New constructions of approximately SIC-POVMs via difference sets☆
- Department of Math, Nanjing University of Aeronautics and Astronautics, Nanjing 211100 (China)
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.
- OSTI ID:
- 22852233
- Journal Information:
- Annals of Physics, Vol. 391; Other Information: © 2018 Elsevier Inc. All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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