Continuous-Variable Quantum State Designs: Theory and Applications

Journal Article · 08 February 2024 · Physical Review. X

DOI: https://doi.org/10.1103/PhysRevX.14.011013 · OSTI ID:2293601

Iosue, Joseph T. ; Sharma, Kunal ; Gullans, Michael J. ; Albert, Victor V.

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 , ], no state designs exist for $t\ge 2$ . Similarly, we prove that no CV unitary $t$ -designs exist for $t\ge 2$ . 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. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• OSTI ID: 2293601
• Journal Information: Physical Review. X, Journal Name: Physical Review. X Vol. 14 Journal Issue: 1; ISSN 2160-3308
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English