Second-Order Intrinsic Randomness for Correlated Non-Mixed and Mixed Sources

Tomohiko Uyematsu, Tetsunao Matsuta

友彦 植松, 哲直 松田

Tomohiko Uyematsu, Tetsunao Matsuta

We consider the intrinsic randomness problem for correlated sources. Specifically, there are three correlated sources, and we want to extract two mutually independent random numbers by using two separate mappings, where each mapping converts one of the output sequences from two correlated sources into a random number. In addition, we assume that the obtained pair of random numbers is also independent of the output sequence from the third source. We first show the δ-achievable rate region where a rate pair of two mappings must satisfy in order to obtain the approximation error within δ ∈ [0,1), and the second-order achievable rate region for correlated general sources. Then, we apply our results to non-mixed and mixed independently and identically distributed (i.i.d.) correlated sources, and reveal that the second-order achievable rate region for these sources can be represented in terms of the sum of normal distributions.

Naofumi Abe, Yasuyoshi Mitsumori, Mark Sadgrove +1 more

Single-photon sources are essential tools for quantum information technology and testing the foundations of quantum theory. To date, single-photon sources which emit purely polarized single photons (e.g. horizontal polarization and vertical polarization) have been realized in various ways. On the other hand, single-photon sources which emit completely unpolarized single photons are also important for applications such as realizing hardware random number generators and testing the foundations of quantum theory such as the error-disturbance relation for mixed states [1, 2] which are quantum states of unpolarized polarization states. Here, we present a dynamically and statically unpolarized single-photon source using a single nitrogen-vacancy (NV) center in diamond. In particular, we demonstrate a new method for evaluation of dynamical unpolarization using the second order correlation function [3].

Ryo Nomura, Te Sun Han

The second-order achievable rates in typical random number generation problems are considered. In these problems, several researchers have derived the first-order and the second-order achievability rates for general sources using the information spectrum methods. Although these formulas are general, their computation are quite hard. Hence, an attempt to address explicit computation problems of achievable rates is meaningful. In this paper, we consider mixed sources of two i.i.d. sources and compute the second-order achievable rates explicitly.

Viktor Galliard