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Masahito Hayashi

Publications and source records attributed to Masahito Hayashi.

At least 235 records · Page 13Linked to original sources
arXiv2013

Large deviation analysis for quantum security via smoothing of Renyi entropy of order 2

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal$_2$ hash functions. Using the smoothing of Renyi entropy of order 2, we derive security bounds for $L_1$ distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decreasing rates. These results are extended to the case when we apply $\varepsilon$-almost dual universal$_2$ hash functions. Further, we apply this analysis to the secret key generation with error correction.

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arXiv2013

Quantum wiretap channel with non-uniform random number and its exponent and equivocation rate of leaked information

A usual code for quantum wiretap channel requires an auxiliary random variable subject to the perfect uniform distribution. However, it is difficult to prepare such an auxiliary random variable. We propose a code that requires only an auxiliary random variable subject to a non-uniform distribution instead of the perfect uniform distribution. Further, we evaluate the exponential decreasing rate of leaked information and derive its equivocation rate. For practical constructions, we also discuss the security when our code consists of a linear error correcting code.

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arXiv2013

Trade-off between Performance and Reversibility of Entanglement Concentration for Pure Entangled State

In quantum information theory, it is widely believed that entanglement concentration for bipartite pure states is asymptotically reversible. In order to examine this, we give a precise formulation of the problem, and show a trade-off relation between performance and reversibility, which implies the irreversibility of entanglement concentration. Then, we regard entanglement concentration as entangled state compression in an entanglement storage with lower dimension. Because of the irreversibility of entanglement concentration, an initial state can not be completely recovered after the compression process and a loss inevitably arises in the process. We numerically calculate this loss and also derive for it a highly accurate analytical approximation.

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arXiv2013

Tight exponential analysis of universally composable privacy amplification and its applications

Motivated by the desirability of universal composability, we analyze in terms of L_1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s in [0,1, we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wire-tap channel model and to secret key generation (distillation) by public discussion.

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arXiv2013

Second Order Asymptotics for Random Number Generation

We treat a random number generation from an i.i.d. probability distribution of $P$ to that of $Q$. When $Q$ or $P$ is a uniform distribution, the problems have been well-known as the uniform random number generation and the resolvability problem respectively, and analyzed not only in the context of the first order asymptotic theory but also that in the second asymptotic theory. On the other hand, when both $P$ and $Q$ are not a uniform distribution, the second order asymptotics has not been treated. In this paper, we focus on the second order asymptotics of a random number generation for arbitrary probability distributions $P$ and $Q$ on a finite set. In particular, we derive the optimal second order generation rate under an arbitrary permissible confidence coefficient.

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arXiv2012

Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy

This paper investigates the privacy amplification problem, and compares the existing two bounds: the exponential bound derived by one of the authors and the min-entropy bound derived by Renner. It turns out that the exponential bound is better than the min-entropy bound when a security parameter is rather small for a block length, and that the min-entropy bound is better than the exponential bound when a security parameter is rather large for a block length. Furthermore, we present another bound that interpolates the exponential bound and the min-entropy bound by a hybrid use of the Renyi entropy and the inf-spectral entropy.

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arXiv2012

Dual universality of hash functions and its applications to quantum cryptography

In this paper, we introduce the concept of dual universality of hash functions and present its applications to quantum cryptography. We begin by establishing the one-to-one correspondence between a linear function family {\cal F} and a code family {\cal C}, and thereby defining \varepsilon-almost dual universal_2 hash functions, as a generalization of the conventional universal_2 hash functions. Then we show that this generalized (and thus broader) class of hash functions is in fact sufficient for the security of quantum cryptography. This result can be explained in two different formalisms. First, by noting its relation to the δ-biased family introduced by Dodis and Smith, we demonstrate that Renner's two-universal hashing lemma is generalized to our class of hash functions. Next, we prove that the proof technique by Shor and Preskill can be applied to quantum key distribution (QKD) systems that use our generalized class of hash functions for privacy amplification. While Shor-Preskill formalism requires an implementer of a QKD system to explicitly construct a linear code of the Calderbank-Shor-Steane type, this result removes the existing difficulty of the construction a linear code of CSS code by replacing it by the combination of an ordinary classical error correcting code and our proposed hash function. We also show that a similar result applies to the quantum wire-tap channel. Finally we compare our results in the two formalisms and show that, in typical QKD scenarios, the Shor-Preskill--type argument gives better security bounds in terms of the trace distance and Holevo information, than the method based on the δ-biased family.

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arXiv2012

Precise evaluation of leaked information with universal2 privacy amplification in the presence of quantum attacker

We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner's, which are based on quantum conditional Rényi entropy of order 1+s. Using those theorems, we derive an exponential decreasing rate for leaked information and the asymptotic equivocation rate, which have not been derived hitherto in the quantum setting.

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arXiv2012

Non-distillable entanglement guarantees distillable entanglement

The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are entangled and non-distillable, then either of them is distillable with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is a novel and effective way to this long-standing problem compared to the means by stochastic local operations and classical communications. Furthermore we systematically indicate the structure of the classified states and generate them. We also extend our results to multipartite states.

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arXiv2012

Irreversibility of Entanglement Concentration for Pure State

For a pure state $ψ$ on a composite system $\mathcal{H}_A\otimes\mathcal{H}_B$, both the entanglement cost $E_C(ψ)$ and the distillable entanglement $E_D(ψ)$ coincide with the von Neumann entropy $H(\mathrm{Tr}_{B}ψ)$. Therefore, the entanglement concentration from the multiple state $ψ^{\otimes n}$ of a pure state $ψ$ to the multiple state $Φ^{\otimes L_n}$ of the EPR state $Φ$ seems to be able to be reversibly performed with an asymptotically infinitesimal error when the rate ${L_n}/{n}$ goes to $H(\mathrm{Tr}_{B}ψ)$. In this paper, we show that it is impossible to reversibly perform the entanglement concentration for a multiple pure state even in asymptotic situation. In addition, in the case when we recover the multiple state $ψ^{\otimes M_n}$ after the concentration for $ψ^{\otimes n}$, we evaluate the asymptotic behavior of the loss number $n-M_n$ of $ψ$. This evaluation is thought to be closely related to the entanglement compression in distant parties.

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arXiv2012

Concise and Tight Security Analysis of the Bennett-Brassard 1984 Protocol with Finite Key Lengths

We present a tight security analysis of the Bennett-Brassard 1984 protocol taking into account the finite size effect of key distillation, and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal approximation of the hypergeometric function. Then next we show that a similarly tight bound can also be obtained by a rigorous argument without relying on any approximation. In particular, for the convenience of experimentalists who wish to evaluate the security of their QKD systems, we also give explicit procedures of our key distillation, and also show how to calculate the secret key rate and the security parameter from a given set of experimental parameters. Besides the exact values of key rates and security parameters, we also present how to obtain their rough estimates using the normal approximation.

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arXiv2011

Quantum hypothesis testing for quantum Gaussian states: Quantum analogues of chi-square, t and F tests

We treat quantum counterparts of testing problems whose optimal tests are given by chi-square, t and F tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning quantum Gaussian states families, and contain disturbance parameters, which have group symmetry. Quantum Hunt-Stein Theorem removes a part of these disturbance parameters, but other types of difficulty still remain. In order to remove them, combining quantum Hunt-Stein theorem and other reduction methods, we establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem. Using these methods, we derive quantum counterparts of chi-square, t and F tests as optimal tests in the respective settings.

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arXiv2011

Exponential decreasing rate of leaked information in universal random privacy amplification

We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett et al(1995)'s bound based on the Rényi entropy of order 2 because the bound obtained here uses the Rényi entropy of order $1+s$ for $s \in [0,1]$. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi(2006)'s exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion.

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arXiv2011

Secure Multiplex Network Coding

In the secure network coding for multicasting, there is loss of information rate due to inclusion of random bits at the source node. We show a method to eliminate that loss of information rate by using multiple statistically independent messages to be kept secret from an eavesdropper. The proposed scheme is an adaptation of Yamamoto et al.'s secure multiplex coding to the secure network coding.

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arXiv2011

Strong security and separated code constructions for the broadcast channels with confidential messages

We show that the capacity region of the broadcast channel with confidential messages does not change when the strong security criterion is adopted instead of the weak security criterion traditionally used. We also show a construction method of coding for the broadcast channel with confidential messages by using an arbitrary given coding for the broadcast channel with degraded message sets.

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arXiv2011

Secure Multiplex Coding with a Common Message

We determine the capacity region of the secure multiplex coding with a common message, and evaluate the mutual information and the equivocation rate of a collection of secret messages to the second receiver (eavesdropper), which were not evaluated by Yamamoto et al.

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arXiv2011

Weaker entanglement guarantees stronger entanglement

The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are weakly entangled, then either of them is generally strongly entangled with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is a novel and effective way to this long-standing problem compared to the means by stochastic local operations and classical communications. We also systematically indicate the structure of the classified states and generate them.

quant-ph↗