Masaru Kada

The efficiency of quantum identity testing of multiple states

We examine two quantum operations, the permutation test and the circle test, which test the identity of n quantum states. These operations naturally extend the well-studied swap test on two quantum states. We first show the optimality of the permutation test for any input size n as well as the optimality of the circle test for three input states. In particular, when n = 3, we present a semi-classical protocol, incorporated with the swap test, which approximates the circle test efficiently. Furthermore, we show that, with the help of classical preprocessing, a single use of the circle test can approximate the permutation test efficiently for an arbitrary input size n.

Cardinal invariants about shrinkability of unbounded sets

Abstract In our previous paper (Eda et al., to appear), we introduced a cardinal invariant b * and studied some properties of the cardinal b * . In the present paper we define new cardinal invariants which are related to Cichofis diagram and generalize the notion of b * . We investigate the relations between them and other cardinals which appear in Cichons diagram.

The Baire category theorem and the evasion number

In this paper we prove that e < cov(M) where e is the evasion number defined by Blass. This answers negatively a question asked by Brendle and Shelah.

Hechler's theorem for the null ideal

Abstract.We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing. The corresponding theorem for the meager ideal was established by Bartoszyński and Kada.

More on Cichoń's diagram and infinite games

Some cardinal invariants from Cichoiis diagram can be characterized using the notion of cut-and-choose games on cardinals. In this paper we give another way to characterize those cardinals in terms of infinite games. We also show that some properties for forcing, such as the Sacks Property. the Laver Property and cow-boundingness, are characterized by cut-and-choose games on complete Boolean

Block branching Miller forcing and covering numbers for prediction

We call a function from ω<ω to ω a predictor. A predictor π predicts f∈ωω constantly if there is n<ω such that for all i<ω there is j∈[i,i+n) with f(j)=π(f↾j). θω is the smallest size of a set P of predictors such that every f∈ωω is constantly predicted by some predictor in P. θubd is the smallest cardinal κ satisfying the following: For every b∈ωω there is a set P of predictors of size κ such that every f∈∏n<ωb(n) is constantly predicted by some predictor in P. We prove that θubd is consistently smaller than θω.