I prove a basic inequality for Schatten q-norms of quantum states on a finite-dimensional bipartite Hilbert space H1H2: 1+ρqTr1ρq+Tr2ρq. This leads to a proof—in the finite-dimensional case—of Raggio’s conjecture [G. A. Raggio, J. Math. Phys.36, 4785 (1995)] that the q-entropies Sq(ρ)=(1Tr[ρq])(q1) are subadditive for q>1; that is, for any state ρ, Sq(ρ) is not greater than the sum of the Sq of its reductions, Sq(ρ)Sq(Tr1ρ)+Sq(Tr2ρ).

1.
R.
Bhatia
,
Matrix Analysis
(
Springer
,
Heidelberg
,
1997
).
2.
C.
Tsallis
,
J. Stat. Phys.
52
,
479
(
1988
).
3.
4.
G. A.
Raggio
,
J. Math. Phys.
36
,
4785
(
1995
).
5.
H.
Bercovici
and
D.
Van Gucht
,
Math. Ineq. Appl.
8,
743
(
2005
).
You do not currently have access to this content.