



01455nas a2200169   4500008004100000245007100041210006900112260001300181300001100194490000700205520093300212100002201145700001801167700002101185700002301206856005601229       2024                        eng d00aContinuous-Variable Quantum State Designs: Theory and Applications0 aContinuousVariable Quantum State Designs Theory and Applications  c2/8/2024  a0110130 v143 a<p>We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state&nbsp;t-designs from [Blume-Kohout et al., Commun. Math. Phys. 326, 755 (2014)], no state designs exist for&nbsp;t&ge;2. Similarly, we prove that no CV unitary&nbsp;t-designs exist for t&ge;2. We propose an alternative definition for CV state designs, which we call rigged&nbsp;t-designs, and provide explicit constructions for&nbsp;t&nbsp;=&nbsp;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.</p>1 aIosue, Joseph, T.1 aSharma, Kunal1 aGullans, Michael1 aAlbert, Victor, V.  uhttps://link.aps.org/doi/10.1103/PhysRevX.14.011013