arXiv subjects

Masahito Hayashi

Publications and source records attributed to Masahito Hayashi.

At least 37 records · Page 2Linked to original sources

arXiv2026

Trajectory-Wise Certification for Vector-Field Mirror Descent with Deterministic Finite Differences

We study mirror descent in which the objective gradient is replaced by a general vector field. Since such a field does not automatically relate the mirror update to the objective gap, we introduce a trajectory-wise generalized relative-smoothness condition and a generalized star-convexity interface. Together they yield a finite-horizon, a posteriori last-iterate certificate with an accumulated-stepsize term and an exceptional-region-dependent error term. We also give a pointwise sufficient condition for positive admissible stepsizes, displaying the effects of objective smoothness, mirror-map conditioning, and vector-field mismatch. We then construct a deterministic zeroth-order instance from coordinate central differences. The function values place the unknown gradient in an explicit uncertainty box, and verification of the interface reduces to robust conic dominance. We derive an explicit scaling of the central-difference vector that guarantees the required dominance over the gradient uncertainty set. Under uniform Hessian bounds, the resulting vector field satisfies the interface outside an explicit resolution-dependent neighborhood. The final guarantee combines a rate term governed by accumulated accepted stepsizes with a finite-resolution error floor.

math.OC↗

arXiv2026

Error exponents of quantum state discrimination with composite correlated hypotheses

We study the error exponents in quantum hypothesis testing between two sets of quantum states, extending the analysis beyond the independent and identically distributed case to encompass composite correlated hypotheses. In particular, we introduce and compare two natural extensions of the quantum Hoeffding divergence and anti-divergence to sets of quantum states, establishing their equivalence or quantitative relations. In the error exponent regime, we generalize the quantum Hoeffding bound to stable sequences of convex, compact sets of quantum states, demonstrating that the optimal Type-I error exponent, under an exponential constraint on the Type-II error, is precisely characterized by the regularized quantum Hoeffding divergence between the sets. In the strong converse exponent regime, we establish a general lower bound on the exponent in terms of the regularized quantum Hoeffding anti-divergence, and we prove a matching upper bound when the null hypothesis is a singleton, under additional assumptions. The generality of these results enables applications in various contexts, including (i) refining the generalized quantum Stein's lemma by [Fang, Fawzi & Fawzi, 2024]; (ii) exhibiting counterexamples to the continuity of the regularized Petz Renyi divergence and Hoeffding divergence; (iii) obtaining error exponents for adversarial channel discrimination and resource detection problems.

quant-ph↗

arXiv2026

Mutually orthogonal anti-Latin squares

Anti-Latin squares were introduced in connection with non-linear secure network coding, and the extremal problem for large mutually orthogonal families is motivated by that setting. We study the maximum size $N_A(d)$ of a family of mutually orthogonal anti-Latin squares of order $d$. We prove that $N_L(d)+1\le N_A(d)\le N_L(d)+2$ for every $d\ge 3$, where $N_L(d)$ denotes the classical maximum size of a family of mutually orthogonal Latin squares of order $d$, and we show that in fact $N_A(3)=N_L(3)+1$ whereas $N_A(d)=N_L(d)+2$ for every $d\ge 4$. The upper bound is obtained by passing through balanced matrices, while the lower bound is given by a deterministic permutation argument. For all $d\ge 8$, and also for the exceptional order $d=6$, the upper bound is shown to be attainable by a general probabilistic construction. On the structural side, we show that a saturated family of size $d+1$ induces an affine plane of order $d$, and that the saturated case is characterized by the existence of an anti-coordinate grid decomposition; after transporting this condition to the fixed cell set $[d]^2$, it becomes a direction-completeness condition on the corresponding row-blocks and column-blocks. The remaining small orders are treated separately: $d=3$ is handled by direct analysis and classification of orthogonal triples, $d=4$ by an explicit saturated construction and an analysis of its finite-geometric structure, and $d=5$ and $d=7$ by explicit saturated examples arising from the random-grid framework. Thus $N_A(d)$ is determined in terms of $N_L(d)$ for every $d\ge3$, and its numerical value is obtained explicitly for every $3\le d\le9$.

math.CO↗

arXiv2026

Robust CHSH Self-Testing with Finite-Energy GKP States

We present a full-oscillator analysis of a finite-energy GKP CHSH test whose observed score yields robust Bell-pair self-testing. Periodically binned position and momentum give the Pauli settings, while a fixed binary coarse-graining of photon number modulo four and its displaced conjugate realize the tilted settings. For a number-filtered GKP source, we retain the finite codeword overlap, define the measurements on all photon-number sectors, and compute the physical correlations without logical post-corrections. With the canonical ideal-logical displacement $d=\sqrtπ$, the CHSH value exceeds the local bound above $4.56$ dB of per-peak squeezing, and Kaniewski's extractability bound becomes nontrivial above $5.02$ dB. Calibrating only $d$ using an independently characterized finite-energy parameter lowers these model thresholds to $4.21$ dB and $4.58$ dB, respectively; at $12$ dB, it raises the score from $2.69486$ to $2.78858$ and the corresponding target-state overlap bound from $0.90758$ to $0.97243$. This calibration is fixed before Bell-test data are collected. The displacement activates the odd modulo-four sectors, so their fixed a priori assignments are a genuine finite-energy component. The large gain is specific to the deterministic phase-bit coarse-graining; independently calibrating the one-bit POVM with randomized odd-sector outcomes gives only a much smaller improvement. These are honest-model predictions, not loss, detection-efficiency, or finite-sample thresholds. In an experiment, a device-independent guarantee for an extracted Bell pair follows by inserting a confidence lower bound on the observed CHSH score into the self-testing theorem.

quant-ph↗

arXiv2026

Two-Way Wiretap Channel under Mixed Secrecy Constraint

This paper studies the two-way wiretap channel (TW-WC) with an external eavesdropper under strong one-sided (mixed) secrecy: only User~1's message is required to be secure from the eavesdropper, while no secrecy constraint is imposed on User~2's message. Secrecy is measured by the information leakage of User~1's message to the eavesdropper. Applying a non-adaptive construction and a one-sided reduction of the key-exchange construction, we obtain exponential error and leakage bounds for every fixed number of adaptive rounds. A quantitative one-time-pad argument propagates the leakage of the key used in the next round, and an explicit padding construction removes the initialization-rate loss for all sufficiently large blocklengths. We derive the corresponding strong mixed-secrecy achievable regions. The non-adaptive construction recovers the previously reported weak one-sided single-letter inner bound under the stronger secrecy criterion. The overall adaptive achievable region includes the non-adaptive construction as a fallback and also contains a key-exchange subregion that can be strictly larger.

cs.IT↗

arXiv2026

Efficient Verification of Entangled Measurements with Local States

We develop a framework for quantum measurement verification (QMV) using only local state preparations. For locally transitive and irreducible projective measurements, we prove that symmetry reduces locality constrained QMV to quantum state verification of a single basis state, thereby reducing protocol design to the optimization of homogeneous verification operators. We apply the framework to generalized Bell measurements, single-parameter measurements on two qubits, elegant joint measurements, and stabilizer state induced measurements, and derive explicit local protocols together with closed form verification operators, success probabilities, and sample complexities. We further show that homogeneous QMV protocols can estimate measurement fidelity directly from observed passing frequencies.

quant-ph↗

arXiv2026

Privacy Implies Stability: Information-Theoretic Generalization Bounds for Quantum Learning

We develop an information-theoretic framework connecting stability, privacy, and generalization for quantum learning algorithms. Learning procedures are modeled as quantum instruments with classical-quantum outputs, and losses are represented by observables. We prove that under a classical-quantum sub-Gaussian condition, an information-theoretic stability measure controls the expected generalization error. Furthermore, we establish a high-probability generalization bound using quantum Rényi divergences to manage higher-order dependencies under non-commutativity. In the trusted Data Processor setting, quantum differential privacy (QDP) provides a mechanism for stability. We show that one-neighbor QDP strictly bounds the information leaked by the classical-quantum output. Combining this with our stability theorem yields a direct privacy-to-generalization guarantee. We also explore an untrusted Data Processor setting. Here, output privacy alone is insufficient since an adversarial processor could perform a highly informative procedure before applying noisy post-processing. To combat this, we introduce Information-Theoretic Admissibility (ITA), a certification condition ensuring the prescribed procedure is not just a degraded version of a strictly more informative, physically allowed operation on the encoded ensemble. We prove a fundamental separation: while admissibility and privacy are in strong tension in classical models, quantum non-orthogonality makes them compatible. A quantum measurement can be ITA - exhausting all relevant accessible information - without perfectly recovering the classical dataset. We illustrate this separation through a concrete quantum ITA example.

quant-ph↗

arXiv2026

Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing

We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states. We establish quantum Hoeffding bounds under a set of structural assumptions, orthogonal to those of our previous framework. A notable consequence is the direct operational interpretation of the reverse sandwiched Renyi divergence for $α\in (0,1)$: for the task of discriminating a thermal equilibrium state from a probe state subject to unknown dephasing in the energy eigenbasis, with free Hamiltonian evolution as a special case, the optimal Hoeffding exponent is given exactly by this divergence evaluated on a single copy of the system. The same task in the Stein regime is governed by the reverse quantum relative entropy, providing its operational interpretation as well. This behavior contrasts both with the simple independent and identically distributed (i.i.d.) setting, where the Petz Renyi divergence and the Umegaki relative entropy govern the Hoeffding and Stein exponents, respectively, and with many composite settings, where only regularized many-copy formulas are available. This finding reveals that passing from simple to composite hypotheses can fundamentally change which quantum divergence determines the operational limits of discrimination, and suggests a new avenue for seeking operational interpretations of quantum divergences by lifting simple hypotheses to richer composite scenarios.

quant-ph↗

arXiv2026

Quantum secure blind decryption with two users

We propose two types of protocols for quantum secure blind decryption, involving two users and servers. User 1 holds the encrypted ciphertext. The servers store several indexed keys including the key encrypting the ciphertext. User 2 aims to obtain the decrypted text. The protocols are designed to preserve the following types of secrecy: Users ensure the secrecy of the text from the servers. Servers maintain the secrecy of the keys from the users. Our protocols enable User 2 to obtain the decrypted text while preserving these secrecy requirements. Additionally, the second protocol ensures the secrecy of the key index to identify the key encrypting the ciphertext from the servers, and the second protocol requires two non-commuting servers. Furthermore, we analyze the secrecy of the second protocol under post-attack scenarios, where the two servers communicates with each other after the completion of the protocol. We show that our quantum protocol satisfies the secrecy under these attacks, whereas its classical counterpart fails to do so.

quant-ph↗

arXiv2026

Tuning microswimmer motility by liposome encapsulation: swimming and cargo transport of Chlamydomonas-encapsulating liposome

Inspired by biology's use of vesicles for targeted transport, many studies have propelled liposomes with active matter, creating synthetic systems that can be viewed as microscale biohybrid robots. Nevertheless, the underlying motility mechanisms from a hydrodynamic perspective are often unresolved, and reliable velocity control remains challenging. Here we present a chlamylipo formed by encapsulating the motile alga Chlamydomonas reinhardtii within a giant liposome. We quantify how the characters of swimming change under controlled perturbations and, from a fluid-mechanical perspective, derive a deformation-velocity expression that incorporates liposome radius, beating frequency, and membrane protrusion. We further show that motility can be reversibly switched by incorporating light-responsive lipids, with the liposome acting as a "clutch" that modulates membrane-coupled propulsion. Thus, liposome encapsulation can function not only as a cargo compartment but also as a tunable motility regulator, enabling speed adjustment and reversible transitions between motile and non-motile states.

physics.bio-ph↗

arXiv2026

Structured quantum learning via em algorithm for Boltzmann machines

Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size. We introduce a quantum version of the em algorithm, an information-geometric generalization of the classical Expectation-Maximization method, which circumvents gradient-based optimization on non-convex functions. Implemented on a semi-quantum restricted Boltzmann machine (sqRBM) -- a hybrid architecture with quantum effects confined to the hidden layer -- our method achieves stable learning and outperforms gradient descent on multiple benchmark datasets. These results establish a structured and scalable alternative to gradient-based training in QML, offering a pathway to mitigate barren plateaus and enhance quantum generative modeling.

quant-ph↗

arXiv2026

Double Markovity for quantum systems

The subadditivity-doubling-rotation (SDR) technique is a powerful route to Gaussian optimality in classical information theory and relies on strict subadditivity and its equality-case analysis, where double Markovity is a standard tool. We establish quantum analogues of double Markovity. For tripartite states, we characterize the simultaneous Markov conditions A-B-C and A-C-B via compatible projective measurements on B and C that induce a common classical label J yielding A-J-(BC). For strictly positive four-party states, we show that A-(BD)-C and A-(CD)-B hold if and only if A-D-(BC) holds. These results remove a key bottleneck in extending SDR-type arguments to quantum systems.

quant-ph↗

arXiv2026

Adversarial Hypothesis Testing for Quantum Channels

This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects the channel input adversarially to minimize Bob's distinguishability. We analyze this problem across four settings based on whether Alice employs i.i.d. or general inputs and whether the receiver, Bob, is informed of the specific input choice (allowing his measurement to depend on the input). We characterize the Stein exponents for each setting and reveal a striking distinction in behavior: for QQ channels with i.i.d. inputs, Bob's knowledge of the input significantly enhances distinguishability, yet this advantage vanishes when general inputs are permitted. In contrast, for CQ channels, Bob being informed provides a consistent advantage over the corresponding entanglement-breaking channels for both i.i.d. and general inputs. These results demonstrate a unique phenomenon in adversarial hypothesis testing where the CQ channel does not merely behave as a special case of the QQ channel.

quant-ph↗

arXiv2026

A Posteriori Certification Framework for Generalized Quantum Arimoto-Blahut Algorithms

The generalized quantum Arimoto--Blahut (QAB) algorithm is a powerful derivative-free iterative method in quantum information theory. A key obstacle to its broader use is that existing convergence guarantees typically rely on analytical conditions that are either overly restrictive or difficult to verify for concrete problems. We address this issue by introducing an a posteriori certification viewpoint: instead of requiring fully a priori verifiable assumptions, we provide convergence and error guarantees that can be validated directly from the iterates produced by the algorithm. Specifically, we prove a generalized global convergence theorem showing that, under convexity and a substantially weaker numerically verifiable condition, the QAB iteration converges to the global minimizer. This theorem yields a practical certification procedure: by checking explicit inequalities along the computed trajectory, one can certify global optimality and bound the suboptimality of the obtained value. As an application, we develop a certified iterative scheme for computing the quantum relative entropy of channels, a fundamental measure of distinguishability in quantum dynamics. This quantity is notoriously challenging to evaluate numerically: gradient-based methods are impeded by the complexity of matrix functions such as square roots and logarithms, while recent semidefinite programming approaches can become computationally and memory intensive at high precision. Our method avoids these bottlenecks by combining the QAB iteration with a posteriori certification, yielding an efficient and scalable algorithm. Numerical experiments demonstrate rapid convergence and improved scalability and adaptivity compared with SDP-based approaches.

quant-ph↗

arXiv2025

Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation

We generalized the mKdV equation in order that the static equations include ${\rm sn}$ differential equation. As a result, a good correspondence was obtained between the KdV equation and the mKdV equation.For general genus two hyperelliptic curves, we obtained differential equations for Weierstrass type and Jacobi type hyperelliptic functions. Considering the special case of $λ_6=0, λ_0=0$, Weierstrass type and Jacobi type hyperelliptic functions are different solutions to the same hyperelliptic differential equations. Then these solutions are connected by the special ${\rm Sp(4, {\bf R})}$ Lie group transformation.

math.CA↗

arXiv2025

Generalized quantum Chernoff bound

We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for discrimination is precisely given by the regularized quantum Chernoff divergence between the sets, thereby establishing a generalized quantum Chernoff bound for the discrimination of multiple sets of quantum states. This extends the classical and quantum Chernoff bounds to the general setting of composite and correlated quantum hypotheses. Furthermore, leveraging minimax theorems, we show that discriminating between sets of quantum states is no harder than discriminating between their worst-case elements in terms of error probability. This implies the existence of an optimal state-agnostic test that achieves the minimum error probability for all states in the sets, matching the performance of the optimal state-dependent test for the most difficult pair of states. We provide explicit characterizations of the optimal state-agnostic test in the binary composite case. Finally, we show that the maximum overlap between a pure state and a set of free states, a quantity that frequently arises in quantum resource theories, is equal to the quantum Chernoff divergence between the sets, thereby providing an operational interpretation of this quantity in the context of symmetric hypothesis testing.

quant-ph↗

arXiv2025

Indefinite causal order strategy does not improve the estimation of group action

We consider estimation of unknown unitary operation when the set of possible unitary operations is given by a projective unitary representation of a compact group. We show that neither indefinite causal order strategy nor adaptive strategy improves the performance of this estimation when error function satisfies group covariance. That is, the optimal parallel strategy gives the optimal performance even under indefinite causal order strategy and adaptive strategy. To study this problem, we newly introduce the concept of generalized positive operator valued measure (GPOVM), and its convariance condition. Using these concepts, we show the above statement.

quant-ph↗

arXiv2025

Universal classical-quantum channel resolvability and private channel coding

We address the problem of constructing fully universal private channel coding protocols for classical-quantum (c-q) channels. Previous work constructed universal decoding strategies, but the encoder relied on random coding, which prevents fully universal code construction. In this work, we resolve this gap by identifying an explicit structural property of codebooks -- namely, the spectral expansion of an associated Schreier graph -- that guarantees universal channel resolvability. Our analysis reveals how this property can be related to channel resolvability through the theory of induced representation. Our main technical result shows that when the transition matrix of a graph associated with a codebook has a large spectral gap, the channel output induced by uniformly sampled codewords is asymptotically indistinguishable from the target output distribution, independently of the channel. This establishes the first deterministic, channel-independent construction of resolvability codebooks. Building on this, we construct a fully universal private channel coding protocol by combining it with universal c-q channel coding based on the Schur-Weyl duality. With appropriate modifications to the requirements on codebooks of universal c-q channel coding, we show that our fully universal private channel coding achieves the known optimal rate. This work thus sheds new light on the expander property of a graph in the context of secure communication.

quant-ph↗