arXiv subjects

Masahito Hayashi

Publications and source records attributed to Masahito Hayashi.

At least 217 records · Page 12Linked to original sources

arXiv2016

Secure Multiplex Coding with Dependent and Non-Uniform Multiple Messages

The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wire-tap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the random bits by other meaningful secret messages, and a collection of secret messages serves as the random bits to hide the rest of messages. In the previous researches, multiple secret messages were assumed to have independent and uniform distributions, which is difficult to be ensured in practice. We remove this restrictive assumption by a generalization of the channel resolvability technique. We also give practical construction techniques for SMC by using an arbitrary given error-correcting code as an ingredient, and channel-universal coding of SMC. By using the same principle as the channel-universal SMC, we give coding for the broadcast channel with confidential messages universal to both channel and source distributions.

cs.IT↗

arXiv2015

Verifiable measurement-only blind quantum computing with stabilizer testing

We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and therefore Alice can obtain the correct computation result. Regarding the security, whatever Bob does, Bob cannot learn any information about Alice's computation because of the no-signaling principle. Furthermore, evil Bob does not necessarily send the copies of the correct graph state, but Alice can check the correctness of Bob's state by directly verifying stabilizers of some copies.

quant-ph↗

arXiv2015

Asymmetric Evaluations of Erasure and Undetected Error Probabilities

The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method, a sequence of codes of increasing blocklengths $n$ is designed to illustrate this tradeoff. Furthermore, for additive discrete memoryless channels with uniform input distribution, we establish that our analysis is tight with respect to the ensemble average. This is done by analysing the ensemble performance in terms of a tradeoff between the code rate, the undetected and the total errors. This tradeoff is parametrized by the threshold in a generalized likelihood ratio test. Two asymptotic regimes are studied. First, the code rate tends to the capacity of the channel at a rate slower than $n^{-1/2}$ corresponding to the moderate deviations regime. In this case, both error probabilities decay subexponentially and asymmetrically. The precise decay rates are characterized. Second, the code rate tends to capacity at a rate of $n^{-1/2}$. In this case, the total error probability is asymptotically a positive constant while the undetected error probability decays as $\exp(- b n^{ 1/2})$ for some $b>0$. The proof techniques involve applications of a modified (or "shifted") version of the Gärtner-Ellis theorem and the type class enumerator method to characterize the asymptotic behavior of a sequence of cumulant generating functions.

cs.IT↗

arXiv2015

Universal steering inequalities

We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint measurement problem. Based on the data-processing inequality for an extended Rényi relative entropy, we then introduce a family of universal steering inequalities, which detect steering much more efficiently than those inequalities known before. As illustrations, we show unbounded violation of a steering inequality for assemblages constructed from mutually unbiased bases and establish an interesting connection between maximally steerable assemblages and complete sets of mutually unbiased bases. We also provide a single steering inequality that can detect all bipartite pure states of full Schmidt rank. In the course of study, we generalize a number of results intimately connected to data-processing inequalities, which are of independent interest.

quant-ph↗

arXiv2015

Asymptotic Compatibility between LOCC Conversion and Recovery

Recently, entanglement concentration was explicitly shown to be irreversible. However, it is still not clear what kind of states can be reversibly converted in the asymptotic setting by LOCC when neither the initial nor the target state is maximally entangled. We derive the necessary and sufficient condition for the reversibility of LOCC conversions between two bipartite pure entangled states in the asymptotic setting. In addition, we show that conversion can be achieved perfectly with only local unitary operation under such condition except for special cases. Interestingly, our result implies that an error-free reversible conversion is asymptotically possible even between states whose copies can never be locally unitarily equivalent with any finite numbers of copies, although such a conversion is impossible in the finite setting. In fact, we show such an example. Moreover, we establish how to overcome the irreversibility of LOCC conversion in two ways. As for the first method, we evaluate how many copies of the initial state is to be lost to overcome the irreversibility of LOCC conversion. The second method is to add a supplementary state appropriately, which also works for LU conversion unlike the first method. Especially, for the qubit system, any non-maximally pure entangled state can be a universal resource for the asymptotic reversibility when copies of the state is sufficiently many. More interestingly, our analysis implies that far-from-maximally entangled states can be better than nearly maximally entangled states as this type of resource. This fact brings new insight to the resource theory of state conversion.

quant-ph↗

arXiv2015

More Efficient Privacy Amplification with Less Random Seeds via Dual Universal Hash Function

We explicitly construct random hash functions for privacy amplification (extractors) that require smaller random seed lengths than the previous literature, and still allow efficient implementations with complexity $O(n\log n)$ for input length $n$. The key idea is the concept of dual universal$_2$ hash function introduced recently. We also use a new method for constructing extractors by concatenating $δ$-almost dual universal$_2$ hash functions with other extractors. Besides minimizing seed lengths, we also introduce methods that allow one to use non-uniform random seeds for extractors. These methods can be applied to a wide class of extractors, including dual universal$_2$ hash function, as well as to conventional universal$_2$ hash functions.

quant-ph↗

arXiv2015

Quantum Merlin-Arthur with Clifford Arthur

We show that the class QMA does not change even if we restrict Arthur's computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called magic states, plus any Clifford gate operations are universal for quantum computing. If Merlin is honest, he sends the witness plus magic states to Arthur. If Merlin is malicious, he might send other states to Arthur, but Arthur can verify the correctness of magic states by himself. We also generalize the result to QIP[3]: we show that the class QIP[3] does not change even if the computational power of the verifier is restricted to only Clifford gate operations (plus classical XOR gate).

quant-ph↗

arXiv2015

Information Geometry Approach to Parameter Estimation in Markov Chains

We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.

math.ST↗

arXiv2015

Finite-length Analysis on Tail probability for Markov Chain and Application to Simple Hypothesis Testing

Using terminologies of information geometry, we derive upper and lower bounds of the tail probability of the sample mean. Employing these bounds, we obtain upper and lower bounds of the minimum error probability of the 2nd kind of error under the exponential constraint for the error probability of the 1st kind of error in a simple hypothesis testing for a finite-length Markov chain, which yields the Hoeffding type bound. For these derivations, we derive upper and lower bounds of cumulant generating function for Markov chain. As a byproduct, we obtain another simple proof of central limit theorem for Markov chain.

math.ST↗

arXiv2014

Security analysis of epsilon-almost dual universal2 hash functions: smoothing of min entropy vs. smoothing of Rényi entropy of order 2

Recently, $\varepsilon$-almost dual universal$_2$ hash functions has been proposed as a new and wider class of hash functions. Using this class of hash functions, several efficient hash functions were proposed. This paper evaluates the security performance when we apply this kind of hash functions. We evaluate the security in several kinds of setting based on the $L_1$ distinguishability criterion and the modified mutual information criterion. The obtained evaluation is based on smoothing of Rényi entropy of order 2 and/or min entropy. We clarify the difference between these two methods.

cs.IT↗

arXiv2014

Strong Converse for a Degraded Wiretap Channel via Active Hypothesis Testing

We establish an upper bound on the rate of codes for a wiretap channel with public feedback for a fixed probability of error and secrecy parameter. As a corollary, we obtain a strong converse for the capacity of a degraded wiretap channel with public feedback. Our converse proof is based on a reduction of active hypothesis testing for discriminating between two channels to coding for wiretap channel with feedback.

cs.IT↗

arXiv2014

Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state

In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state and the completely mixed state by one-way LOCC, two-way LOCC, and separable POVMs. As a result, we derive single-letterized formulas for the Stein's lemma type of optimal error exponents under one-way LOCC, two-way LOCC and separable POVMs, the Chernoff bounds under one-way LOCC POVMs and separable POVMs, and the Hoeffding bounds under one-way LOCC POVMs in the whole region of a parameter and under separable POVMs on a restricted region of a parameter. We also numerically calculate the Chernoff and the Hoeffding bounds under a class of three-step LOCC protocols in low-dimensional systems and show that these bounds not only outperform the bounds for one-way LOCC POVMs but also almost approximates the bounds for separable POVMs in the parameter region where analytical bounds for separable POVMs are derived.

quant-ph↗

arXiv2014

Fourier Analytic Approach to Quantum Estimation of Group Action

This article proposes a unified method to estimation of group action by using the inverse Fourier transform of the input state. The method provides optimal estimation for commutative and non-commutative group with/without energy constraint. The proposed method can be applied to projective representations of non-compact groups as well as of compact groups. This paper addresses the optimal estimation of R, U(1), SU(2), SO(3), and R^2 with Heisenberg representation under a suitable energy constraint.

quant-ph↗

arXiv2014

Relating different quantum generalizations of the conditional Renyi entropy

Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and conditional Renyi entropies based on the quantum relative Renyi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Renyi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Renyi entropies and derive a new entropic uncertainty relation.

quant-ph↗

arXiv2014

Strong Converse and Second-Order Asymptotics of Channel Resolvability

We study the problem of channel resolvability for fixed i.i.d. input distributions and discrete memoryless channels (DMCs), and derive the strong converse theorem for any DMCs that are not necessarily full rank. We also derive the optimal second-order rate under a condition. Furthermore, under the condition that a DMC has the unique capacity achieving input distribution, we derive the optimal second-order rate of channel resolvability for the worst input distribution.

cs.IT↗

arXiv2013

Optimal decoy intensity for decoy quantum key distribution

In the decoy quantum key distribution, we show that a smaller decoy intensity gives a better key generation rate in the asymptotic setting when we employ only one decoy intensity and the vacuum pulse. In particular, the counting rate of single photon can be perfectly estimated when the decoy intensity is infinitesimal. The same property holds even when the intensities cannot be perfectly identified. Further, we propose a protocol to improve the key generation rate over the existing protocol under the same decoy intensity.

quant-ph↗

arXiv2013

Security analysis of the decoy method with the Bennett-Brassard 1984 protocol for finite key lengths

This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett-Brassard 1984 protocol for finite key lengths when we employ the decoy method. Using the formula, we can guarantee the security parameter for realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.

quant-ph↗

arXiv2013

A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks

We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using so-called one-shot entropies. We show that these characterizations - in contrast to earlier results - enable us to derive tight second order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The one-shot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree up to logarithmic terms with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our techniques also naturally yields bounds on operational quantities for finite block lengths.

quant-ph↗