Masahito Hayashi

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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>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(More)
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(More)
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 's bound based on the Re&#x0301;nyi entropy of order 2 because the bound obtained here uses the Re&#x0301;nyi entropy of order 1+<i>s</i> for <i>s</i> &#x2208; [0,1]. This bound is applied to a wire-tap(More)
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(More)
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. These characterizations-in contrast to earlier results-enable us to derive tight second-order(More)
Masahito Hayashi ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 201 Daini Hongo White Bldg. 5-28-3, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. Superrobust Computation Project, Information Science and Technology Strategic Core (21st Century COE by MEXT), Graduate School of Information Science and Technology, The(More)
We derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing. Using an information-spectrum method, we discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error(More)
From an arbitrary given channel code over a discrete or Gaussian memoryless channel, we construct a wiretap code with the strong security. Our construction can achieve the wiretap capacity under mild assumptions. The key tool is the new privacy amplification theorem bounding the eavesdropped information in terms of the Gallager function.
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(More)