论文标题
连续变量量子状态设计：理论和应用
Continuous-variable quantum state designs: theory and applications
论文作者
论文摘要
我们将量子态设计的概念推广到无限维空间。我们首先证明，根据连续变量（CV）状态$ t $ designs的定义。数学。物理。 326，755（2014），$ t \ geq2 $不存在州设计。同样，我们证明，对于$ t \ geq 2 $，不存在简历统一$ t $ designs。我们为简历状态设计提出了一个替代定义，我们称之为索具的$ t $ - 设计，并为$ t = 2 $提供明确的构造。作为操纵设计的应用，我们为简历状态开发了基于设计的阴影摄影协议。使用索具设计的能源约束版本，我们定义了CV量子通道的平均保真度，并将这种保真度与CV纠缠忠诚度相关联。作为独立利息的另一个结果，我们在torus $ 2 $ designs和完整的相互无偏见的基础之间建立了联系。
We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state $t$-designs from Comm. Math. Phys. 326, 755 (2014), no state designs exist for $t\geq2$. Similarly, we prove that no CV unitary $t$-designs exist for $t\geq 2$. We propose an alternative definition for CV state designs, which we call rigged $t$-designs, and provide explicit constructions for $t=2$. As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus $2$-designs and complete sets of mutually unbiased bases.
