Abstract :
A geometric characterization is given for invertible quantum measurement maps. Denote by S(H) the
convex set of all states (i.e., trace 1 positive operators) on Hilbert space H with dimH ∞, and [ρ1,ρ2]
the line segment joining two elements ρ1,ρ2 in S(H). It is shown that a bijective map φ : S(H)→S(H)
satisfies φ([ρ1,ρ2]) ⊆ [φ(ρ1),φ(ρ2)] for any ρ1,ρ2 ∈ S if and only if φ has one of the following forms
ρ → MρM
∗
tr(MρM
∗
)
or ρ → MρTM
∗
tr(MρTM
∗
)
,
where M is an invertible bounded linear operator and ρT is the transpose of ρ with respect to an arbitrarily
fixed orthonormal basis.
© 2012 Published by Elsevier Inc.
