TY - JOUR
AU - D. Markham
AU - Jaroslaw Miszczak
AU - Zbigniew Puchała
AU - Karol Życzkowski
AB - We 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.
BT - Phys. Rev. A
LA - eng
M1 - 4
N1 - arXiv:0711.4286 IF=2.908(2008);
N2 - We 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.
PY - 2008
EP - 042111
T2 - Phys. Rev. A
TI - Quantum state discrimination: A geometric approach
VL - 77
SN - 1094-1622
ER -