Squash Operator and Symmetry

Details Squash Operator and Symmetry Squash Operator and Symmetry

2009-10-13

arxiv.org/abs/0910.2326v2

Phys. Rev. A 81, 012328 (2010)

Physics

Quantum Physics

4 pages, no figures; minor grammatical corrections

Scientific paper

10.1103/PhysRevA.81.012328

This paper begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol which suits single-mode as well as multi-mode 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.

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