arXiv subjects

Takaya Matsuura

Publications and source records attributed to Takaya Matsuura.

At least 19 recordsLinked to original sources

arXiv2026

Universality Sacrifices Reliability in Classical-Quantum Channel Coding

Universal channel coding enables communication without a complete description of the channel. For classical channels, universal codes can attain both capacity and the optimal high-rate reliability. We show that this compatibility fails for classical-quantum channels in general; that is, the optimal reliability in the channel-aware scenario is not always achievable with universal coding due to the ignorance of the unitary rotation of the output system. We exhibit a family of classical-quantum channels for which one cannot achieve the channel-aware optimal reliability by a fixed coding scheme. We further derive a converse bound on the reliability for unitary-invariant decoders, a natural assumption for the universal coding scheme, that can be strictly smaller than the optimal channel-aware error exponent. Conversely, we construct a channel-independent encoder-decoder pair and establish a universally achievable bound on the reliability that matches this converse bound in the high-rate regime, thereby characterizing the optimal universal reliability. Specifically, the channel-aware and universal exponents are governed by the Petz and sandwiched Rényi divergences, respectively. These divergences coincide for commuting outputs but differ for noncommuting ones, explaining why universality preserves optimal reliability classically but can reduce it quantumly. Our results showcase the fundamental reliability cost of performing the classical-quantum channel coding task universally.

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arXiv2026

Universal distillation of quantum entanglement

Distillable entanglement---the maximum rate of Bell states extractable from the given noisy entangled states via local operations and classical communication (LOCC)---has been a central quantity to characterize the operational value of entangled states. However, this operational meaning had been known to be valid only under a crucial assumption: both parties know the description of the input state and can choose the protocol tailored to it, which does not necessarily reflect the natural operational setting. Here, we show that the distillable entanglement is the fundamental operational quantity even without this assumption. We present a universal LOCC protocol---whose description does not depend on the input state and thus works universally for any input---that achieves the distillable entanglement of an arbitrary unknown input state. Our result therefore lifts the distillable entanglement to a robust notion of an operationally meaningful quantity and clarifies that input-state knowledge is not necessary to achieve the optimal rate of entanglement distillation. Our protocol is based on state merging for compound states, together with the uniform convergence property of the finite-block quantity toward distillable entanglement.

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arXiv2026

Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates

Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.

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arXiv2026

When Classical Correlations Certify Entanglement Recovery

Entanglement and state distinguishability have long been central topics in quantum foundations. While each has developed into a rich subject in its own right, they can be connected through measurements in complementary bases. This connection provides insights into quantum and classical correlations and underlies many information-processing tasks, most notably quantum error correction (QEC). However, it has remained largely open whether the connection between entanglement and distinguishability extends to general measurements without assuming complementarity. We answer this question in the affirmative: the key is irreducibility induced by measurements, a much more relaxed condition than complementarity. Specifically, for POVMs satisfying an irreducibility condition, we establish a quantitative relation between the infidelity of one-sided local transformation into a maximally entangled state and the failure probability in state discrimination. We then characterize when both errors can vanish simultaneously. Our results have direct applications to entanglement distillation and QEC. Their errors can be certified by estimating classical input-output correlations from experimentally accessible local measurements, without requiring complementarity. The results also extend to quantum measurement theory. We derive novel trade-off relations that bridge two historically distinct approaches: information gain--irreversibility and observable noise--disturbance. Our connection between entanglement and distinguishability via irreducibility thus offers a common framework for entanglement distillation, QEC, and measurement trade-offs.

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arXiv2026

All you need is the universal correlation detector: A unified approach to universalize communication protocols over quantum channels

Constructing optimal quantum information protocols without complete knowledge of the underlying states or channels is a central challenge. We address this challenge by developing universal correlation detection as a common building block for quantum communication. Our detectors distinguish a bipartite state from the product of its marginals and attain the same first-order asymptotic performance as optimal tests constructed with complete state information. For general bipartite quantum states, knowledge of a single marginal suffices: a detector depending only on that marginal is first-order optimal for every compatible state. For classical-quantum states, the detector is fully universal and requires no prior state information. By combining these detectors with position-based decoding and convex splitting, we construct channel-independent coding schemes that achieve capacity for a range of communication tasks. These results turn universal correlation detection into a systematic tool for universal protocol design, providing a unified route to designing capacity-achieving protocols for many communication tasks over unknown quantum channels.

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arXiv2026

Asymptotically tight security analysis of quantum key distribution based on universal source compression

Practical quantum key distribution (QKD) protocols require a finite-size security proof. The phase error correction (PEC) approach is one of the general strategies for security analyses that has successfully proved finite-size security for many protocols. However, the conventional PEC approach cannot achieve the asymptotically optimal key rate in general, as long as the failure probability of PEC is estimated through the phase error rate. In this work, we propose a new PEC-type strategy that can provably achieve the asymptotically optimal key rate. The key piece for this is a virtual protocol based on universal source compression with quantum side information, which is of independent interest. A universal source compression with quantum side information protocol is first constructed for fixed-length independent and identically distributed (i.i.d.)~setups and then extended to adaptive-length setups with the restrictions on possible states imposed by joint random variables. Combined with the reduction method to collective attacks, this enables us to tightly evaluate the failure probability of PEC for permutation-symmetric QKD protocols, and thus leads to asymptotically tight analyses. As a result, the security of any permutation-symmetrizable QKD protocol gets reduced to the estimation problem of a single conditional Rényi entropy, which can be efficiently solved by a convex optimization.

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arXiv2025

Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code

Photon loss is the dominant source of noise in optical quantum systems. The Gottesman-Kitaev-Preskill (GKP) bosonic code provides significant protection; however, even low levels of loss can generate uncorrectable errors that another concatenated code must handle. In this work, we characterize these errors by deriving analytic expressions for the logical channel that arises from pure loss acting on approximate GKP qubits. Unlike random displacement noise, we find that the loss-induced logical channel is not a stochastic Pauli channel. We also provide analytic expressions for the logical channel for "heralded loss," when the light scattered out of the signal mode is measured either by photon number counting -- i.e., photon subtraction -- or heterodyne detection. These offer a pathway to intentionally inducing non-Pauli channels for, e.g., magic-state production.

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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.

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arXiv2025

Linear-optical quantum computation with arbitrary error-correcting codes

High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties, compatible with arbitrary codes and Gottesman-Kitaev-Preskill qubits on generic lattices, and featuring a natural way to leverage physical noise bias. Simulations of hyperbolic surface codes and bivariate bicycle codes, promising families of quantum low-density parity-check codes, reveal a threshold comparable to the 2D surface code with substantially better encoding rates.

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arXiv2025

Decoding general error correcting codes and the role of complementarity

Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper, we show that a decoding circuit for Calderbank-Shor-Steane (CSS) codes can be straightforwardly extended to handle general QECCs. The key to the extension lies in the use of a pair of classical-quantum (CQ) codes associated with the QECC to be decoded. The decoding error of the proposed decoding circuit depends on the classical decoding errors of the CQ codes and their degree of complementarity. We demonstrate the power of the decoding circuit in a toy model of the black hole information paradox, improving decoding errors compared to previous results. In addition, we reveal that black hole dynamics may optimally encode quantum information but poorly encode classical information.

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arXiv2024

Tight concentration inequalities for quantum adversarial setups exploiting permutation symmetry

We developed new concentration inequalities for a quantum state on an $N$-qudit system or measurement outcomes on it that apply to an adversarial setup, where an adversary prepares the quantum state. Our one-sided concentration inequalities for a quantum state require the $N$-qudit system to be permutation invariant and are thus de-Finetti type, but they are tighter than the one previously obtained. We show that the bound can further be tightened if each qudit system has an additional symmetry. Furthermore, our concentration inequality for the outcomes of independent and identical measurements on an $N$-qudit quantum system has no assumption on the adversarial quantum state and is much tighter than the conventional one obtained through Azuma's inequality. We numerically demonstrate the tightness of our bounds in simple quantum information processing tasks.

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arXiv2024

Continuous-Variable Fault-Tolerant Quantum Computation under General Noise

The quantum error-correcting code in the continuous-variable (CV) system attracts much attention due to its flexibility and high resistance against specific noise. However, the theory of fault tolerance in CV systems is premature and lacks the general strategy to translate the noise in CV systems into the noise in logical qubits, leading to severe restrictions on the correctable noise models. In this paper, we show that the Markovian-type noise in CV systems is translated into the Markovian-type noise in the logical qubits through the Gottesman-Kitaev-Preskill code with an explicit bound on the noise strength. Combined with the established threshold theorem of the concatenated code against Markovian-type noise, we show that CV quantum computation has a fault-tolerant threshold against general Markovian-type noise, closing the existing crucial gap in CV quantum computation. We also give a new insight into the fact that careful management of the energy of the state is required to achieve fault tolerance in the CV system.

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arXiv2023

Efficient Concatenated Bosonic Code for Additive Gaussian Noise

Bosonic codes offer noise resilience for quantum information processing. Good performance often comes at a price of complex decoding schemes, limiting their practicality. Here, we propose using a Gottesman-Kitaev-Preskill (GKP) code to detect and discard error-prone qubits, concatenated with a quantum parity code to handle the residual errors. Our method employs a simple, linear-time decoder that nevertheless offers significant performance improvements over the standard decoder. Our work may have applications in a wide range of quantum computation and communication scenarios.

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arXiv2023

Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution

Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.

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arXiv2023

General treatment of Gaussian trusted noise in continuous variable quantum key distribution

Continuous Variable (CV) quantum key distribution (QKD) is a promising candidate for practical implementations due to its compatibility with the existing communication technology. A trusted device scenario assuming that an adversary has no access to imperfections such as electronic noises in the detector is expected to provide significant improvement in the key rate, but such an endeavor so far was made separately for specific protocols and for specific proof techniques. Here, we develop a simple and general treatment that can incorporate the effects of Gaussian trusted noises for any protocol that uses homodyne/heterodyne measurements. In our method, a rescaling of the outcome of a noisy homodyne/heterodyne detector renders it equivalent to the outcome of a noiseless detector with a tiny additional loss, thanks to a noise-loss equivalence well-known in quantum optics. Since this method is independent of protocols and security proofs, it is applicable to Gaussian-modulation and discrete-modulation protocols, to the finite-size regime, and to any proof techniques developed so far and yet to be discovered as well.

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arXiv2023

Equivalent noise properties of scalable continuous-variable cluster states

Optical continuous-variable cluster states (CVCSs) in combination with Gottesman-Kitaev-Preskill~(GKP) qubits enable fault-tolerant quantum computation so long as these resources are of high enough quality. Previous studies concluded that a particular CVCS, the quad rail lattice~(QRL), exhibits lower GKP gate-error rate than others do. We show in this work that many other experimentally accessible CVCSs also achieve this level of performance by identifying operational equivalences to the QRL. Under this equivalence, the GKP Clifford gate set for each CVCS maps straightforwardly from that of the QRL, inheriting its noise properties. Furthermore, each cluster state has at its heart a balanced four-splitter -- the four-mode extension to a balanced beam splitter. We classify all four-splitters, show they form a single equivalence class under SWAP and parity operators, and we give a construction of any four-splitter with linear optics, thus extending the toolbox for theoretical and experimental cluster-state design and analysis.

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arXiv2022

Finite-size security proof of binary-modulation continuous-variable quantum key distribution using only heterodyne measurement

Continuous-variable quantum key distribution (CV-QKD) has many practical advantages including compatibility with current optical communication technology. Implementation using heterodyne measurements is particularly attractive since it eliminates the need for active phase locking of the remote pair of local oscillators, but the full security of CV QKD with discrete modulation was only proved for a protocol using homodyne measurements. Here we propose an all-heterodyne CV-QKD protocol with binary modulation and prove its security against general attacks in the finite-key regime. Although replacing a homodyne measurement with a heterodyne measurement would be naively expected to incur a 3-dB penalty in the rate-distance curve, our proof achieves a key rate with only a 1-dB penalty.

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arXiv2021

Fault-tolerant quantum computation with static linear optics

The scalability of photonic implementations of fault-tolerant quantum computing based on Gottesman-Kitaev-Preskill (GKP) qubits is injured by the requirements of inline squeezing and reconfigurability of the linear optical network. In this work we propose a topologically error-corrected architecture that does away with these elements at no cost - in fact, at an advantage - to state preparation overheads. Our computer consists of three modules: a 2D array of probabilistic sources of GKP states; a depth-four circuit of static beamsplitters, phase shifters, and single-time-step delay lines; and a 2D array of homodyne detectors. The symmetry of our proposed circuit allows us to combine the effects of finite squeezing and uniform photon loss within the noise model, resulting in more comprehensive threshold estimates. These jumps over both architectural and analytical hurdles considerably expedite the construction of a photonic quantum computer.

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