arXiv subjects

Donghwa Ji

Publications and source records attributed to Donghwa Ji.

5 recordsLinked to original sources

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.

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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.

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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.

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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.

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arXiv2025

Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network.

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