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Subnormalized states and trace-nonincreasing maps
Valerio Cappellini, Hans-Juergen Sommers, Karol Zyczkowski
abstract: We investigate the set of completely positive, trace-nonincreasing linear
maps acting on the set M_N 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 (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 M_N induced by partial trace of mixed quantum states distributed
uniformly with respect to HS-measure in $M_{N^2}$.
- oai_identifier:
- oai:arXiv.org:quant-ph/0701143
- categories:
- quant-ph math-ph math.MP
- comments:
- LaTeX, 21 pages, 4 Encapsuled PostScript figures, 1 table
- doi:
- 10.1063/1.2738359
- arxiv_id:
- quant-ph/0701143
- journal_ref:
- J. Math. Phys. 48(5), 052110 (2007)
- created:
- 2007-01-19
- updated:
- 2007-06-01
Full article ▸
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