Affiliation of Author(s):理学院

Journal:ANNALS OF PHYSICS

Key Words:SIC-POVM Quantum information theory Difference set Partial geometric difference set

Abstract:In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are related to quantum state tomography (Caves et al., 2004), quantum cryptography (Fuchs and Sasaki, 2003) [1], and foundational studies (Fuchs, 2002) [2]. However, constructing SIC-POVMs is notoriously hard. Although some SIC-POVMs have been constructed numerically, there does not exist an infinite class of them. In this paper, we propose two constructions of approximately SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. We employ difference sets to present the first construction and the dimension of the approximately SIC-POVMs is q + 1, where q is a prime power. Notably, the dimension of this framework is new. The second construction is based on partial geometric difference sets and works whenever the dimension of the framework is a prime power. (C) 2018 Elsevier Inc. All rights reserved.

ISSN No.:0003-4916

Translation or Not:no

Date of Publication:2018-04-01

Co-author:Luo, Gaojun

Correspondence Author:cxw