zum Hauptkapitel Emerging Quantum Mechanics:

## Interpretation

• The coupling to the phonon is suppressed, because the D-wave eigenstate is spread out over the environmental degrees of freedom. The environmental degrees of freedom do not couple to the phonon directly, only indirectly via phonon <-> eigenstate <-> environment. The coupling to the environmental degrees of freedom is very small and entanglement between D-wave eigenstates and environmental states occurs only on the energy shell. The broadening of the eigenvalues due to coupling to the environment is much smaller than the energetic separation of the eigenvalues. Therefore the coupling to the environment cannot induce transitions between the eigenstates. In this way the D-wave system stays in an eigenstate, once it is there. This is not only valid for the ground state (global minimum), but also for
excited eigenstates.

The found results can be interpreted in the usual decoherence picture: Due to entanglement with the environment the non-diagonal matrix elements of the density matrix vanish \cite{kiefer}.
• This does not contradict the short live time (50 nano seconds) of the Rabi oscillations of a single qubit. In this case a magnetic flux is first applied, which makes the two current directions energetically inequivalent. When the qubit is in its ground state, a (resonant) microwave photon is injected such that ground state plus photon is energetically degenerate with the first excited state (current in opposite direction). The qubit then oscillates bewteen the two states (ground state + photon and excited state). These are the Rabi oscillations. At any time "collapses" of the following kind are possible:
a) The photon escapes or is absorbed by the matter and the qubit remains in its ground state.
b) The current absorbs the photon and the qubit stays in the excited state. If these two processes occur with equal probability and the read out of the qubit occurs after the collapses, the measured switching probability will be 0.5. The measured decay time of 50 nano seconds then just means that after this time the collapse has already occurred with high probability. The coupling to the environment has no influence on the Rabi oscillations, because the photon drives the qubit to switch between different eigenstates and it provides the necessary energy. The coupling to the environment might, however,
protect the Rabi oscillations from disturbances by phonons.

In the case a) the qubit cannot collapse, because it is already in the ground state and it is not driven by a photon.

There remains the question why the coupling to the environment does not protect the eigenstates from coupling to the photon. The answer is that the photon couples to charge and charge is conserved. The charge will not vanish, if the eigenstates entangle to the environment. Therefore, even when entangled to the environment, the photon can still drive the current states between their two directions.