Subadditivity of q-entropies for q>1

2007/05/09 by Koenraad M. R. Audenaert · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1063/1.2771542

published as J. Math. Phys. 48, 083507 (2007) · 2 pages

arxiv created 2007/05/09 · arxiv updated 2009/12/01

Abstract

I prove a basic inequality for Schatten q-norms of quantum states on a finite-dimensional bipartite Hilbert space H₁⊗ H₂: 1+||ρ||_q ≥ ||\trace₁ρ||_q + ||\trace₂ρ||_q. This leads to a proof--in the finite dimensional case--of Raggio's conjecture (G.A. Raggio, J. Math. Phys. 36, 4785--4791 (1995)) that the q-entropies S_q(ρ)=(1-\trace[ρ^q])/(q-1) are subadditive for q > 1; that is, for any state ρ, S_q(ρ) is not greater than the sum of the S_q of its reductions, S_q(ρ) ≤ S_q(\trace₁ρ)+S_q(\trace₂ρ).

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