论文标题
相互无偏的等法紧密框架
Mutually Unbiased Equiangular Tight Frames
论文作者
论文摘要
等缘紧密的框架（ETF）在欧几里得空间中产生一种最佳的线条包装。 ETF似乎很少见，并且所有已知的无限家庭都来自某种类型的组合设计。在本文中，我们引入了一种构建ETF的新方法。我们首先表明有时可以在相同的空间中构造多个ETF，这些ETF以类似于互无偏见的量子信息理论概念的方式“相互无偏”。然后，我们表明，将这些相互无偏的ETF的某些张量产物与其他ETF有时产生新的复杂ETF的无限家族。
An equiangular tight frame (ETF) yields a type of optimal packing of lines in a Euclidean space. ETFs seem to be rare, and all known infinite families of them arise from some type of combinatorial design. In this paper, we introduce a new method for constructing ETFs. We begin by showing that it is sometimes possible to construct multiple ETFs for the same space that are "mutually unbiased" in a way that is analogous to the quantum-information-theoretic concept of mutually unbiased bases. We then show that taking certain tensor products of these mutually unbiased ETFs with other ETFs sometimes yields infinite families of new complex ETFs.
