ua nt - p h / 05 06 21 0 v 1 2 4 Ju n 20 05 On divergence , relative entropy and the substate property

ua nt - p h / 05 06 17 9 v 1 2 1 Ju n 20 05 Velocity quantization approach of the one - dimensional dissipative harmonic oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the consta...

ua nt - p h / 05 06 18 9 v 1 2 2 Ju n 20 05 General paradigm for distilling classical key from quantum states

Karol Horodecki, Micha l Horodecki, Pawe l Horodecki, Jonathan Oppenheim Department of Mathematics Physics and Computer Science, University of Gdańsk, 80–952 Gdańsk, Poland Institute of Theoretical Physics and Astrophysics University of Gdańsk, 80–952 Gdańsk, Poland Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80–952 Gdańsk, Poland and Department of Applied Mathem...

ua nt - p h / 05 09 21 8 v 1 3 0 Se p 20 05 N - qubit entanglement via the J 2 y - type collective interaction

ar X iv : q ua nt - p h / 05 06 09 5 v 1 1 3 Ju n 20 05 Schmidt states and positivity of linear maps

Using pure entangled Schmidt states, we show that m-positivity of a map is bounded by the ranks of its negative Kraus matrices. We also give an algebraic condition for a map to be m-positive. We interpret these results in the context of positive maps as entanglement witnesses, and find that only 1-positive maps are needed for testing entanglement.

ar X iv : q ua nt - p h / 05 06 24 1 v 1 2 8 Ju n 20 05 Classification of n - qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...