arXiv subjects

Xuan Du Trinh

Publications and source records attributed to Xuan Du Trinh.

9 recordsLinked to original sources

arXiv2026

Full-Rank Noise Forbids Long-Range Entanglement Swapping

Quantum repeaters extend entanglement by swapping noisy elementary links. We prove that full-rank noise forbids this at long range: for any entangled full-rank two-qubit link, there is a finite depth beyond which no end-to-end entanglement can be established regardless of the measurement outcomes on intermediate qubits, even under any adaptive postselected strategy. This limit is set by one spectral parameter of the link, giving a no-go criterion for repeater routing. In contrast, we construct link state families of rank three and rank two that admit postselected measurement outcome branches of exponentially small probability but with strictly positive concurrence at every finite depth. Swapping experiments on a superconducting processor show that links of equal initial concurrence but different rank behave differently under postselected swapping. In the language of many-body physics, the chain is a matrix-product density operator, and full-rank bonds forbid long-range localizable entanglement, while rank-deficient bonds can sustain it.

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arXiv2026

One Relative Phase Orders Operational Thresholds of Noisy Bell Pairs

Unlike the two-qubit entangled and CHSH-nonlocal sets, the steerable and Bell-nonlocal ones have no known general closed-form criterion. For any such operational ability whose failing states form a convex set closed under local unitaries, and for a Bell mixture with arbitrary noise, the $X$ part of the noise gives an upper bound on the definitive threshold, the Bell weight above which the mixture attains the ability. That bound is the tightest that the seven of the fifteen Pauli expectation values fixing the $X$ part can support. The same theorem shows that a state has the ability whenever its $X$ part does, so partial tomography of a state can certify its ability. When noise is of $X$ form, the mixture carries a relative phase between the noise and Bell coherences that cannot be gauged away by local unitaries, and it controls the threshold through interference. We prove a monotonicity law: the threshold is nondecreasing in this phase, whether or not a closed-form criterion for the ability exists.

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arXiv2026

Operational thresholds of Bell mixtures with complex X noise

Noisy Bell mixtures may carry entanglement, standard teleportation usefulness, projective-measurement steerability, and optimized Cavalcanti-Jones-Wiseman-Reid (CJWR) and Clauser-Horne-Shimony-Holt (CHSH) violations. If the noise already has an ability, the mixture may lose and later recover it at distinct boundary crossings as the Bell weight decreases. We characterize ability-absence intervals and definitive thresholds for mixtures of $|Φ^+\rangle$ with arbitrary complex two-qubit $X$ noise. A closed-form singular-value flow of the Pauli correlation tensor gives the exact teleportation-useless, CJWR-satisfying, and CHSH-local intervals, while the positive partial transpose criterion gives the exact separable interval. At fixed populations and coherence magnitudes, these intervals widen as the relative phase between the $Φ$-block coherence of the noise and the Bell coherence increases from $0$ to $π$. The definitive thresholds form a universal chain from entanglement through teleportation usefulness and the three-setting CJWR witness to the common two-setting CJWR witness and CHSH-nonlocal threshold. Replacing teleportation usefulness by steerability gives a second chain, although their thresholds are not mutually ordered. For arbitrary pure two-qubit noise, the steerability thresholds in both directions for projective measurements and arbitrary positive operator-valued measures equal the entanglement threshold. For arbitrary product noise, an effective $X$-state singular-value flow gives the teleportation usefulness, CJWR witness, and CHSH-nonlocal thresholds. If a local noise factor is pure, the entanglement threshold and all four steerability thresholds are zero. For generic full-rank mixed $X$ noise, finite-setting semidefinite programs give upper bounds on the unknown directional projective-measurement steerability thresholds.

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arXiv2026

Absorption capacity of separable noise: Bell-mixing thresholds on entanglement and teleportation

We study Bell-mixing lines $ρ_λ=λΦ^+ +(1-λ)σ$, where $Φ^+$ is a fixed Bell reference and $σ$ is a separable two-qubit noise state. Along this line there are two operational crossings: the state becomes entangled, and it reaches quantum teleportation advantage over classical strategies. We package these crossings as capacities of the noise state. The entanglement absorption capacity $C_{\rm abs}(σ)$ is the largest amount of Bell reference that $σ$ can absorb while the partial transpose remains positive. The fidelity absorption capacity $C_F(σ)$ is the largest amount of Bell reference that $σ$ can absorb while keeping the maximal teleportation fidelity at or below the classical bound $2/3$. The thresholds corresponding to the two crossing points are obtained from the same Möbius map, $λ_* = C_{\rm abs}/(1+C_{\rm abs})$ and $λ_F = C_F/(1+C_F)$. We derive closed-form capacities and thresholds for product noise states and separable complex $X$ noise states. For product noise, $C_{\rm abs}$ depends only on local marginal purities, while $C_F$ also depends on orientation relative to the maximally entangled reference. For $X$ noise states, both capacities are explicit in all four Bell frames. We also study three extensions: arbitrary pure-state references, the evolution of $X$ noise states and their capacities under local amplitude-damping and dephasing channels, and decomposition certificates that give lower bounds on the capacities, hence on the thresholds, for general separable noise.

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arXiv2026

On the emergence of classical stochasticity

We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not automatically justify classical reasoning based on the assumption that the system exists in a definite state at intermediate times. On the other hand, we show that this assumption is crucial for the standard calculation of stochastic times such as the persistent time and the time of first arrivals. We then consider examples of single particles, bosons, and fermions in the so-called ultradecoherence limit to illustrate how classical stochasticity may emerge from quantum mechanics.

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arXiv2026

Manjushri: A Tool for Equivalence Checking of Quantum Circuits

Verifying whether two quantum circuits are equivalent is a central challenge in the compilation and optimization of quantum programs. We introduce \textsc{Manjushri}, a new automated framework for scalable quantum-circuit equivalence checking. \textsc{Manjushri} uses local projections as discriminative circuit fingerprints, implemented with weighted binary decision diagrams (WBDDs), yielding a compact and efficient symbolic representation of quantum behavior. We present an extensive experimental evaluation that, for random 1D Clifford+$T$ circuits, explores the trade-off between \textsc{Manjushri} and \textsc{ECMC}, a tool for equivalence checking based on a much different approach. \textsc{Manjushri} is much faster up to depth 30 (with the crossover point varying from 39--49, depending on the number of qubits and whether the input circuits are equivalent or inequivalent): when inputs are equivalent, \textsc{Manjushri} is about 10$\times$ faster (or more); when inputs are inequivalent, \textsc{Manjushri} is about 8$\times$ faster (or more). For both kinds of equivalence-checking outcomes, \textsc{ECMC}'s success rate out to depth 50 is impressive on 32- and 64-qubit circuits: on such circuits, \textsc{ECMC} is almost uniformly successful. However, \textsc{ECMC} struggled on 128-qubit circuits for some depths. \textsc{Manjushri} is almost uniformly successful out to about depth 38, before tailing off to about 75\% at depth 50 (falling to 0\% at depth 48 for 128-qubit circuits that are equivalent). These results establish that \textsc{Manjushri} is a practical and scalable solution for large-scale quantum-circuit verification, and would be the preferred choice unless clients need to check equivalence of circuits of depth $>$38.

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arXiv2025

Adaptivity is not helpful for Pauli channel learning

We prove that adaptive strategies offer no advantage over non-adaptive ones for learning and testing Pauli channels using entangled inputs. This key observation allows us to characterize the query complexity for several fundamental tasks by translating optimal classical estimation algorithms into the quantum setting. First, we determine the tight query complexity for learning a Pauli channel under the general $\ell_p$ norm, providing results that improve upon or match the best-known bounds for the $\ell_1, \ell_2,$ and $\ell_\infty$ distances. Second, we resolve the complexity of testing whether a Pauli channel is a white noise source. Finally, we show that the optimal query complexities for estimating the Shannon entropy and support size of the channel's error distribution, and for estimating the diamond distance between two Pauli channels, are all $Θ\left(\tfrac{4^n}{nε^2}\right)$.

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arXiv2025

Entanglement Certification by Measuring Nonlocality

Reliable verification of entanglement is a central requirement for quantum networks. This paper presents a practical verification approach based on violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality. We derive tight mathematical bounds that relate the CHSH value to entanglement fidelity and introduce a statistical framework that optimizes resource usage while ensuring reliable certification. Our main contributions are: (i) fidelity bounds derived directly from the CHSH measure, which also enable nonlocality certification at sufficiently high fidelities; (ii) a sample-complexity analysis that quantifies the number of measurements required to achieve desired confidence levels for the CHSH measure and the entanglement fidelity; and (iii) verification protocols, some with rigorous mathematical guarantees and others with numerical evaluation. Using NetSquid, we develop a simulation framework that models diverse network conditions and enables systematic exploration of trade-offs in CHSH-based verification. This framework highlights the interplay between accuracy, efficiency, and operational parameters, providing concrete guidelines for deploying entanglement verification in resource-constrained quantum networks.

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arXiv2025

Scalable Equivalence Checking and Verification of Shallow Quantum Circuits

This paper concerns the problem of checking if two shallow (i.e., constant-depth) quantum circuits perform equivalent computations. Equivalence checking is a fundamental correctness question -- needed, e.g., for ensuring that transformations applied to a quantum circuit do not alter its behavior. For quantum circuits, the problem is challenging because a straightforward representation on a classical computer of each circuit's quantum state can require time and space that are exponential in the number of qubits $n$. The paper presents decision procedures for two variants of the equivalence-checking problem. Both can be carried out on a classical computer in time and space that, for any fixed depth, is linear in $n$. Our critical insight is that local projections are precise enough to completely characterize the output state of a shallow quantum circuit. Instead of explicitly computing the output state of a circuit, we generate a set of local projections that serve as constraints on the output state. Moreover, the circuit's output state is the unique quantum state that satisfies all the constraints. Beyond equivalence checking, we show how to use the constraint representation to check a class of assertions, both statically and at run time. Our assertion-checking methods are sound and complete for assertions expressed as conjunctions of local projections. Our experiments show that on a server equipped with 2 x Intel\textsuperscript{\textregistered} Xeon\textsuperscript{\textregistered} Gold 6338 CPUs (128 threads total) and 1.0~TiB of RAM, running Ubuntu 20.04.6 LTS, the constraint representation of a random 100-qubit circuit of depth 6 can be computed in 19.8 seconds. For fixed inputs $\ket{0}^{\otimes 100}$, equivalence checking of {random} 100-qubit circuits of depth 3 takes 4.46 seconds; for arbitrary inputs, it takes no more than 31.96 seconds.

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