01188nas a2200157   4500000000100000008004100001100001500042700002200057700002200079700002200101245005500123300001100178490000700189520082000196022001401016       2008                            d1 aD. Markham1 aJaroslaw Miszczak1 aZbigniew Puchała1 aKarol Życzkowski00aQuantum state discrimination: A geometric approach  a0421110 v773 aWe analyze the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view, this problem is equivalent to that of embedding a simplex of points whose distances are maximal with respect to the Bures distance (or trace distance). We derive upper and lower bounds for the trace distance and for the fidelity between two quantum states, which imply bounds for the Bures distance between the unitary orbits of both states. We thus show that, when analyzing minimal and maximal distances between states of fixed spectra, it is sufficient to consider diagonal states only. Hence when optimal discrimination is considered, given freedom up to unitary orbits, it is sufficient to consider diagonal states. This is illustrated geometrically in terms of Weyl chambers.  a1094-1622