Superselection Rules and Quantum Protocols

          @misc{ pirsa_PIRSA:03080007,
            doi = {10.48660/03080007},
            url = {https://pirsa.org/03080007},
            author = {Mayers, Dominic},
            keywords = {Quantum Information},
            language = {en},
            title = {Superselection Rules and Quantum Protocols},
            publisher = {Perimeter Institute},
            year = {2003},
            month = {aug},
            note = {PIRSA:03080007 see, \url{https://pirsa.org}}
          }
          

Abstract

Superselection rules are limitations on the physically realizable quantum operations that can be carried out by a local agent. For example, it is impossible to cre­ate or destroy an isolated particle that carries locally conserved charges, such as an electrically charged particle, a fermion, or (in a two­ dimensional medium) an anyon. Recently, Popescu has suggested that su­perselection rules might have interesting implications for the security of quantum cryptographic protocols. The intuitive idea behind this suggestion is that superselec­tion rules could place inescapable limits on the cheat­ing strategies available to the dishonest parties, thus en­hancing security. Might, say, unconditionally secure bit commitment be possible in worlds (perhaps including the physical world that we inhabit) governed by suitable su­perselection rules? An affirmative answer could shake the foundations of cryptography. The purpose of this paper is to answer Popescu's in­triguing question. Sadly, our conclusion is that superse­lection rules can never foil a cheater who has unlimited quantum­ computational power.