Masahito Hayashi

In this paper, second-order coding rate of channel coding is discussed for general sequence of channels. The optimum second-order transmission rate with a constant error constraint <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">epsiv</i> is obtained by using the information spectrum method. We apply this result to the discrete memoryless case, the discrete memoryless case with a cost constraint, the additive Markovian case, and the Gaussian channel c

The capacity of a classical-quantum channel (or, in other words, the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. A capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of Verdu-Han (1994) which are based on the so-called information-spectrum method. The general results

Several nonasymptotic formulas are established in channel resolvability and identification capacity, and they are applied to the wiretap channel. By using these formulas, the epsi capacities of the above three problems are considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. As a result, we solve an open problem proposed by Han and Verduacute. Moreover, we obtain lower bounds of the exponents of error probabilit

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 s

An upper bound on simple quantum hypothesis testing in the asymmetric setting is shown using a useful inequality by Audenaert et al. [Phys. Rev. Lett. 98, 160501 (2007)] which was originally invented for symmetric setting. Using this upper bound, we obtain the Hoeffding bound, which is identical with the classical counterpart if the hypotheses, composed of two density operators, are mutually commutative. Its attainability has been a long-standing open problem. Further, using this bound, we obtai

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement.

There is a difference between the optimal rates of fixed-length source coding and intrinsic randomness when we care about the second-order asymptotics. We prove this difference for general information sources and then investigate independent and identically distributed (i.i.d.) random variables and Markovian variables as examples. The difference is demonstrated through an investigation of the second-order asymptotic behavior of the rates. A universal fixed-length source code attaining the second

Hypothesis Testing Quantum Cramer-Rao Bound in Mixed States Model Quantum Cramer-Rao Bound in Pure States Model Group Symmetric Approach to Pure States Model Large Deviation Theory in Quantum Estimation Futher Topics on Quantum Statistical Inference.

We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits (cbits) transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed. The presented result concerns only th

Security formulas of quantum key distribution (QKD) with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector. We compare the asymptotic key generation rate in the presence of dark counts to that without the presence of dark counts.

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator’s deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normali

We derive an asymptotic bound for the error of state estimation when we are allowed to use the quantum correlation in the measuring apparatus. It is also proven that this bound can be achieved in any statistical model in the qubit system. Moreover, we show that this bound cannot be attained by any quantum measurement with no quantum correlation in the measuring apparatus except for several specific statistical models. That is, in such a statistical model, the quantum correlation can improve the

A variety of new measures of quantum Rényi mutual information and quantum Rényi conditional entropy have recently been proposed, and some of their mathematical properties explored. Here, we show that the Rényi mutual information attains operational meaning in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state and the alternative hypothesis consists of all product states that share one marginal with the null hypothesis. This hypothesis testing problem