to quantify this constraint, relating the average success probability of a single measurement to that of an ordered pair of distinct measurements. For measurements on a common state, we derive the optimal lower bound on consecutive-measurement success as a function of single-measurement success and provide matching constructions over the entire parameter range. We also establish the first robust CMTs for measurements on different but nearby states, with closeness quantified by fidelity or trace distance. We use these results to strengthen sum-binding guarantees for relativistic bit commitment and soundness bounds for relativistic zero-knowledge proofs, and to obtain improved no-go results for quantum oblivious transfer and quantum private query. Our results establish CMTs as a versatile tool for translating consecutive-measurement constraints into concrete cryptographic bounds and suggest applications in other quantum-information settings.

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arXiv2023

The Computational Advantage of MIP* Vanishes in the Presence of Noise

Quantum multiprover interactive proof systems with entanglement MIP* are much more powerful than its classical counterpart MIP (Babai et al. '91, Ji et al. '20): while MIP = NEXP, the quantum class MIP* is equal to RE, a class including the halting problem. This is because the provers in MIP* can share unbounded quantum entanglement. However, recent works of Qin and Yao '21 and '23 have shown that this advantage is significantly reduced if the provers' shared state contains noise. This paper attempts to exactly characterize the effect of noise on the computational power of quantum multiprover interactive proof systems. We investigate the quantum two-prover one-round interactive system MIP*[poly, O(1)], where the verifier sends polynomially many bits to the provers and the provers send back constantly many bits. We show noise completely destroys the computational advantage given by shared entanglement in this model. Specifically, we show that if the provers are allowed to share arbitrarily many noisy EPR states, where each EPR state is affected by an arbitrarily small constant amount of noise, the resulting complexity class is equivalent to NEXP = MIP. This improves significantly on the previous best-known bound of NEEEXP (nondeterministic triply exponential time) by Qin and Yao '21. We also show that this collapse in power is due to the noise, rather than the O(1) answer size, by showing that allowing for noiseless EPR states gives the class the full power of RE = MIP*[poly, poly]. Along the way, we develop two technical tools of independent interest. First, we give a new, deterministic tester for the positivity of an exponentially large matrix, provided it has a low-degree Fourier decomposition in terms of Pauli matrices. Secondly, we develop a new invariance principle for smooth matrix functions having bounded third-order Fr\'echet derivatives or which are Lipschitz continous.

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arXiv2023

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 $\epsilon$-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.

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arXiv2023

Decidability of fully quantum nonlocal games with noisy maximally entangled states

This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee performs a binary POVM measurement to decide whether they win the game after receiving the quantum answers from the players. The quantum value of a fully quantum nonlocal game is the supremum of the probability that they win the game, where the supremum is taken over all the possible entangled states shared between the players and all the valid quantum operations performed by the players. The seminal work $\mathrm{MIP}^*=\mathrm{RE}$ implies that it is undecidable to approximate the quantum value of a fully nonlocal game. This still holds even if the players are only allowed to share (arbitrarily many copies of) maximally entangled states. This paper investigates the case that the shared maximally entangled states are noisy. We prove that there is a computable upper bound on the copies of noisy maximally entangled states for the players to win a fully quantum nonlocal game with a probability arbitrarily close to the quantum value. This implies that it is decidable to approximate the quantum values of these games. Hence, the hardness of approximating the quantum value of a fully quantum nonlocal game is not robust against the noise in the shared states. This paper is built on the framework for the decidability of non-interactive simulations of joint distributions and generalizes the analogous result for nonlocal games. We extend the theory of Fourier analysis to the space of super-operators and prove several key results including an invariance principle and a dimension reduction for super-operators. These results are interesting in their own right and are believed to have further applications.

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arXiv2021

Nonlocal games with noisy maximally entangled states are decidable

This paper considers a special class of nonlocal games $(G,ψ)$, where $G$ is a two-player one-round game, and $ψ$ is a bipartite state independent of $G$. In the game $(G,ψ)$, the players are allowed to share arbitrarily many copies of $ψ$. The value of the game $(G,ψ)$, denoted by $ω^*(G,ψ)$, is the supremum of the winning probability that the players can achieve with arbitrarily many copies of preshared states $ψ$. For a noisy maximally entangled state $ψ$, a two-player one-round game $G$ and an arbitrarily small precision $ε>0$, this paper proves an upper bound on the number of copies of $ψ$ for the players to win the game with a probability $ε$ close to $ω^*(G,ψ)$. Hence, it is feasible to approximately compute $ω^*(G,ψ)$ to an arbitrarily precision. Recently, a breakthrough result by Ji, Natarajan, Vidick, Wright and Yuen showed that it is undecidable to approximate the values of nonlocal games to a constant precision when the players preshare arbitrarily many copies of perfect maximally entangled states, which implies that $\mathrm{MIP}^*=\mathrm{RE}$. In contrast, our result implies the hardness of approximating nonlocal games collapses when the preshared maximally entangled states are noisy. The paper develops a theory of Fourier analysis on matrix spaces by extending a number of techniques in Boolean analysis and Hermitian analysis to matrix spaces. We establish a series of new techniques, such as a quantum invariance principle and a hypercontractive inequality for random operators, which we believe have further applications.

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