Classical Protocols and Quantum Privacy Ampli cation Sample Clauses

Classical Protocols and Quantum Privacy Ampli cation jXj jYj X Y It is a natural question whether the analogy between entanglement and intrinsic information (see Section 3.1) carries over to the protocol level. The examples given in Section 3.5 support this belief. A quite interesting and surprising conse- quence would be that there exists a classical counterpart to bound entanglement, namely intrinsic information that cannot be distilled into a secret key by any classical protocol, if + > 5, where and are the ranges of X and Y , respectively. In other words, the conjecture in [22] that such information can always be distilled would be proved for jXj + jYj 5, but disproved otherwise. Conjecture 1 Let 2 HA HB HE and AB = TrHE (P ). Assume that for all generating sets fjzig of HE there are bases fjxig and fjyig of HA and HB , respectively, such that S(X; Y jjZ) > 0 holds for the distribution PXY Z(x; y; z) := jhx; y; zj ij . Then quantum privacy ampli cation is possible with the state AB, i.e., AB is free entangled. Conjecture 2 Let 2 HA HB HE and AB = TrHE (P ). Assume that there exists a generating set fjzig of HE such that for all bases fjxig and fjyig of HA and HB , respectively, S(X; Y jjZ) = 0 holds for the distribution PXY Z(x; y; z) := jhx; y; zj ij . Then quantum privacy ampli cation is impossible with the state AB, i.e., AB is bound entangled or separable.
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