2007/01/31 by Valerio Cappellini, Hans-Jürgen Sommers, Hans-Juergen Sommers +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum many-body systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.2738359
published as J. Math. Phys. 48(5), 052110 (2007) · LaTeX, 21 pages, 4 Encapsuled PostScript figures, 1 table
openalex publication_date 2007/05/01 · arxiv created 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate the set of completely positive, trace-nonincreasing linear maps acting on the set MN of mixed quantum states of size N. Extremal point of this set of maps are characterized and its volume with respect to the Hilbert-Schmidt (HS) (Euclidean) measure is computed explicitly for an arbitrary N. The spectra of partially reduced rescaled dynamical matrices associated with trace-nonincreasing completely positive maps belong to the N cube inscribed in the set of subnormalized states of size N. As a by-product we derive the measure in MN induced by partial trace of mixed quantum states distributed uniformly with respect to the HS measure in MN2.