Subnormalized states and trace-nonincreasing maps

Details Subnormalized states and trace-nonincreasing maps Subnormalized states and trace-nonincreasing maps

2007-01-19

arxiv.org/abs/quant-ph/0701143v2

J. Math. Phys. 48(5), 052110 (2007)

Physics

Quantum Physics

LaTeX, 21 pages, 4 Encapsuled PostScript figures, 1 table

Scientific paper

10.1063/1.2738359

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 $M_{N^2}$.

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