2005/05/11 by G. A. Raggio, G A Raggio
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/3/013
Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of the earlier version 2
arxiv created 2005/05/11 · openalex publication_date 2005/12/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The separability modulus ℓ(ρ) of a state ρ of an arbitrary finite composite quantum system is the largest t in [0, 1] such that t ⋅ ρ + (1 − t ) ⋅ τ is separable, where τ is the normalized trace. The basic properties of ℓ, introduced by Vidal and Tarrach in another guise, are briefly established. With these properties, we obtain conditions on the spectrum of a state which imply that it is separable. As a consequence, we show that for any Hamiltonian H the thermal equilibrium states e − H / T /Tr(e − H / T ) are separable if T is large enough. Also, for F a unitarily invariant, convex continuous real-valued function on states, for which F (ρ) > F (τ) whenever ρ ≠ τ, there is a critical C F such that F (ρ) ⩽ C F implies that ρ is separable, and for each possible c > C F there are entangled states ϕ with F (ϕ) = c . This class includes all strictly convex unitarily invariant continuous functions, and also every non-trivial partial eigenvalue-sum. Some C F are computed. General upper and lower bounds for C F are given, and then improved for bipartite systems.