We investigate the role of quantum coherence in modulating the energy transfer rate between two independent energy donors and a single acceptor participating in an excitonic energy transfer process. The energy transfer rate depends explicitly on the
nature of the initial coherent superposition state of the two donors and we connect it to the observed absorption profile of the acceptor and the stimulated emission profile of the energy donors. We consider simple models with mesoscopic environments interacting with the donors and the acceptor and compare the expression we obtained for the energy transfer rate with the results of numerical integration.
Examples of repeatable procedures and maps are found in the open quantum dynamics of one qubit that interacts with another qubit. They show that a mathematical map that is repeatable can be made by a physical procedure that is not.
A Markov approximation in open quantum dynamics can give unphysical results when a map acts on a state that is not in its domain. This is examined here in a simple example, an open quantum dynamics for one qubit in a system of two interacting qubits,
for which the map domains have been described quite completely. A time interval is split into two parts and the map from the exact dynamics for the entire interval is replaced by the conjunction of that same map for both parts. If there is any correlation between the two qubits, unphysical results can appear as soon as the map conjunction is used, even for infinitesimal times. If the map is repeated an unlimited number of times, every state is at risk of being taken outside the bounds of physical meaning. Treatment by slippage of initial conditions is discussed.
Simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. One of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with
either of the two entangled qubits and is never entangled, but becomes correlated, with the system of those two qubits. The two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. Similar changes for the two qubits are made with a swap operation between one of the qubits and a control; then there are compensating changes of entanglement that involve the control. When the entanglement increases, the map that describes the change of the state of the two entangled qubits is not completely positive. Combination of two independent interactions that individually give exponential decay of the entanglement can cause the entanglement to not decay exponentially but, instead, go to zero at a finite time.
