Year: 2010
Type: article
Abstract: 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 ${C}_{4}$, 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.
Source: Physical Review A
Author: Toyohiro Tsurumaru
Institution: Mitsubishi Electric (Japan)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2119715958