2009/10/19 by Toyohiro Tsurumaru
Computer Science · Mathematics · Physics and Astronomy · #Biology #Genetics #Geometry #Horticulture #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #Squash #Symmetry (geometry) #Theoretical physics #quant-ph
paper · pdf · doi:10.1103/physreva.81.012328
published as Phys. Rev. A 81, 012328 (2010) · 4 pages, no figures; minor grammatical corrections
arxiv created 2009/10/19 · openalex publication_date 2010/01/27 · arxiv updated 2010/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of ``rank two'' can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.