论文标题
量子测量的兼容性维度
The compatibility dimension of quantum measurements
论文作者
论文摘要
我们介绍了一组量子测量值的兼容性维度的概念：它是希尔伯特空间的最大维度，在该空间上，给定的测量值兼容。在Schrödinger图片中，该概念对应于使用Carmeli，Heinosaari和Toigo的不兼容见证人，测试与子空间支持的量子状态的兼容性。我们使用受量子误差校正启发的近似量子克隆或代数技术为兼容性维度提供了几个界限。我们详细分析了两个正统碱基，尤其是相互无偏基的情况。
We introduce the notion of compatibility dimension for a set of quantum measurements: it is the largest dimension of a Hilbert space on which the given measurements are compatible. In the Schrödinger picture, this notion corresponds to testing compatibility with ensembles of quantum states supported on a subspace, using the incompatibility witnesses of Carmeli, Heinosaari, and Toigo. We provide several bounds for the compatibility dimension, using approximate quantum cloning or algebraic techniques inspired by quantum error correction. We analyze in detail the case of two orthonormal bases, and, in particular, that of mutually unbiased bases.
