Bill Fefferman, Soumik Ghosh, et al.
PRX Quantum
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 [Blume-Kohout et al., Commun. Math. Phys. 326, 755 (2014)CMPHAY0010-361610.1007/s00220-014-1894-3], no state designs exist for t≥2. Similarly, we prove that no CV unitary t-designs exist for t≥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.
Bill Fefferman, Soumik Ghosh, et al.
PRX Quantum
Soorya Rethinasamy, Rochisha Agarwal, et al.
Physical Review A
Yuri Alexeev, Maximilian Amsler, et al.
Future Generation Computer Systems
Junyu Liu, Khadijeh Najafi, et al.
Physical Review Letters