Subadditivity of q-entropies for q>1

Abstract

I prove a basic inequality for Schatten q-norms of quantum states on a finite-dimensional bipartite Hilbert space H_1\otimes H_2: 1+||ρ||_q \ge ||\trace_1ρ||_q + ||\trace_2ρ||_q. This leads to a proof--in the finite dimensional case--of Raggio's conjecture (G.A. Raggio, J. Math. Phys.\ \textbf{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) \le S_q(\trace_1ρ)+S_q(\trace_2ρ).

2 pages

Cited by in corpus (17)

• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Some general properties of unified entropies
• Genuine multipartite entanglement measure
• Partial separability revisited: Necessary and sufficient criteria
• New Quantum Algorithms for Computing Quantum Entropies and Distances
• Entanglement polygon inequality in qudit systems
• Sharp Continuity Bounds for Entropy and Conditional Entropy
• Complete monogamy of the multipartite quantum mutual information
• Faithful geometric measures for genuine tripartite entanglement
• Quantum logical entropy: fundamentals and general properties
• Probing multipartite entanglement through persistent homology
• Complete Genuine Multipartite Entanglement Monotone
• Entanglement and entropy in multipartite systems: a useful approach
• Comment on "Quantum discord through the generalized entropy in bipartite quantum states"
• New Partial Trace Inequalities and Distillability of Werner States
• The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement
• Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures