Furthermore, open quantum systems are of paramount importance in quantum information, quantum computing, and cavity optomechanics, among other fields, because interaction between a quantum system and the surrounding environment causes decoherence in the quantum system, and a consequent loss of the system's quantum properties, thus rendering the system unusable in quantum computing or quantum information
Understanding the dynamics of an open quantum system will enable one to control the system appropriately in order to delay the emergence of decoherence in the system, prolonging the time in which the system behaves quantum mechanically.
There are three main elements to an open quantum system, namely the system itself, the environment, and the interaction between the system and the environment, each of which correspond to a separate Hamiltonian. The Hamiltonian gives us information about how each element of the open quantum system evolves over time. However, the bigger the environment, the more information is available about the open quantum system, and the more difficult it is to analyze the dynamics of the system, as there is too much information available about the system, most of which is useless. Thus, there is a need to reduce the amount of information available about the open quantum system to those which are absolutely necessary to describe the dynamics of the system, which is done by treating the system probabilistically. In doing so, we can eliminate the information which is irrelevant in describing the dynamics of the system, and focus only on those few relevant events.
An analogy to the probabilistic approach can be seen in the treatment of a system undergoing a random walk. Here, if the system is located at a given point at a given instant of time, there is a 1 in N chance that the system will move in one of N possible directions. In particular, if the system can only move on a line, then if it is located at a given point x at a given instant of time t, then there is a 1 in 2 chance that it will move to the point x-1 or x+1.
