Approximate solutions of two-way diffusion equations

Abstract

In this paper, a general and systematic scheme is formulated for finding approximate solutions of two-way diffusion equations. This expansion scheme is valid for arbitrary mean-free path and can be carried out to any desired accuracy. Its potential is demonstrated by constructing approximate solutions for two problems concerning the kinetics of an electron beam, and the accuracy is found to be very good even when only a few terms are included in the expansion. The approximate solutions found are compared with numerical calculations and previous analytical work in the literature.

Optimal sequential measurements for bipartite state discrimination

“…where a depends on the geometry of the set and the prior probabilities [38]: for our case we find a = 1 5 √ 3 . The optimal measurements for j = 1, 2 are obtained by symmetry (10) 1.…”

“…For each j, the states with these probabilities have socalled mirror symmetry -the set is invariant under reflection about |ψ j . For such a set, the minimum error problem was considered by Andersson et al [38]: using their results we find for j = 0 the optimal measurement is of the form:…”

Minimum-error discrimination between two sets of similarity-transformed quantum states

“…, i m of ρ 1 with the same eigenvalue a max . Then, p opt is again given by (19) and by Eq. (16), these eigenvectors must correspond to the eigenvalue zero of τ 1 .…”

“…By the same argument, we can get for the second set relations similar to Eqs. (19), (20) and (21). If this equality do not hold, all elements of one of sets…”

Optimal minimum-cost quantum measurements for imperfect detection

“…The optimal measurements for such mirror-symmetric situations are known [22,23]. For small q, the optimal measurement strategy has three measurement operators.…”