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Superselection Rules and Quantum Protocols

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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.