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Dense Coding with Locality Restriction on Decoders: Quantum Encoders versus Superquantum Encoders 査読有り

Hayashi, M; Wang, K

PRX QUANTUM 3 巻 ( 3 ) 2022年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：PRX Quantum

We investigate practical dense coding by imposing locality restrictions on decoders and symmetry restrictions on encoders within the resource theory of asymmetry framework. In this task, the sender Alice and the helper Fred preshare an entangled state. Alice encodes a classical message into the quantum state using a symmetric preserving encoder and sends the encoded state to Bob through a noiseless quantum channel. The receiver Bob and helper Fred are limited to performing quantum measurements satisfying certain locality restrictions to decode the classical message. We are interested in the ultimate dense coding capacity under these constraints. Our contributions are summarized as follows. First, we derive both one-shot and asymptotic optimal achievable transmission rates of the dense coding task under different encoder and decoder combinations. Surprisingly, our results reveal that the transmission rate cannot be improved even when the decoder is relaxed from one-way local operations and classical communication (LOCC) to two-way LOCC, separable measurements, and partial transpose positive measurements of the bipartite system. Second, depending on the class of allowed decoders with certain locality restrictions, we relax the class of encoding operations to superquantum encoders in the general probability theory framework and derive dense coding transmission rates under this setting. For example, when the decoder is fixed to a separable measurement, theoretically, a positive operation is allowed as an encoding operation. Remarkably, even under this superquantum relaxation, the transmission rate still cannot be lifted. This fact highlights the universal validity of our analysis on practical dense coding beyond quantum theory.

DOI： 10.1103/PRXQuantum.3.030346

Graph-Theoretic Approach for Self-Testing in Bell Scenarios 査読有り Open Access

Bharti, K; Ray, M; Xu, ZP; Hayashi, M; Kwek, LC; Cabello, A

PRX QUANTUM 3 巻 ( 3 ) 2022年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：PRX Quantum

Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that BQ is strictly contained in an easy-to-characterize set associated with a graph, Θ(G). Therefore, whenever the optimum over BQ and the optimum over Θ(G) coincide, self-testing can be demonstrated by simply proving self-testability with Θ(G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.

DOI： 10.1103/PRXQuantum.3.030344

Quantum verifiable protocol for secure modulo zero-sum randomness 査読有り

Hayashi, M; Koshiba, T

QUANTUM INFORMATION PROCESSING 21 巻 ( 8 ) 2022年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Quantum Information Processing

We propose a new cryptographic resource, secure modulo zero-sum randomness, as a resource to implement a task of secure modulo summation, and its quantum protocol. Secure modulo summation is the calculation of modulo summation Y1+ ⋯ + Ym when m players have their individual variables Y1, … , Ym with keeping the secrecy of the individual variables. Secure modulo zero-sum randomness is a set of m variables X1, … , Xm held by m players that satisfy the zero sum condition X1+ ⋯ + Xm= 0 with a certain security condition. This paper explains the relation between these two concepts and proposes a quantum verifiable protocol for secure modulo summation. The advantage for quantum protocol is the verifiability based on self-testing, which does not need to trust measurement devices and can be realized by using a statistical concept, significance level, while any classical method needs to trust several components of the protocol. Then, we propose various cryptographic applications for secure modulo zero-sum randomness. We also compare our quantum verifiable protocol with the conventional method for secure modulo summation.

DOI： 10.1007/s11128-022-03639-x

Quantum causal unravelling 査読有り Open Access

Bai, G; Wu, YD; Zhu, Y; Hayashi, M; Chiribella, G

NPJ QUANTUM INFORMATION 8 巻 ( 1 ) 2022年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：npj Quantum Information

Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, under the assumption that the process has bounded information loss and induces causal dependencies whose strength is above a fixed (but otherwise arbitrary) threshold. Our method is based on a quantum algorithm whose complexity scales polynomially in the total number of input/output systems, in the dimension of the systems involved in each interaction, and in the inverse of the chosen threshold for the strength of the causal dependencies. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in quantum networks, and to test the internal structure of uncharacterized quantum circuits.

DOI： 10.1038/s41534-022-00578-4

Quantum Secure Direct Communication with Private Dense Coding Using a 査読有り Open Access

Wu, JW; Long, GL; Hayashi, M

PHYSICAL REVIEW APPLIED 17 巻 ( 6 ) 2022年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review Applied

We study quantum secure direct communication using a general preshared quantum state and a generalization of dense coding. In this scenario, Alice is allowed to apply a unitary operation on the preshared state to encode her message, and the set of allowed unitaries forms a group. To decode the message, Bob is allowed to apply a measurement across his system and the system he receives. In the worst scenario, we guarantee that Eve obtains no information for the message even when Eve accesses the joint system between the system that she intercepts and her original system of the preshared state. For a practical application, we propose a concrete protocol and derive an upper bound of information leakage in the finite-length setting. We also discuss how to apply our scenario to the case with discrete Weyl-Heisenberg representation when the preshared state is unknown.

DOI： 10.1103/PhysRevApplied.17.064011

Secure List Decoding and its Application to Bit-String Commitment 査読有り国際共著 Open Access

Hayashi, M

IEEE TRANSACTIONS ON INFORMATION THEORY 68 巻 ( 6 ) 頁： 3620 - 3642 2022年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE Transactions on Information Theory

We propose a new concept of secure list decoding, which is related to bit-string commitment. While the conventional list decoding requires that the list contains the transmitted message, secure list decoding requires the following additional security conditions to work as a modification of bit-string commitment. The first additional security condition is the receiver's uncertainty for the transmitted message, which is stronger than the impossibility of the correct decoding, even though the transmitted message is contained in the list. The other additional security condition is the impossibility for the sender to estimate another element of the decoded list except for the transmitted message. The first condition is evaluated by the equivocation rate. The asymptotic property is evaluated by three parameters, the rates of the message and list sizes, and the equivocation rate. We derive the capacity region of this problem. We show that the combination of hash function and secure list decoding yields the conventional bit-string commitment. Our results hold even when the input and output systems are general probability spaces including continuous systems. When the input system is a general probability space, we formulate the abilities of the honest sender and the dishonest sender in a different way.

DOI： 10.1109/TIT.2022.3150498

Global Heisenberg scaling in noisy and practical phase estimation 査読有り Open Access

Hayashi, M; Liu, ZW; Yuan, HD

QUANTUM SCIENCE AND TECHNOLOGY 7 巻 ( 2 ) 2022年4月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Quantum Science and Technology

Heisenberg scaling characterizes the ultimate precision of parameter estimation enabled by quantum mechanics, which represents an important quantum advantage of both theoretical and technological interest. Here, we present a comprehensive and rigorous study of the attainability of strong, global notions of Heisenberg scaling (in contrast to the commonly studied local estimation based on e.g. quantum Fisher information) in the fundamental problem of quantum metrology, in noisy environments. As our first contribution, we formally define two useful notions of Heisenberg scaling in global estimation respectively based on the average estimation error and the limiting distribution of estimation error (which we highlight as a practically important figure of merit). A main result of this work is that for the standard phase damping noise, an O(n -1) noise rate is a necessary and sufficient condition for attaining global Heisenberg scaling. We first prove that O(n -1) is an upper bound on the noise rate for Heisenberg scaling to be possible, and then show by constructing a 'robust' estimation procedure that global Heisenberg scaling in both senses can indeed be achieved under Θ(n -1) noise. In addition, we provide a practically more friendly adaptive protocol using only an one-qubit memory, which achieves global Heisenberg scaling in terms of limiting distribution as well under O(n -1) noise.

DOI： 10.1088/2058-9565/ac5d7e

Equivalence of Non-Perfect Secret Sharing and Symmetric Private Information Retrieval With General Access Structure 査読有り国際共著国際誌 Open Access

Song, S; Hayashi, M

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 40 巻 ( 3 ) 頁： 999 - 1012 2022年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE Journal on Selected Areas in Communications

We study the equivalence between non-perfect secret sharing (NSS) and symmetric private information retrieval (SPIR) with arbitrary response and collusion patterns. NSS and SPIR are defined with an access structure, which corresponds to the authorized/forbidden sets for NSS and the response/collusion patterns for SPIR. We prove the equivalence between NSS and SPIR in the following two senses. 1) Given any SPIR protocol with an access structure, an NSS protocol is constructed with the same access structure and the same rate. 2) Given any linear NSS protocol with an access structure, a linear SPIR protocol is constructed with the same access structure and the same rate. We prove the first relation even if the SPIR protocol has imperfect correctness and secrecy. From the first relation, we derive an upper bound of the SPIR capacity for arbitrary response and collusion patterns. For the special case of \mathsf {n} -server SPIR with \mathsf {r} responsive and \mathsf {t} colluding servers, this upper bound proves that the SPIR capacity is (\mathsf {r}-\mathsf {t})/\mathsf {n}. From the second relation, we prove that a SPIR protocol exists for any response and collusion patterns.

DOI： 10.1109/JSAC.2022.3142375

On the Capacity of Quantum Private Information Retrieval From MDS-Coded and Colluding Servers 査読有り国際共著 Open Access

Allaix, M; Song, S; Holzbaur, L; Pllaha, T; Hayashi, M; Hollanti, C

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 40 巻 ( 3 ) 頁： 885 - 898 2022年3月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE Journal on Selected Areas in Communications

In quantum private information retrieval (QPIR), a user retrieves a classical file from multiple servers by downloading quantum systems without revealing the identity of the file. The QPIR capacity is the maximal achievable ratio of the retrieved file size to the total download size. In this paper, the capacity of QPIR from MDS-coded and colluding servers is studied for the first time. Two general classes of QPIR, called stabilizer QPIR and dimension-squared QPIR induced from classical strongly linear PIR are defined, and the related QPIR capacities are derived. For the non-colluding case, the general QPIR capacity is derived when the number of files goes to infinity. A general statement on the converse bound for QPIR with coded and colluding servers is derived showing that the capacities of stabilizer QPIR and dimension-squared QPIR induced from any class of PIR are upper bounded by twice the classical capacity of the respective PIR class. The proposed capacity-achieving scheme combines the star-product scheme by Freij-Hollanti et al. and the stabilizer QPIR scheme by Song et al. by employing (weakly) self-dual Reed-Solomon codes.

DOI： 10.1109/JSAC.2022.3142363

Universal Classical-Quantum Superposition Coding and Universal Classical-Quantum Multiple Access Channel Coding 査読有り

Hayashi, M; Cai, N

IEEE TRANSACTIONS ON INFORMATION THEORY 68 巻 ( 3 ) 頁： 1822 - 1850 2022年3月

Usefulness of adaptive strategies in asymptotic quantum channel discrimination 査読有り国際共著 Open Access

Salek, F; Hayashi, M; Winter, A

PHYSICAL REVIEW A 105 巻 ( 2 ) 2022年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Physical Review A

Adaptiveness is a key principle in information processing including statistics and machine learning. We investigate the usefulness adaptive methods in the framework of asymptotic binary hypothesis testing, when each hypothesis represents asymptotically many independent instances of a quantum channel, and the tests are based on using the unknown channel and observing outputs. Unlike the familiar setting of quantum states as hypotheses, there is a fundamental distinction between adaptive and nonadaptive strategies with respect to the channel uses, and we introduce a number of further variants of the discrimination tasks by imposing different restrictions on the test strategies. The following results are obtained: (1) We prove that for classical-quantum channels, adaptive and nonadaptive strategies lead to the same error exponents both in the symmetric (Chernoff) and asymmetric (Hoeffding, Stein) settings. (2) The first separation between adaptive and nonadaptive symmetric hypothesis testing exponents for quantum channels, which we derive from a general lower bound on the error probability for nonadaptive strategies; the concrete example we analyze is a pair of entanglement-breaking channels. (3) We prove, in some sense generalizing the previous statement, that for general channels adaptive strategies restricted to classical feed-forward and product state channel inputs are not superior in the asymptotic limit to nonadaptive product state strategies. (4) As an application of our findings, we address the discrimination power of an arbitrary quantum channel and show that adaptive strategies with classical feedback and no quantum memory at the input do not increase the discrimination power of the channel beyond nonadaptive tensor product input strategies.

DOI： 10.1103/PhysRevA.105.022419

Information geometry approach to parameter estimation in hidden Markov model 査読有り国際共著

Hayashi, M

BERNOULLI 28 巻 ( 1 ) 頁： 307 - 342 2022年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Bernoulli

We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of k-memory data is used for the estimation. To establish our method, we focus on a partial observation model with the Markovian process and we propose an efficient estimator whose asymptotic estimation error is given as the inverse of projective Fisher information of transition matrices. This estimator is applied to the estimation of the transition matrix of the hidden Markovian process. In this application, we carefully discuss the equivalence problem for hidden Markovian process on the tangent space.

DOI： 10.3150/21-BEJ1344

Secure Physical Layer Network Coding versus Secure Network Coding 査読有り国際共著 Open Access

Hayashi, M

ENTROPY 24 巻 ( 1 ) 2022年1月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Entropy

When a network has relay nodes, there is a risk that a part of the information is leaked to an untrusted relay. Secure network coding (secure NC) is known as a method to resolve this problem, which enables the secrecy of the message when the message is transmitted over a noiseless network and a part of the edges or a part of the intermediate (untrusted) nodes are eavesdropped. If the channels on the network are noisy, the error correction is applied to noisy channels before the application of secure NC on an upper layer. In contrast, secure physical layer network coding (secure PLNC) is a method to securely transmit a message by a combination of coding operation on nodes when the network is composed of set of noisy channels. Since secure NC is a protocol on an upper layer, secure PLNC can be considered as a cross-layer protocol. In this paper, we compare secure PLNC with a simple combination of secure NC and error correction over several typical network models studied in secure NC.

DOI： 10.3390/e24010047

Quantum-Inspired Secure Wireless Communication Protocol Under Spatial and Local Gaussian Noise Assumptions 査読有り Open Access

Hayashi, M

IEEE ACCESS 10 巻頁： 29040 - 29068 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE Access

Inspired by quantum key distribution, we consider wireless communication between Alice and Bob when the noise generated in the intermediate space between Alice and Bob is controlled by Eve. Our model divides the channel noise into two parts, the noise generated during the transmission and the noise generated in the detector. Eve is allowed to control the former, but is not allowed to do the latter. While the latter is assumed to be a Gaussian random variable, the former is not assumed to be a Gaussian random variable. In this situation, using backward reconciliation and random sampling, we propose a protocol to generate secure keys between Alice and Bob under the assumption that Eve's detector has a Gaussian noise and Eve is not so close to Alice's transmitting device. In our protocol, the security criteria are quantitatively guaranteed even with finite block-length code based on the evaluation of error of the estimation of the channel.

DOI： 10.1109/ACCESS.2022.3159331

Analytical calculation formulas for capacities of classical and classical-quantum channels 査読有り Open Access

Hayashi M.

IEEE International Symposium on Information Theory - Proceedings 2022-June 巻頁： 91 - 96 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE International Symposium on Information Theory - Proceedings

We derive an analytical calculation formula for the channel capacity of a classical channel without any iteration while its existing algorithms require iterations and the number of iteration depends on the required precision level. Hence, our formula is its first analytical formula without any iteration. We apply the obtained formula to examples and see how the obtained formula works in these examples.

DOI： 10.1109/ISIT50566.2022.9834600

Exponents in smoothing the max-relative entropy and of randomness extraction against quantum side information 査読有り

Li K., Yao Y., Hayashi M.

IEEE International Symposium on Information Theory - Proceedings 2022-June 巻頁： 1862 - 1867 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE International Symposium on Information Theory - Proceedings

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award.The smooth max-relative entropy is a basic tool in quantum information theory and cryptography. In this paper, we derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy. We then apply this result to the problem of privacy amplification against quantum side information and obtain an upper bound for the exponent of the 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.Lastly, we investigate the asymptotics of equivocation and its exponent under the security measure using the sandwiched Rényi divergence of order between 1 and 2, which has not been addressed previously in the quantum setting.

DOI： 10.1109/ISIT50566.2022.9834595

Commitment capacity of classical-quantum channels 査読有り Open Access

Hayashi M., Warsi N.A.

IEEE International Symposium on Information Theory - Proceedings 2022-June 巻頁： 1058 - 1063 2022年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：IEEE International Symposium on Information Theory - Proceedings

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/ISIT50566.2022.9834801

Refined Density Evolution Analysis of LDPC Codes for Successive Interference Cancellation 査読有り国際共著

Takabe S., Wadayama T., Hayashi M.

2021年12月

Erratum: Concise and tight security analysis of the Bennett-Brassard 1984 protocol with finite key lengths (New Journal of Physics (2012) 14 (093014) DOI: 10.1088/1367-2630/14/9/093014) 査読有り国際共著

Hayashi M., Tsurumaru T.

New Journal of Physics 23 巻 ( 12 ) 2021年12月

担当区分：筆頭著者,　最終著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：New Journal of Physics

The paper (Hayashi M and Tsurumaru T 2012 New J. Phys. 14 093014) contains an error at the definition of g t (x) in section 5.3 while g t (x) is used for the second order asymptotic expansion for the sacrifice bit. This corrigendum corrects this error and shows its derivation.

DOI： 10.1088/1367-2630/ac3c61

Asymptotic Separation Between Adaptive and Non-adaptive Strategies in Quantum Channel Discrimination 査読有り国際共著

Salek M., Hayashi M., Winter A.

2021年7月

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