On the Contractivity of Hilbert-Schmidt distance under open system dynamics

Details On the Contractivity of Hilbert-Schmidt distance under open system dynamics On the Contractivity of Hilbert-Schmidt distance under open system dynamics

2009-01-28

arxiv.org/abs/0901.4547v2

Phys. Rev. A 79, 052326 (2009)

Physics

Quantum Physics

Major revision. We would particularly like to thank D Perez-Garcia for constructive feedback

Scientific paper

10.1103/PhysRevA.79.052326

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.

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