Open quantum system

In physics, an open quantum system is a quantum-mechanical system which interacts with an external quantum system, the environment. In reality, no quantum system is completely isolated from its surroundings, thus every quantum system is open to some extent, which leads to dissipation. Techniques developed in the context of open quantum systems have proven powerful in fields such as quantum optics, quantum measurement theory, quantum statistical mechanics, quantum information science, quantum thermodynamics, quantum cosmology and semi-classical approximations.

No quantum system can be completely isolated from its environment. As a direct result a quantum system can never be in a pure state. A pure state is unitary equivalent to a zero temperature ground state forbidden by the third law of thermodynamics. A complete description of a quantum system requires to include the environment. The outcome of this process of embedding is that ultimately we end with the state of whole universe described by a wavefunction ${\displaystyle \Psi }$.

Even if the combined system is pure state and can be described by a wavefunction ${\displaystyle \Psi }$, a subsystem in general cannot be described by a wavefunction. This observation motivated the formalism of density matrices or density operators introduced by John von Neumann in 1927 and independently, but less systematically by Lev Landau in 1927 and Felix Bloch in 1946. In general, the state of a subsystem is described by the density operator ${\displaystyle \rho }$ and an observable by the scalar product ${\displaystyle (\rho \cdot {\bf {A}})=Tr\{\rho {\bf {A}}\}}$. There is no way to know if the combined system is pure from the knowledge of the observables of the subsystem. In particular if the combined system has quantum entanglement, the system state is not a pure state.

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