arXiv subjects

Masahito Hayashi

Publications and source records attributed to Masahito Hayashi.

At least 127 records · Page 7Linked to original sources

arXiv2021

Graph-Theoretic Framework for Self-Testing in Bell Scenarios

Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely, with minimal assumptions about the underlying quantum system. It is based on the observation that some extremal points in the set of quantum correlations can only be achieved, up to isometries, with specific states and measurements. Here, we present a new approach for quantum self-testing in Bell non-locality scenarios, motivated by the following observation: the quantum maximum of a given Bell inequality is, in general, difficult to characterize. However, it is strictly contained in an easy-to-characterize set: the \emph{theta body} of a vertex-weighted induced subgraph $(G,w)$ of the graph in which vertices represent the events and edges join mutually exclusive events. This implies that, for the cases where the quantum maximum and the maximum within the theta body (known as the Lovász theta number) of $(G,w)$ coincide, self-testing can be demonstrated by just proving self-testability with the theta body of $G$. This graph-theoretic framework allows us to (i) recover the self-testability of several quantum correlations that are known to permit self-testing (like those violating the Clauser-Horne-Shimony-Holt (CHSH) and three-party Mermin Bell inequalities for projective measurements of arbitrary rank, and chained Bell inequalities for rank-one projective measurements), (ii) prove the self-testability of quantum correlations that were not known using existing self-testing techniques (e.g., those violating the Abner Shimony Bell inequality for rank-one projective measurements). Additionally, the analysis of the chained Bell inequalities gives us a closed-form expression of the Lovász theta number for a family of well-studied graphs known as the Möbius ladders, which might be of independent interest in the community of discrete mathematics.

quant-ph↗

arXiv2021

Capacity of Quantum Private Information Retrieval with Colluding Servers

Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple files from $\mathsf{n}$ non-communicating servers by downloading quantum systems without revealing which file is retrieved. As variants of QPIR with stronger security requirements, symmetric QPIR is a protocol in which no other files than the target file are leaked to the user, and $\mathsf{t}$-private QPIR is a protocol in which the identity of the target file is kept secret even if at most $\mathsf{t}$ servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the file size to the size of downloaded quantum systems, and we prove that the symmetric $\mathsf{t}$-private QPIR capacity is $\min\{1,2(\mathsf{n}-\mathsf{t})/\mathsf{n}\}$ for any $1\leq \mathsf{t}< \mathsf{n}$. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.

quant-ph↗

arXiv2021

Information Geometry Approach to Parameter Estimation in Hidden Markov Models

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.

math.ST↗

arXiv2021

Capacity of Quantum Private Information Retrieval with Collusion of All But One of Servers

Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple classical files by downloading quantum systems from non-communicating $\mathsf{n}$ servers each of which contains a copy of all files, while the identity of the retrieved file is unknown to each server. Symmetric QPIR (QSPIR) is QPIR in which the user only obtains the queried file but no other information of the other files. In this paper, we consider the $(\mathsf{n} - 1)$-private QSPIR in which the identity of the retrieved file is secret even if any $\mathsf{n} - 1$ servers collude, and derive the QSPIR capacity for this problem which is defined as the maximum ratio of the retrieved file size to the total size of the downloaded quantum systems. For an even number n of servers, we show that the capacity of the $(\mathsf{n}-1)$-private QSPIR is $2/\mathsf{n}$, when we assume that there are prior entanglements among the servers. We construct an $(\mathsf{n} - 1)$-private QSPIR protocol of rate $\lceil\mathsf{n}/2\rceil^{-1}$ and prove that the capacity is upper bounded by $2/\mathsf{n}$ even if any error probability is allowed. The $(\mathsf{n} - 1)$-private QSPIR capacity is strictly greater than the classical counterpart.

quant-ph↗

arXiv2021

Quantum Private Information Retrieval for Quantum Messages

Quantum private information retrieval (QPIR) for quantum messages is the protocol in which a user retrieves one of the multiple quantum states from one or multiple servers without revealing which state is retrieved. We consider QPIR in two different settings: the blind setting, in which the servers contain one copy of the message states, and the visible setting, in which the servers contain the description of the message states. One trivial solution in both settings is downloading all states from the servers and the main goal of this paper is to find more efficient QPIR protocols. First, we prove that the trivial solution is optimal for one-server QPIR in the blind setting. In one-round protocols, the same optimality holds even in the visible setting. On the other hand, when the user and the server share entanglement, we prove that there exists an efficient one-server QPIR protocol in the blind setting. Furthermore, in the visible setting, we prove that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages. We construct three two-server symmetric QPIR protocols for pure states. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.

quant-ph↗

arXiv2021

Capacity of Quantum Private Information Retrieval with Multiple Servers

We study the capacity of quantum private information retrieval (QPIR) with multiple servers. In the QPIR problem with multiple servers, a user retrieves a classical file by downloading quantum systems from multiple servers each of which contains the copy of a classical file set while the identity of the downloaded file is not leaked to each server. The QPIR capacity is defined as the maximum rate of the file size over the whole dimension of the downloaded quantum systems. When the servers are assumed to share prior entanglement, we prove that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files. We construct a rate-one protocol only with two servers. This capacity-achieving protocol outperforms its classical counterpart in the sense of capacity, server secrecy, and upload cost. The strong converse bound is derived concisely without using any secrecy condition. We also prove that the capacity of multi-round QPIR is 1.

quant-ph↗

arXiv2020

Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction

We give the first systematic study on the second order asymptotics of the operational task of coherence distillation with and without assistance. In the unassisted setting, we introduce a variant of randomness extraction framework where free incoherent operations are allowed before the incoherent measurement and the randomness extractors. We then show that the maximum number of random bits extractable from a given quantum state is precisely equal to the maximum number of coherent bits that can be distilled from the same state. This relation enables us to derive tight second order expansions of both tasks in the independent and identically distributed setting. Remarkably, the incoherent operation classes that can empower coherence distillation for generic states all admit the same second order expansions, indicating their operational equivalence for coherence distillation in both asymptotic and large block length regime. We then generalize the above line of research to the assisted setting, arising naturally in bipartite quantum systems where Bob distills coherence from the state at hand, aided by the benevolent Alice possessing the other system. More precisely, we introduce a new assisted incoherent randomness extraction task and establish an exact relation between this task and the assisted coherence distillation. This strengthens the one-shot relation in the unassisted setting and confirms that this cryptographic framework indeed offers a new perspective to the study of quantum coherence distillation. Likewise, this relation yields second order characterizations to the assisted tasks. As by-products, we show the strong converse property of the aforementioned tasks from their second order expansions.

quant-ph↗

arXiv2020

Communication Cost of Quantum Processes

A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired computation. Here we extend this problem to the quantum domain, analyzing the total amount of (classical and quantum) communication needed by a server in order to accurately execute a quantum process chosen by a client from a parametric family of quantum processes. We derive a general lower bound on the communication cost, establishing a relation with the precision limits of quantum metrology: if a $ν$-dimensional family of processes can be estimated with mean squared error $n^{-β}$ by using $n$ parallel queries, then the communication cost for $n$ parallel executions of a process in the family is at least $(βν/2-ε)\log n$ qubits at the leading order in $n$, for every $ε>0$. For a class of quantum processes satisfying the standard quantum limit ($β=1$), we show that the bound can be attained by transmitting an approximate classical description of the desired process. For quantum processes satisfying the Heisenberg limit ($β=2$), our bound shows that the communication cost is at least twice as the cost of communicating standard quantum limited processes with the same number of parameters.

quant-ph↗

arXiv2020

Quantum state estimation with nuisance parameters

In parameter estimation, nuisance parameters refer to parameters that are not of interest but nevertheless affect the precision of estimating other parameters of interest. For instance, the strength of noises in a probe can be regarded as a nuisance parameter. Despite its long history in classical statistics, the nuisance parameter problem in quantum estimation remains largely unexplored. The goal of this article is to provide a systematic review of quantum estimation in the presence of nuisance parameters, and to supply those who work in quantum tomography and quantum metrology with tools to tackle relevant problems. After an introduction to the nuisance parameter and quantum estimation theory, we explicitly formulate the problem of quantum state estimation with nuisance parameters. We extend quantum Cramer-Rao bounds to the nuisance parameter case and provide a parameter orthogonalization tool to separate the nuisance parameters from the parameters of interest. In particular, we put more focus on the case of one-parameter estimation in the presence of nuisance parameters, as it is most frequently encountered in practice.

quant-ph↗

arXiv2020

Secure list decoding

We propose a new concept of secure list decoding. While the conventional list decoding requires that the list contains the transmitted message, secure list decoding requires the following additional security conditions. The first additional security condition is the impossibility of the correct decoding, i.e., the receiver cannot uniquely identify the transmitted message even though the transmitted message is contained in the list. This condition can be trivially satisfied when the transmission rate is larger than the channel capacity. The other additional security condition is the impossibility for the sender to estimate another element of the decoded list except for the transmitted message. This protocol can be used for anonymous auction, which realizes the anonymity for bidding.

cs.IT↗

arXiv2020

Elliptic Solutions for Higher Order KdV Equations

We study higher order KdV equations from the GL(2,$\mathbb{R}$) $\cong$ SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth order. We argue that the main structure of the trigonometric/hyperbolic/elliptic $N$-soliton solutions for higher order KdV equations is the same as that of the original KdV equation. Pointing out that the difference is only the time dependence, we find $N$-soliton solutions of higher order KdV equations can be constructed from those of the original KdV equation by properly replacing the time-dependence. We discuss that there always exist elliptic solutions for all higher order KdV equations.

nlin.SI↗

arXiv2020

Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories

As a modern approach for the foundation of quantum theory, existing studies of General Probabilistic Theories gave various models of states and measurements that are quite different from quantum theory. In this paper, to seek a more realistic situation, we investigate models approximately close to quantum theory. We define larger measurement classes that are smoothly connected with the class of POVMs via a parameter, and investigate the performance of perfect discrimination. As a result, we give a sufficient condition of perfect discrimination, which shows a significant improvement beyond the class of POVMs.

quant-ph↗

arXiv2020

Common Hirota Form Bäcklund Transformation for the Unified Soliton System

We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb R$) $\cong$ Möbius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we construct the $N$-soliton solutions through the KdV type Bäcklund transformation, we can transform different KdV/mKdV/sinh-Gordon equations and the Bäcklund transformations of the standard form into the same common Hirota form and the same common Bäcklund transformation except the equation which has the time-derivative term. The difference is only the time-dependence and the main structure of the $N$-soliton solutions has same common form for KdV/mKdV/sinh-Gordon systems. Then the $N$-soliton solutions for the sinh-Gordon equation is obtained just by the replacement from KdV/mKdV $N$-soliton solutions. We also give general addition formulae coming from the KdV type Bäcklund transformation which plays not only an important role to construct the trigonometric/hyperbolic $N$-soliton solutions but also an essential role to construct the elliptic $N$-soliton solutions. In contrast to the KdV type Bäcklund transformation, the well-known mKdV/sinh-Gordon type Bäcklund transformation gives the non-cyclic symmetric $N$-soliton solutions. We give an explicit non-cyclic symmetric 3-soliton solution for KdV/mKdV/sinh-Gordon equations.

nlin.SI↗

arXiv2020

Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network with Free One-Way Public Communication

It is natural in a quantum network system that multiple users intend to send their quantum message to their respective receivers, which is called a multiple unicast quantum network. We propose a canonical method to derive a secure quantum network code over a multiple unicast quantum network from a secure classical network code. Our code correctly transmits quantum states when there is no attack. It also guarantees the secrecy of the transmitted quantum state even with the existence of an attack when the attack satisfies a certain natural condition. In our security proof, the eavesdropper is allowed to modify wiretapped information dependently on the previously wiretapped messages. Our protocol guarantees the secrecy by utilizing one-way classical information transmission (public communication) in the same direction as the quantum network although the verification of quantum information transmission requires two-way classical communication. Our secure network code can be applied to several networks including the butterfly network.

quant-ph↗

arXiv2020

Asymptotically Secure Network Code for Active Attacks and its Application to Network Quantum Key Distribution

When there exists a malicious attacker in the network, we need to be careful of eavesdropping and contamination. This problem is crucial for network communication when the network is realized by a partially trusted relay of quantum key distribution. We discuss the asymptotic rate in a linear network with the secrecy and robustness conditions when the above type of attacker exists. Also, under the same setting, we discuss the asymptotic rate in a linear network when we impose the secrecy condition alone. Then, we apply these results to the network composed of a partially trusted relay of quantum key distribution, which enables us to realize secure long-distance communication via short-distance quantum key distribution.

cs.IT↗

arXiv2020

Secure network code over one-hop relay network

When there exists a malicious attacker in the network, we need to consider the possibilities of eavesdropping and the contamination simultaneously. Under an acyclic broadcast network, the optimality of linear codes was shown when Eve is allowed to attack any $r$ edges. The optimality of linear codes is not shown under a different assumption for Eve. As a typical example of an acyclic unicast network, we focus on the one-hop relay network under the single transmission scheme by assuming that Eve attacks only one edge in each level. Surprisingly, as a result, we find that a non-linear code significantly improves the performance on the one-hop relay network over linear codes. That is, a non-liner code realizes the imperfect security on this model that cannot be realized by linear codes. This kind of superiority of a linear code still holds even with considering the effect of sequential error injection on information leakage.

cs.IT↗

arXiv2020

Secure Network Code for Adaptive and Active Attacks with No-Randomness in Intermediate Nodes

In secure network coding, there is a possibility that the eavesdropper can improve her performance when she changes (contaminates) the information on the attacked edges (active attack) and chooses the attacked edges adaptively (adaptive attack). We analyze the security for network code over such types of attacks. We show that active and adaptive attacks cannot improve the performance of the eavesdropper when the code is linear. Further, we give a non-linear example, in which an adaptive attack improves the performance of the eavesdropper. We derive the capacity for the unicast case and the capacity region for the multicast case or the multiple multicast case in several examples of relay networks, beyond the minimum cut theorem, when no additional random number is allowed as scramble variables in the intermediate nodes. No prior study compared the difference of the capacity and the capacity region between the existence and the non-existence of randomness in the intermediate nodes under these network models even with non-adaptive and non-active attacks.

cs.IT↗

arXiv2020

Reduction Theorem for Secrecy over Linear Network Code for Active Attacks

We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdropper cannot improve the power of eavesdropping by sequential error injection when the operations in the network are linear operations. We demonstrate the usefulness of this reduction theorem by applying a concrete example of network.

cs.IT↗