Recently, position-based quantum cryptography has been claimed to beunconditionally secure. In contrary, here we show that the existing proposalsfor position-based quantum cryptography are, in fact, insecure if entanglementis shared among two adversaries. Specifically, we demonstrate how theadversaries can incorporate ideas of quantum teleportation and quantum secretsharing to compromise the security with certainty. The common flaw to allcurrent protocols is that the Pauli operators always map a codeword to acodeword (up to an irrelevant overall phase). We propose a modified schemelacking this property in which the same cheating strategy used to undermine theprevious protocols can succeed with a rate at most 85%. We conjecture that themodified protocol is unconditionally secure and prove this to be true when theshared quantum resource between the adversaries is a two- or three- levelsystem.
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