Faculty Profiles - HAYASHI Masahito

Papers - HAYASHI Masahito

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<i>q</i>-Racah probability distribution Reviewed

Hayashi, M; Hora, A; Yanagida, S

RAMANUJAN JOURNAL Vol. 64 ( 3 ) page： 963 - 990 2024.7

Language：English Publishing type：Research paper (scientific journal) Publisher：Ramanujan Journal

We introduce a certain discrete probability distribution Pn,m,k,l;q having non-negative integer parameters n, m, k, l and quantum parameter q which arises from a zonal spherical function of the Grassmannian over the finite field Fq with a distinguished spherical vector. Using representation theoretic arguments and hypergeometric summation technique, we derive the presentation of the probability mass function by a single q-Racah polynomial, and also the presentation of the cumulative distribution function in terms of a terminating 4ϕ3-hypergeometric series.

DOI： 10.1007/s11139-024-00859-w

Non-Adaptive Coding for Two-Way Wiretap Channel With or Without Cost Constraints Reviewed Open Access

Hayashi, M; Chen, YL

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 70 ( 7 ) page： 4611 - 4633 2024.7

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

This paper studies the secrecy results for the two-way wiretap channel (TW-WC) with an external eavesdropper under a strong secrecy metric. Employing non-adaptive coding, we analyze the information leakage and the decoding error probability, and derive inner bounds on the secrecy capacity regions for the TW-WC under strong joint and individual secrecy constraints. For the TW-WC without cost constraint, both the secrecy and error exponents could be characterized by the conditional Rényi mutual information in a concise and compact form. And, some special cases secrecy capacity region and sum-rate capacity results are established, demonstrating that adaption is useless in some cases or the maximum sum-rate that could be achieved by non-adaptive coding. For the TW-WC with cost constraint, we consider the peak cost constraint and extend our secrecy results by using the constant composition codes. Accordingly, we characterize both the secrecy and error exponents by a modification of Rényi mutual information, which yields inner bounds on the secrecy capacity regions for the general discrete memoryless TW-WC with cost constraint. Our method works even when a pre-noisy processing is employed based on a conditional distribution in the encoder and can be easily extended to other multi-user communication scenarios.

DOI： 10.1109/TIT.2023.3343362

When quantum memory is useful for dense coding Reviewed

Takagi, R; Hayashi, M

LETTERS IN MATHEMATICAL PHYSICS Vol. 114 ( 3 ) 2024.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Letters in Mathematical Physics

We discuss dense coding with n copies of a specific preshared state between the sender and the receiver when the encoding operation is limited to the application of group representation. Typically, to act on multiple local copies of these preshared states, the receiver needs quantum memory, because in general the multiple copies will be generated sequentially. Depending on available encoding unitary operations, we investigate what preshared state offers an advantage of using quantum memory on the receiver’s side.

DOI： 10.1007/s11005-024-01831-x

Derivation of standard quantum theory via state discrimination Reviewed Open Access

Arai, H; Hayashi, M

NEW JOURNAL OF PHYSICS Vol. 26 ( 5 ) 2024.5

Language：English Publishing type：Research paper (scientific journal) Publisher：New Journal of Physics

It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of general probabilistic theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality, are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory given by the trace norm. Besides, by applying the equivalent condition, we characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.

DOI： 10.1088/1367-2630/ad4d18

Two-Server Oblivious Transfer for Quantum Messages Reviewed International coauthorship Open Access

Hayashi, M; Song, SH

ADVANCED QUANTUM TECHNOLOGIES Vol. 7 ( 4 ) 2024.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Advanced Quantum Technologies

Oblivious transfer is considered as a cryptographic primitive task for quantum information processing over a quantum network. It is an essential building block for secure multiparty computation. It is known that one-server oblivious transfer is impossible. When the task is the transmission of classical messages, protocols for two-server oblivious transfer exist, i.e., existing protocols work under the assumption that two servers do not communicate with each other. However, when the task is the transmission of a quantum state, no existing method works even under the above two-server assumption. Two-server oblivious transfer protocols for quantum messages are proposed for the first time.

DOI： 10.1002/qute.202300184

Equivocations, Exponents, and Second-Order Coding Rates Under Various Renyi Information Measures ( vol 63, pg 975, 2016) Reviewed

Hayashi, M; Tan, VYF

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 70 ( 4 ) page： 3046 - 3048 2024.4

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

There exists a gap for the proofs of the converse parts of (49) and (50) in Theorem 1 and (74) of Theorem 3. These converse parts use Lemma 4, whose proofs contain a gap. We fix these errors when the rate is larger than the critical rate. A special case of (50) does not coincide the recent result (Li and Yao, 2022, arXiv:2209.00554v1) when the rate is smaller than the critical rate.

DOI： 10.1109/TIT.2024.3355506

Covert Communication With Gaussian Noise: From Random Access Channel to Point-to-Point Channel Reviewed Open Access

Hayashi, M; Vázquez-Castro, A

IEEE TRANSACTIONS ON COMMUNICATIONS Vol. 72 ( 3 ) page： 1516 - 1531 2024.3

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Communications

We propose a covert communication protocol for the spread-spectrum multiple random access with additive white Gaussian noise (AWGN) channel. No existing paper has studied covert communication for the random access channel. Our protocol assumes binary discrete phase-shift keying (BPSK) modulation, and it works well under imperfect channel state information (I-CSI) for both the legitimate and adversary receivers, which is a realistic assumption in the low power regime. Also, our method assumes that the legitimate users share secret variables in a similar way as the preceding studies. Although several studies investigated the covert communication for the point-to-point communication, no existing paper considers the covert communication under the above uncertainty assumption even for point-to-point communication. Our protocol under the above uncertainty assumption allows O(n) legitimate senders and O(n/n) active legitimate senders. Furthermore, our protocol can be converted to a protocol for point-to-point communication that works under the above uncertainty assumption.

DOI： 10.1109/TCOMM.2023.3332861

Universal Adaptive Construction of Verifiable Secret Sharing and Its Application to Verifiable Secure Distributed Data Storage Reviewed International coauthorship

Hayashi, M; Koshiba, T

IEEE-ACM TRANSACTIONS ON NETWORKING Vol. 32 ( 1 ) page： 253 - 267 2024.2

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE/ACM Transactions on Networking

Secret sharing is a useful method for secure distributed data storage. Such a distributed data storage can avoid the information leakage under an attack to a limited number of distributed servers. While such distributed servers send their shares to an end user according to the request, there is a risk that malicious distributed servers send incorrect shares. To detect or identify such malicious servers, we need verifiable secure distributed data storage, which can be constructed from verifiable secret sharing. However, many of previous protocols for verifiable secret sharing are constructed in a specific form. This paper proposes an adaptive construction of verifiable secret sharing, which uses an existing secret sharing protocol as a subprotocol. Also, our method can be applied to any existing secret sharing protocol. This type construction realizes an economical construction.

DOI： 10.1109/TNET.2023.3283577

Asymmetry activation and its relation to coherence under permutation operation Reviewed Open Access

Hayashi M.

Quantum Vol. 8 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：Quantum

A Dicke state and its decohered state are invariant for permutation. However, when another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation. The amount of asymmetry can be measured by the number of distinguishable states under the group action or the mutual information. Generally, the amount of asymmetry of the whole state is larger than the amount of asymmetry of the added state. That is, the asymmetry activation happens in this case. This paper investigates the amount of the asymmetry activation under Dicke states. To address the asymmetry activation asymptotically, we introduce a new type of central limit theorem by using several formulas on hypergeometric functions. We reveal that the amounts of the asymmetry and the asymmetry activation with a Dicke state have a strictly larger order than those with the decohered state in a specific type of the limit.

DOI： 10.22331/q-2024-11-07-1517

Non-Iterative Algorithm for Channel Capacity Reviewed

Hayashi M.

2024 IEEE Information Theory Workshop, ITW 2024 page： 651 - 656 2024

Language：English Publishing type：Research paper (scientific journal) Publisher：2024 IEEE Information Theory Workshop, ITW 2024

Generalizing the algorithm by (IEEE Trans. IT 69, 1681), we propose a non-iterative algorithm to calculate the channel capacity. Unlike the preceding method, which is limited to a specific class of channels, our method is applicable to all channels. Leveraging the information geometrical structure, our approach avoids any iteration steps.

DOI： 10.1109/ITW61385.2024.10806936

Robust and efficient verification of graph states in blind measurement-based quantum computation Reviewed International coauthorship Open Access

Li, ZH; Zhu, HJ; Hayashi, M

NPJ QUANTUM INFORMATION Vol. 9 ( 1 ) 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：npj Quantum Information

Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. Measurement-based quantum computation (MBQC) is a promising approach for realizing BQC. To obtain reliable results in blind MBQC, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource-consuming or noise-susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying the resource state in blind MBQC. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.

DOI： 10.1038/s41534-023-00783-9

Comments on 'Analytical Algorithm for Capacities of Classical and Classical-Quantum Channels' Reviewed

Hayashi M.

IEEE Transactions on Information Theory Vol. 69 ( 11 ) 2023.11

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

After completing the review process of the above article, the author found the reference Muroga (1953), which has already derived an analytical calculation method for the channel capacity under a certain condition. This comment explains the relation between Muroga's article and this article.

DOI： 10.1109/TIT.2023.3299885

Unified Approach to Secret Sharing and Symmetric Private Information Retrieval With Colluding Servers in Quantum Systems Reviewed Open Access

Hayashi, M; Song, S

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 69 ( 10 ) page： 6537 - 6563 2023.10

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

This paper unifiedly addresses two kinds of key quantum secure tasks, i.e., quantum versions of secret sharing (SS) and symmetric private information retrieval (SPIR) by using multi-target monotone span program (MMSP), which characterizes the classical linear protocols of SS and SPIR. SS has two quantum extensions; One is the classical-quantum (CQ) setting, in which the secret to be sent is classical information and the shares are quantum systems. The other is the quantum-quantum (QQ) setting, in which the secret to be sent is a quantum state and the shares are quantum systems. The relation between these quantum protocols and MMSP has not been studied sufficiently. We newly introduce the third setting, i.e., the entanglement-assisted (EA) setting, which is defined by modifying the CQ setting with allowing prior entanglement between the dealer and the end-user who recovers the secret by collecting the shares. Showing that the linear version of SS with the EA setting is directly linked to MMSP, we characterize linear quantum versions of SS with the CQ ad QQ settings via MMSP. Further, we introduce the EA setting of SPIR, which is shown to link to MMSP. In addition, we discuss the quantum version of maximum distance separable codes.

DOI： 10.1109/TIT.2023.3282940

Commitment Capacity of Classical-Quantum Channels Reviewed Open Access

Hayashi, M; Warsi, NA

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 69 ( 8 ) page： 5083 - 5099 2023.8

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

We study commitment scheme for classical-quantum channels. To accomplish this we define various notions of commitment capacity for these channels and prove matching upper and lower bound on it in terms of the conditional entropy. Our achievability (lower bound) proof is quantum generalisation of the work of one of the authors (arXiv:2103.11548) which studied the problem of secure list decoding and its application to bit-string commitment. The techniques we use in the proof of converse (upper bound) is similar in spirit to the techniques introduced by Winter, Nascimento and Imai (Cryptography and Coding 2003) to prove upper bound on the commitment capacity of classical channels. However, generalisation of this technique to the quantum case is not so straightforward and requires some new constructions, which can be of independent interest.

DOI： 10.1109/TIT.2023.3268321

Bregman Divergence Based Em Algorithm and its Application to Classical and Quantum Rate Distortion Theory Reviewed Open Access

Hayashi, M

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 69 ( 6 ) page： 3460 - 3492 2023.6

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

We formulate em algorithm in the framework of Bregman divergence, which is a general problem setting of information geometry. That is, we address the minimization problem of the Bregman divergence between an exponential subfamily and a mixture subfamily in a Bregman divergence system. Then, we show the convergence and its speed under several conditions. We apply this algorithm to rate distortion and its variants including the quantum setting, and show the usefulness of our general algorithm. In fact, existing applications of Arimoto-Blahut algorithm to rate distortion theory make the optimization of the weighted sum of the mutual information and the cost function by using the Lagrange multiplier. However, in rate distortion theory, it is needed to minimize the mutual information under the constant constraint for the cost function. Our algorithm directly solves this minimization. In addition, we have numerically checked the convergence speed of our algorithm in the classical case of rate distortion problem.

DOI： 10.1109/TIT.2023.3239955

Analytical Algorithm for Capacities of Classical and Classical-Quantum Channels Reviewed Open Access

Hayashi, M

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 69 ( 3 ) page： 1381 - 1393 2023.3

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

We derive an analytical algorithm for the channel capacity of a classical channel without any iteration, while its existing algorithms require iterations and the number of iterations depends on the required precision level. Hence, our algorithm is its first analytical algorithm for this task without any iteration, while this algorithm needs several conditions for the channel. We apply the obtained algorithm to examples, and see how the obtained algorithm works in these examples. Then, we extend it to the channel capacity of a classical-quantum (cq-) channel. Many existing studies proposed algorithms for a cq-channel and all of them require iterations. Our extended analytical algorithm has also no iteration, and outputs the exactly optimum value.

DOI： 10.1109/TIT.2022.3215178

Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification Reviewed Open Access

Li, K; Yao, YS; Hayashi, M

IEEE TRANSACTIONS ON INFORMATION THEORY Vol. 69 ( 3 ) page： 1680 - 1694 2023.3

Language：English Publishing type：Research paper (scientific journal) Publisher：IEEE Transactions on Information Theory

The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance. We then apply this result to the problem of privacy amplification against quantum side information, and we obtain an upper bound for the exponent of the asymptotic decreasing of the insecurity, measured using either purified distance or relative entropy. Our upper bound complements the earlier lower bound established by Hayashi, and the two bounds match when the rate of randomness extraction is above a critical value. Thus, for the case of high rate, we have determined the exact security exponent. Following this, we give examples and show that in the low-rate case, neither the upper bound nor the lower bound is tight in general. This exhibits a picture similar to that of the error exponent in channel coding. Lastly, we investigate the asymptotics of equivocation and its exponent under the security measure using the sandwiched Rényi divergence of order s (1,2] , which has not been addressed previously in the quantum setting.

DOI： 10.1109/TIT.2022.3217671

Efficient algorithms for quantum information bottleneck Reviewed International coauthorship Open Access

Hayashi, M; Yang, YX

QUANTUM Vol. 7 2023.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Quantum

The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of relevant information from a large system. The advent of the age of quantum computing calls for efficient methods that work on information regarding quantum systems. Here we address this by proposing a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. It also works for a much broader range of problems, including the quantum extension of deterministic information bottleneck, an important variant of the original information bottleneck problem. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck, providing new vision on justifying the advantage of quantum machine learning.

DOI： 10.22331/q-2023-03-02-936

Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure Reviewed Open Access

Arai, H; Hayashi, M

NEW JOURNAL OF PHYSICS Vol. 25 ( 2 ) 2023.2

Language：English Publishing type：Research paper (scientific journal) Publisher：New Journal of Physics

An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose that the local subsystems are fully equal to quantum systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure (SES) is valid. To examine this issue, we introduce pseudo SES as a structure of quantum composite system under natural assumptions based on the existence of projective measurements and the existence of approximations of all maximally entangled standard states. Surprisingly, there exist infinitely many pseudo SESs different from the SES. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure. On the other hand, such pseudo structures never possess global unitary symmetry, i.e. global unitary symmetry is essential condition for the SES.

DOI： 10.1088/1367-2630/acb565

Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming Reviewed Open Access

Hayashi M., Ouyang Y.

Quantum Vol. 7 2023

Language：English Publishing type：Research paper (scientific journal) Publisher：Quantum

In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known how to find practical measurements with optimal precisions, even for uncorrelated measurements over probe states. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We solve this fundamental problem by introducing a framework of conic programming that unifies the theory of precision bounds for multiparameter estimates for uncorrelated and correlated measurement strategies under a common umbrella. Namely, we give precision bounds that arise from linear programs on various cones defined on a tensor product space of matrices, including a particular cone of separable matrices. Subsequently, our theory allows us to develop an efficient algorithm that calculates both upper and lower bounds for the ultimate precision bound for uncorrelated measurement strategies, where these bounds can be tight. In particular, the uncorrelated measurement strategy that arises from our theory saturates the upper bound to the ultimate precision bound. Also, we show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.

DOI： 10.22331/Q-2023-08-29-1094

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