arXiv subjects

Hyunho Cha

Publications and source records attributed to Hyunho Cha.

At least 19 recordsLinked to original sources

arXiv2026

CHSH inequality always holds in bipartite qutrits with spin-1 observables

Bell inequalities reveal when quantum correlations cannot be explained by any local hidden-variable model, and the CHSH inequality is the most fundamental test of this phenomenon. While entangled two-qubit states can violate CHSH inequalities with suitable local measurements, the situation is more subtle for higher-dimensional systems when the allowed observables are physically restricted. In this work, we study bipartite qutrit systems in which each party is restricted to spin-1 observables $S(u)=u_xS_x+u_yS_y+u_zS_z$, with $u\in\mathbb R^3$ a unit vector. Hanotel and Loubenets conjectured that nonseparable pure states of two qutrits do not violate the CHSH inequality under this measurement restriction. We prove the stronger result that every bipartite state on $\mathbb C^3\otimes\mathbb C^3$, pure or mixed, satisfies the CHSH inequality for all choices of local spin-1 observables. Thus the absence of CHSH violation is not a property of special states, but a structural limitation of the spin-1 measurement family. Our result clarifies a distinction between two-qutrit entanglement and CHSH nonlocality under natural spin-component measurements.

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arXiv2026

Refining transposition bounds from traceless quantum perturbations

The transpose map is the canonical nonphysical map in quantum information that is central to entanglement tests and to converse bounds for quantum capacity. It is a longstanding conjecture that transposition satisfies a dimension-independent strict submultiplicativity for physically relevant channel differences. We answer this affirmatively by proving that for every quantum channel $T$ on $\mathsf{L}(\mathbb{C}^d)$, $\|Θ\circ(\mathrm{id}-T)\|_\diamond \le \frac{1}{\sqrt{2}}\|Θ\|_\diamond \|\mathrm{id}-T\|_\diamond$. The same bound holds for all Hermiticity-preserving trace-annihilating maps. Because a trace-preserving channel produces a traceless deviation from the identity, transposition cannot act as strongly on such physically generated errors as it can on arbitrary perturbations. Thus, although transposition is extremal in the unrestricted diamond-norm geometry, physical constraints mandate a universal margin in the submultiplicative bound. As one immediate consequence, the finite-error Holevo--Werner converse extends from decoding errors $\varepsilon<1/2$ to $\varepsilon<1/\sqrt{2}$. The same tracelessness mechanism also yields rank-sensitive continuity refinements for negativity and logarithmic negativity, demonstrating its potential for broader application in quantum information.

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arXiv2026

One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture

Positivity of matrix trace exponentials is a basic structural principle behind finite-temperature quantum statistical mechanics. The Bessis-Moussa-Villani conjecture, a central manifestation of this principle, was proved by Stahl after an influential reformulation by Lieb and Seiringer. A later refinement asks whether the normalized average over all words with $n$ letters $A$ and $m$ letters $B$ is always bounded above by $\mathrm{tr}(A^nB^m)$ and below by $\mathrm{tr}\exp(n\log A+m\log B)$. In this work, we study a specific one-parameter family $(A_x, B_x)$ and show that the correct small-$x$ invariant of a word is not its degree of fragmentation, but a weighted shortest-bridge cost on its cyclic run decomposition. Our results yield a class of counterexamples to the suggested refinement. Remarkably, the ratio of the normalized word average to the trace $\mathrm{tr}(A^nB^m)$ can become arbitrarily large.

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arXiv2026

Online Estimation of Partial Transpose Moments via Fast Classical Updates

Partial-transpose (PT) moments are among the most practically relevant nonlinear quantities accessible from local Pauli classical shadows, because they directly underpin mixed-state entanglement certification and recent PT-moment-based phase diagnostics. The online framework of Marso \emph{et al.} rewrote the exact PT-moment statistic into a fixed-memory recurrence that updates a small collection of accumulated matrices after each new shadow snapshot. Its update cost is independent of the shot number, but each step treats the incoming partially transposed snapshot as a generic dense matrix. Therefore, the arithmetic cost scales cubically with the dimension of the Hilbert space. We show that the same estimator can be updated exactly in subcubic time per shot while retaining the same memory. The key point is that the accumulated matrices become dense, but the fresh partially transposed snapshot still factorizes into local factors. Right-multiplication by that factorized snapshot can therefore be executed by exact column-pair sweeps. For the second PT moment, we further optimize the process by utilizing a Pauli basis update.

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arXiv2026

Exactness of the doubly nonnegative relaxation for qubit-output quantum channels

The resource theory for nonnegativity of quantum amplitudes distinguishes completely positive completely positive (CPCP) quantum channels from the larger class of completely positive doubly nonnegative (CPDNN) quantum channels. Johnston and Sikora showed that all qubit-to-qubit quantum channels that are CPDNN are also CPCP. However, they left open the question of whether a qutrit-to-qubit quantum channel exists that is CPDNN but not CPCP. We prove that no such channel exists and, more generally, that every CPDNN quantum channel with qubit output is CPCP. Thus the doubly nonnegative relaxation is exact for all qubit-output quantum channels. Our argument yields an explicit structural picture in which, after a canonical permutation of the Choi matrix, every qubit-output CPDNN channel is determined by a nonnegative vector and a nonnegative matrix, subject to a single positive-semidefinite block constraint. This gives a complete binary-output normal form, an explicit formula for the action of the channel, and quantitative population-coherence tradeoff inequalities governing the unique output off-diagonal mode. In this sense, qubit output is the nontrivial binary regime in which trace preservation and double nonnegativity collapse the free-channel cone to a fully describable geometry.

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arXiv2026

Disjoint Bell measurements enable near-projective GHZ certification

Certifying multipartite entangled states is a basic task in quantum information processing, but the achievable copy complexity depends crucially on the measurements available to the verifier. The strongest possible certification measurement for a known pure target state $|ψ\rangle$ is the two-outcome projector $\{|ψ\rangle\langleψ|,\mathsf{I}-|ψ\rangle\langleψ|\}$, which is copy-optimal but often experimentally unrealistic or outside the intended measurement model. In this work, we introduce BM-Cert, a single-copy verification protocol for the $n$-qubit Greenberger--Horne--Zeilinger (GHZ) state using only disjoint two-qubit Bell-basis measurements, together with one single-qubit $X$-basis measurement when $n$ is odd. Surprisingly, a simple combinatorial effect yields perfect completeness and a verification spectral gap $ν_\mathrm{BM}(n)=1-O(1/n)$, so our depth-2 protocol already approaches the ideal projective verification asymptotically as $n$ grows. This contrasts with local Pauli GHZ verification, whose optimal spectral gap remains bounded away from $1$. Thus, allowing only two-qubit entangling measurements on disjoint pairs is enough to achieve asymptotically ideal projective certification. The same Bell-matching outcomes also yield BM-Fid, an unbiased estimator of the GHZ fidelity whose leading Hoeffding coefficient in the sample complexity tends to the ideal value achieved by direct projection. For the open-boundary linear nearest neighbor setting, we further introduce Brick-Cert, a disjoint 2-local certification protocol whose spectral gap $4/5$ is optimal within that restricted architecture.

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arXiv2026

Every architecture of six two-qubit gates is locally universal on three qubits

We present the \emph{first} analytical determination of the exact accessible dimension for every fixed architecture of arbitrary two-qubit gates on three qubits. A support word represents which pair of qubits each two-qubit gate acts on, and its reduced length is obtained by merging consecutive gates on the same pair. If the reduced length is $r$, then the set of implementable three-qubit unitaries has accessible dimension $d(w)=\min\{63,9r+9\}$. Consequently, six arbitrary two-qubit gates are \emph{necessary and sufficient for local universality}: every fixed architecture reaches a nonempty open subset of $\mathrm{SU}(8)$ when its reduced length is at least six. The result is stronger than existence of one favorable architecture. Every reduced six-slot support word is locally universal, including the alternating nearest-neighbor line $AB,BC,AB,BC,AB,BC$. The upper bound follows from a standard parameter-counting argument. The matching lower bounds are proved by Jacobian certificates in the Pauli basis. Up to qubit relabeling and reversal, there are $22$ reduced architectures of lengths two through six. For each one, a product of rational Pauli rotations yields a nonzero maximal minor modulo the prime $1{,}000{,}003$. Thus, any obstruction to global universality with six two-qubit gates must go beyond parameter counting, connectivity, and differential rank.

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arXiv2026

Structural perspectives from quantum states and measurements in optimal state discrimination

Quantum state discrimination refers to a class of techniques to identify a specific quantum state through a \textit{positive operator-valued measure}. In this work, we investigate how structural information can influence our ability to determine or bound the optimal discrimination probability. First, as background, we note that for single-qubit pure-state ensembles, pairwise fidelities determine the optimal discrimination probability, whereas in higher dimensions they do not in general. As an illustrative application of this observation, we give a closed-form fidelity-based reformulation of the optimal discrimination probability for three equiprobable single-qubit states with equal pairwise fidelities. Secondly, we show that the information of measurement operators that vanish in the optimal solution can be used to refine upper bounds on the optimal discrimination probability, often yielding tighter bounds.

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arXiv2026

Re-uploading quantum data: a universal function approximator for quantum inputs

Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a qubit-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.

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arXiv2026

Optimal dense materialization of the stabilizer formalism without polynomial overhead

Stabilizer states and Clifford transformations constitute the exactly tractable backbone of quantum information science, from error correction and fault tolerance to benchmarking and simulation. Although these objects admit compact classical descriptions, many physical and computational workflows still require their explicit dense forms such as a full wavefunction for a stabilizer state or a full matrix for a Clifford transformation. In such explicit output tasks, exponential scaling is unavoidable because the outputs themselves have sizes $2^n$ and $4^n$. The fundamental question is therefore whether compact stabilizer and Clifford descriptions can be expanded with no additional polynomial overhead. Here we answer this question affirmatively. We present optimal algorithms that materialize an $n$-qubit stabilizer state vector in $O(2^n)$ time and a full dense Clifford matrix in $O(4^n)$ time. The same framework also yields an optimal conversion from standard stabilizer check matrices to state vectors and, for every fixed odd prime qudit dimension $\ell$, gives $O(\ell^n)$-time materialization of qudit stabilizer states. As an additional compact-to-compact result, we design a sign-aware Four Russians method for converting stabilizer check matrices to quadratic forms faster than Gaussian elimination. These results close the asymptotic gap between compact descriptions of the stabilizer formalism and their dense representations.

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arXiv2026

Counting anticommuting Pauli pairs in linear time

Many quantum computing workflows manipulate long lists of Pauli strings. A basic classical subroutine involves taking $m$ Pauli strings on $n$ qubits, each of weight bounded by a constant, to determine if they are pairwise commuting, identify any counterexamples, or calculate the exact number of anticommuting unordered pairs. The standard general-purpose route represents Pauli strings in binary symplectic form and checks pairs in $O(m^2)$ time. Here, we provide an $O(m)$ algorithm for the bounded locality regime. It maintains counts of all labeled subpatterns of previously inserted strings and answers each new string query by a subset zeta identity. Our algorithm is particularly useful for processing large collections of Pauli strings within the bounded locality regime.

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arXiv2026

End-to-End Neural and Quantum Transcoding for Compressed Latent Representation under Channel Noise

Recent advancements in quantum computing highlight the need for efficient encoding of classical data into quantum states to ensure robust quantum information processing. Traditional encoding schemes often impose impractical requirements about the knowledge of quantum states and lack adaptability to noisy quantum channels and broader tasks. To address these limitations, we propose a novel end-to-end learnable quantum transcoding scheme explicitly optimized for compactness and robustness in noisy quantum communication scenarios. Our approach integrates neural network-based data compression with Cholesky decomposition-based quantum encoding and bypasses full density matrix reconstruction. Through normalized quantum observables, our method enables efficient tomography and achieves high reconstruction and classification performance even under extreme noise conditions.

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arXiv2026

Toward the Goldilocks blind compression of quantum states

Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a $k$-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a \emph{Goldilocks} regime. We prove that for every distribution of pure $n$-qubit states, there exists a QAE with exactly $k$ encoder ancillas and $n$ decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least $k$ encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are exactly optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.

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arXiv2026

Spectral Minimax Direct Fidelity Estimation for Generic Target States

Direct fidelity estimation benefits from tailoring measurements to a fixed target, but the operator-aware shadow importance sampling (OASIS) method optimizes an outcome-wise linear-program surrogate rather than the exact worst-case variance over physical states. We propose an exact spectral replacement for arbitrary target states under the same non-adaptive single-copy measurement model. Specifically, we characterize unbiased linear estimators by a single operator identity, determine the state-wise optimal sampling law for fixed reconstruction coefficients, and convert the exact minimax problem into a semidefinite program. The resulting offline design and online estimator are presented as an algorithm and implemented with local Pauli measurements. Numerical simulations under depolarizing noise demonstrate that our exact spectral optimization outperforms the OASIS surrogate in terms of estimation variance.

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arXiv2026

Verifying random matrix product states with autoregressive local measurements

Matrix product states (MPS) are a central language for one-dimensional quantum matter and a practical target for near-term quantum simulators and variational algorithms. Yet, while substantial effort has focused on preparing MPS with shallow circuits, scalable methods to \emph{verify} that a many-body device has actually produced the intended state remain underdeveloped. Direct fidelity estimation (DFE) relies only on local Pauli measurements, but in many-body settings it suffers an exponential classical overhead from the preprocessing needed to sample Pauli strings. We eliminate this obstacle by introducing an \emph{autoregressive} importance sampler that draws Pauli strings sequentially from efficiently computable conditional distributions, reducing the per-shot classical overhead to linear scaling in the number of qubits. We further develop a grouped extension that constructs qubit-wise commuting measurement settings via a \emph{sorting string} and simultaneously estimates the entire commuting group from a single setting, significantly reducing estimator variance while preserving efficient postprocessing. Our approach extends naturally to matrix product operators (MPO), enabling scalable verification of tensor-network states and observables in long one-dimensional quantum systems. We utilize random MPS as a natural benchmark for generic 1D entangled states.

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arXiv2026

Non-existence of stabilizer absolutely maximally entangled states across infinitely many configurations

We prove a general reduction theorem for stabilizer absolutely maximally entangled states in composite local dimension. If a stabilizer $\mathrm{AME}(n,D)$ state exists and $D=\prod_{i=1}^m q_i$ is the prime-power factorization of $D$, then for every nonempty subset of factors there exists a stabilizer $\mathrm{AME}\bigl(n,\prod_{i\in M} q_i\bigr)$ state. Thus any obstruction at a prime-power factor immediately obstructs stabilizer AME states in the composite dimension.

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arXiv2026

Operator-aware shadow importance sampling for accurate fidelity estimation

Estimating the fidelity between an unknown quantum state and a fixed target is a fundamental task in quantum information science. Direct fidelity estimation (DFE) enables this without full tomography by sampling observables according to a target-dependent distribution. However, existing approaches face notable trade-offs. Grouping-based DFE achieves strong accuracy for small systems but suffers from exponential scaling, and its applicability is restricted to Pauli measurements. In contrast, classical-shadow-based DFE offers scalability but yields lower accuracy on structured states. In this work, we address these limitations by developing two classes of operator-aware shadow importance sampling algorithms using informationally overcomplete positive operator-valued measures. Instantiated with local Pauli measurements, our algorithm improves upon the grouping-based algorithms for Haar-random states. For structured states such as the GHZ and W states, our algorithm also eliminates the exponential memory requirements of previous grouping-based methods. Numerical experiments confirm that our methods achieve state-of-the-art performance across Haar-random, GHZ, and W targets.

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arXiv2026

QFlowNet: Fast, Diverse, and Efficient Unitary Synthesis with Generative Flow Networks

Unitary Synthesis, the decomposition of a unitary matrix into a sequence of quantum gates, is a fundamental challenge in quantum compilation. Prevailing reinforcement learning (RL) approaches are often hampered by sparse reward signals, which necessitate complex reward shaping or long training times, and typically converge to a single policy, lacking solution diversity. In this work, we propose QFlowNet, a novel framework that learns efficiently from sparse signals by pairing a Generative Flow Network (GFlowNet) with Transformers. Our approach addresses two key challenges. First, the GFlowNet framework is fundamentally designed to learn a diverse policy that samples solutions proportional to their reward, overcoming the single-solution limitation of RL while offering faster inference than other generative models like diffusion. Second, the Transformers act as a powerful encoder, capturing the non-local structure of unitary matrices and compressing a high-dimensional state into a dense latent representation for the policy network. Our agent achieves an overall success rate of 99.7% on a 3-qubit benchmark(lengths 1-12) and discovers a diverse set of compact circuits, establishing QFlowNet as an efficient and diverse paradigm for unitary synthesis.

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