arXiv subjects

Kabgyun Jeong

Publications and source records attributed to Kabgyun Jeong.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement Structure Across $\mathbb{Z}_n$ Phase Transitions in 1D Rydberg Atom Arrays

Multipartite quantum entanglement plays a crucial role in the emergence of different quantum phases and their transitions in quantum many-body systems. It is of general interest to know what sort of analysis on quantum entanglement can bring us a profound insight to understand the rich dynamics of quantum many-body systems. In this work we study the characteristics of quantum entanglement in relation to $\mathbb{Z}_n$-ordered phases emerging under a varied strength of 1-dim Rydberg interaction. We propose an approach based on the structure of pair-wise entanglement across the Rydberg chain using two-qubit concurrence as an entanglement measure. We define an entanglement-structure factor via Fourier analysis of total concurrence at each site and address $\mathbb{Z}_n$ phase transitions in comparison with the conventional order-parameter based on local density, i.e. magnetization. We also discuss how the required two-qubit concurrence can be measured in analog Rydberg atom arrays using site-selective erasure and parametrized laser pulses. Our investigation suggests that an entanglement-structure-based approach can provide a powerful tool in analyzing symmetry-breaking in quantum phase transitions.

quant-ph↗

arXiv2026

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator

We revisit Lévy's lemma, a widely used analytical tool in quantum information theory. Concentration inequalities quantify the phenomenon in which Lipschitz observables concentrate around a median or mean, and serve as fundamental analytical tools across information theory, statistical physics, and learning theory. In particular, Lévy's lemma provides a crucial framework for describing functionals on pure quantum states, with applications in quantum entanglement and quantum statistical query learning. In this work, we isolate the hyper-equatorial part of the standard spherical concentration argument. The resulting estimate is a Lévy-type bound for Lipschitz functions on a fixed hyperequator, with the natural dimension parameter $d-1$. We also formulate the accompanying geometric localization in terms of neighborhoods of the boundary, hyperequator, and a codimension-two antipodal great subsphere. This viewpoint clarifies the structure of the usual proof and points to the measure-theoretic formulation needed for sharper constant-level statements.

quant-ph↗

arXiv2026

Fundamental Limitations of Post-Quantum Cryptographic Architectures

Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries of this noise-reliant model across four interconnected domains: computational complexity, information-theoretic thermodynamics, quantum error correction, and quantum learning theory. Starting from the algorithmic foundation, our analysis notes that these frameworks rely on provisional complexity-theoretic assumptions that remain vulnerable to future quantum algorithmic advancements. Furthermore, by translating this cryptographic mechanism into physical thermodynamics, we illustrate that intentionally injected discrete Gaussian noise does not equate to the permanent erasure of information. Because the structural integrity of the cryptographic secret remains preserved within the ciphertext, advanced quantum error correction protocols and quantum learning models can efficiently extract the underlying mathematical kernel. Ultimately, we suggest that while lattice-based cryptography provides a robust transitional alternative, definitively classifying these frameworks as unconditionally post-quantum represents a premature classification relying on transient physical bottlenecks rather than impenetrable theoretical boundaries.

quant-ph↗

arXiv2026

Projected Dynamic Programming for Sequential Quantum State Discrimination

Sequential Quantum State Discrimination (SQSD) can be naturally framed as a sequential decision-making problem: at each time step, an agent must decide whether to perform an additional measurement to gather more information or to conclude with an optimal decision based on the current belief. In this paper, we formally cast SQSD into a static-hidden-state Partially Observable Markov Decision Process (POMDP) framework. We demonstrate that this formulation precisely subsumes the conventional minimum-error discrimination (MED) scheme as a special one-step case. Furthermore, we apply a regular grid-based discretization to the continuous belief simplex and approximate the possibly continuous measurement space using a finite library. Then we provide rigorous mathematical bounds on the resulting errors and analyze the computational complexity for both offline planning and online execution. Our analysis confirms that the inherent trade-off between accuracy and complexity, as well as the curse of dimensionality regarding the number of hypotheses, are also prominently observed in the quantum regime. Finally, we provide a working example of binary state discrimination to derive explicit forms of various functions and present numerical simulations for trine state discrimination to visualize the sequential structure of our POMDP-based SQSD.

quant-ph↗

arXiv2026

A Mutual Information-based Metric for Temporal Expressivity and Trainability Estimation in Quantum Policy Gradient Pipelines

In recent years, various limitations of conventional supervised learning have been identified, motivating the development of reinforcement learning--and quantum reinforcement learning that leverages quantum resources such as entanglement and superposition. Among the various reinforcement learning methodologies, the policy gradient method is considered to have many benefits; for instance, it allows an agent to learn without explicitly knowing the crucial information of the environment such as state transition probabilities and initial state distribution. Meanwhile, from the perspective of learning, two indicators are often regarded as significant: expressivity and trainability (for gradient-based methods). While a number of attempts have been made to quantify the expressivity and trainability of Neural Network models and PQCs, clear efforts suitable for reinforcement learning settings have so far been lacking, despite the inherent differences between conventional supervised learning and reinforcement learning. Therefore, in this study, we propose revising the notion of expressivity into a temporal expressivity suited to reinforcement learning dynamics, and show that the mutual information between the action distribution and the discretized reward signal provides an upper bound for the scaled gradient norm, while yielding an information-theoretic decomposition and a residual-aware upper bound for the proposed temporal expressivity metric. Finally, under explicit concentration assumptions, we show that MI-TET induces an assumption-based, one-sided prescreening criterion for initialization-time gradient fragility across PQC architectures.

quant-ph↗

arXiv2026

Opposite amplitude phase entropy responses at a non Hermitian avoided crossing

Avoided crossings (A.C.) in open resonators arise from non-Hermitian mode interaction, where leakage produces complex spectra and biorthogonal eigenmodes. Intensity-based entropies are robust markers of mode mixing but discard the phase structure of the complex field. Here we introduce a field-level information-theoretic analysis based on the joint statistics of local amplitude and phase under Born-weighted sampling on the cavity grid. For an open elliptical microcavity in the strong-interaction A.C. regime, we find a distinctive sector-resolved response: amplitude statistics tighten while phase statistics broaden maximally at the mixing point, and conditioning reveals strong amplitude-phase dependence. By introducing a coarse position label and the associated co-information, we further show that the enhancement of global amplitude-phase coupling is strongly shaped by spatial heterogeneity across the cavity.

physics.optics↗

arXiv2026

Near optimal quantum algorithm for estimating Shannon entropy

We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude amplification, followed by the application of quantum singular value transformation. On the lower bound side, we construct probability distributions encoded via Hamming weights in the oracle, establishing a tight query lower bound up to logarithmic factors. Consequently, our results show that the tight query complexity for estimating the Shannon entropy within $ε$-additive error is given by $\tildeΘ\left(\tfrac{\sqrt{n}}ε\right)$.

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arXiv2025

Chaos-controlled switching between entanglement and coherence

Controlling entanglement and coherence is central to quantum information, yet the two resources often exhibit antagonistic trends and are difficult to optimize within a single platform. Here we show that chaos enables switchable eigenstate resources: avoided crossings in soft- versus strong- chaos windows selectively realize an entanglement-peak mode or a coherence-peak mode within the same system. Crucially, this chaos-controlled inversion is not tied to a particular notion of subsystems, appearing both in single-wave settings and in genuine many-body settings. From the quantum-chaos perspective, conventional diagnostics based on avoided-crossing phenomenology and eigenmode delocalization are insufficient; eigenfunction entanglement and basis coherence provide the missing discriminants. Using two wave-chaotic billiards and a tilted-field Ising chain, we track the information-theoretic response of eigenstates across localized hybridization windows. Even when avoided-crossing phenomenology and delocalization are comparable, the entanglement and coherence responses invert between soft- and strong-chaos regimes. In the Ising chain, a single microscopic knob, the global field tilt, toggles between the two operating modes and reveals a trade-off in which off-diagonal correlations grow as diagonal populations dip. Our diagnostics require only reduced states (or their spectra) and are compatible with mode imaging in wave-chaos resonators and randomized measurements in programmable spin simulators.

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arXiv2025

Singularity Selector: Topological Chirality via Non-Abelian Loops around Exceptional Points

Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs.

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arXiv2025

Correlated Entropic Uncertainty as a Signature of Exceptional Points

Non-Hermitian physics has become a fundamental framework for understanding open systems where gain and loss play essential roles, with impact across photonics, quantum science, and condensed matter. While the role of complex eigenvalues is well established, the nature of the corresponding eigenfunctions has remained a long-standing problem. Here we show that it arises from a fundamental entropic uncertainty trade-off between phase entropy and its Fourier representation. This trade-off enforces a correlated behavior of phase and Fourier entropies near avoided crossings and exceptional points, precisely where the Petermann factor diverges and phase rigidity collapses. Our results establish biorthogonality is not as an anomaly but an intrinsic property of eigenfunctions, arising universal manifestation of uncertainty relation in non-Hermitian systems. Beyond resolving this foundational question, our framework provides a unifying and testable principle that advances the fundamentals of non-Hermitian physics and can be directly verified with existing interferometric techniques.

quant-ph↗

arXiv2025

Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection

Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification, leading to significant resource overhead and operational complexity. In this study, we propose a novel fault-tolerant and secure quantum communication scheme based on uncorrectable error injection. Our method exploits a quantum state encoding scheme based on quantum error correction codes, which strategically introduces uncorrectable errors to enhance security. It eliminates the need for entanglement distribution while reducing resource requirements. The injected errors protect against eavesdropping by preventing unauthorized parties from retrieving meaningful information. Security analysis shows that as the data length and encoded message size increase, information leakage becomes negligible relative to the size of the total message. Comparative performance analysis with existing approaches indicates that our method reduces transmission overhead while maintaining comparable fidelity in low-error regimes. These findings suggest that the proposed method offers a scalable and practical alternative for secure long-distance quantum communication, distributed quantum computing, and future quantum internet applications.

quant-ph↗

arXiv2025

Bounding quantum uncommon information with quantum neural estimators

In classical information theory, uncommon information refers to the amount of information that is not shared between two messages, and it admits an operational interpretation as the minimum communication cost required to exchange the messages. Extending this notion to the quantum setting, quantum uncommon information is defined as the amount of quantum information necessary to exchange two quantum states. While the value of uncommon information can be computed exactly in the classical case, no direct method is currently known for calculating its quantum analogue. Prior work has primarily focused on deriving upper and lower bounds for quantum uncommon information. In this work, we propose a new approach for estimating these bounds by utilizing the quantum Donsker-Varadhan representation and implementing a gradient-based optimization method. Our results suggest a pathway toward efficient approximation of quantum uncommon information using variational techniques grounded in quantum neural architectures.

quant-ph↗

arXiv2025

Local Wigner-Mass Maps and Integrated Negativity as Measures of nonclassicality in Quantum Chaotic Billiards

The Wigner function is a phase space quasi-probability distribution whose negative regions provide a direct, local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we introduce local positive- and negative Wigner-mass maps and adopt the integrated Wigner negativity as a compact scalar measure of nonclassical phase space structure. A decomposition of the density operator reveals that off-diagonal coherences between hybridizing components generate oscillatory, sign-alternating patterns, with the negative contribution maximized when component weights are comparable. Non-Gaussian chaotic eigenmodes exhibit a baseline negativity that is further amplified by such hybridization. We validate these diagnostics across two billiard geometries and argue that the framework is transferable to other wave-chaotic platforms, where it can aid mode engineering and coherence control.

physics.optics↗

arXiv2025

Mutual information maximizing quantum generative adversarial networks

One of the most promising applications in the era of Noisy Intermediate-Scale Quantum (NISQ) computing is quantum generative adversarial networks (QGANs), which offer significant quantum advantages over classical machine learning in various domains. However, QGANs suffer from mode collapse and lack explicit control over the features of generated outputs. To overcome these limitations, we propose InfoQGAN, a novel quantum-classical hybrid generative adversarial network that integrates the principles of InfoGAN with a QGAN architecture. Our approach employs a variational quantum circuit for data generation, a classical discriminator, and a Mutual Information Neural Estimator (MINE) to explicitly optimize the mutual information between latent codes and generated samples. Numerical simulations on synthetic 2D distributions and Iris dataset augmentation demonstrate that InfoQGAN effectively mitigates mode collapse while achieving robust feature disentanglement in the quantum generator. By leveraging these advantages, InfoQGAN not only enhances training stability but also improves data augmentation performance through controlled feature generation. These results highlight the potential of InfoQGAN as a foundational approach for advancing quantum generative modeling in the NISQ era.

quant-ph↗

arXiv2025

Information-theoretic analysis of complex eigenmodes across avoided crossings in open microcavities

Avoided crossings (ACs) are hallmark signatures of mode interaction in quantum and wave systems. Open microcavities whose resonances are naturally described as quasi-normal modes (QNMs) with complex eigenfrequencies offer a convenient platform to observe how openness and loss reorganize modal structure. We introduce a compact \emph{quadrature space} framework that represents a complex QNM by probability weights on its real and imaginary quadratures, and we apply Shannon-type measures to these distributions. This representation separates marginal spreading of each quadrature from inter quadrature correlation and is robust to nodal sets and exterior zero amplitude points. Applying the method to AC regions, we find that delocalization is driven not only by broadening of individual quadratures but also by a pronounced increase in internal correlation near at the AC, revealing an internal reorganization of resonant modes in non-Hermitian settings. The approach is broadly transferable to other open resonator platforms and provides a general information-theoretic diagnostic for openness-driven mode interactions.

quant-ph↗

arXiv2025

Quantum entanglement and extractable work for Gaussian states

The study of quantum thermodynamics aims to elucidate the role played by quantum principles in the emergent features of quantum thermodynamic processes. Specifically, it is of fundamental importance to understand how quantum correlation among different parties enables thermodynamic features distinguishable from those arising in classical thermodynamics. In this work, we investigate the relation between extractable work and quantum correlations for two-mode Gaussian states. We examine the change in local energy occurring at one party due to a Gaussian measurement performed on the other in relation to the quantum correlations of two-mode states classified as separable, entangled, and steerable states. Our analysis reveals a clear quantitative difference in the extractable work, depending on the class of states to which the two-mode state belongs.

quant-ph↗

arXiv2025

Resource-efficient algorithm for estimating the trace of quantum state powers

Estimating the trace of quantum state powers, $\text{Tr}(ρ^k)$, for $k$ identical quantum states is a fundamental task with numerous applications in quantum information processing, including nonlinear function estimation of quantum states and entanglement detection. On near-term quantum devices, reducing the required quantum circuit depth, the number of multi-qubit quantum operations, and the copies of the quantum state needed for such computations is crucial. In this work, inspired by the Newton-Girard method, we significantly improve upon existing results by introducing an algorithm that requires only $\mathcal{O}(\widetilde{r})$ qubits and $\mathcal{O}(\widetilde{r})$ multi-qubit gates, where $\widetilde{r} = \min\left\{\text{rank}(ρ), \left\lceil\ln\left({2k}/ε\right)\right\rceil\right\}$. This approach is efficient, as it employs the $\tilde{r}$-entangled copy measurement instead of the conventional $k$-entangled copy measurement, while asymptotically preserving the known sample complexity upper bound. Furthermore, we prove that estimating $\{\text{Tr}(ρ^i)\}_{i=1}^{\tilde{r}}$ is sufficient to approximate $\text{Tr}(ρ^k)$ even for large integers $k > \widetilde{r}$. This leads to a rank-dependent complexity for solving the problem, providing an efficient algorithm for low-rank quantum states while also improving existing methods when the rank is unknown or when the state is not low-rank. Building upon these advantages, we extend our algorithm to the estimation of $\text{Tr}(Mρ^k)$ for arbitrary observables and $\text{Tr}(ρ^k σ^l)$ for multiple quantum states.

quant-ph↗

arXiv2025

Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy

We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and analyzing uniqueness in quantum-classical PCPs, we clarify how various constraints influence computational power. Our main contributions are: (1) We show that restricting quantum-classical PCPs to unique proofs does not reduce their power: $\mathsf{UniqueQCPCP} = \mathsf{QCPCP}$ under $\mathsf{BQ}$-operator and randomized reductions. This parallels the known $\mathsf{UniqueQCMA} = \mathsf{QCMA}$ result, indicating robustness of uniqueness even in quantum PCP-type systems. (2) We prove a non-uniform quantum analogue of the Karp-Lipton theorem: if $\mathsf{QMA} \subseteq \mathsf{BQP}/\mathsf{qpoly}$, then $\mathsf{QPH} \subseteq \mathsf{QΣ}_2/\mathsf{qpoly}$. This conditional collapse suggests limits on quantum advice for $\mathsf{QMA}$-complete problems. (3) We define a bounded-entanglement version of the quantum polynomial hierarchy, $\mathsf{BEQPH}$, and prove that it collapses above the fourth level. We also introduce the separable hierarchy $\mathsf{SepQPH}$ (zero entanglement), for which the same collapse result holds. These collapses stem not from entanglement, as in prior work, but from the convex structure of the protocols, which renders higher levels tractable. Collectively, these results offer new insights into the structure of quantum proof systems and the role of entanglement, uniqueness, and advice in defining their complexity.

quant-ph↗