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On the Contractivity of Hilbert-Schmidt distance under open system dynamics by Wang, Xiaoting; Schirmer, Sonia is a scholarly article available to read on EtoBox.

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We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient conditions for contractivity of the Hilbert-Schmidt norm in terms of the dissipation generators are given. Although these conditions are not necessary, simulations suggest that non-contractivity is the typical case, i.e., that systems for which the Hilbert-Schmidt distance between quantum states is monotonically decreasing form only a small set of all possible dissipative systems for N>2, in contrast to the case N=2 where the Hilbert-Schmidt distance is always monotonically decreasing.

Author

Wang, Xiaoting; Schirmer, Sonia

Published

2009

Language

EN