The fundamental equation of non-relativistic quantum mechanics, the ► Schrödinger equation, is linear. Thus, superpositions of its solutions (quantum states) constitute solutions as well. This is the famous ► superposition principle. Given a composite quantum system, i.e. a quantum system that consists of two or more subsystems, superpositions of its states can be either separable or entangled [1]. The quantum state of a bipartite system, i.e. a system consisting of two subsystems A (located at Alice's lab) and B (located at Bob's lab), is an element of the tensored Hilbert space H = H A ⊗ H B. A pure bipartite state | ψ⟩ ∈ H A ⊗ H B is called separable if and only if | ψ⟩ = | a⟩ ⊗ | b⟩, where | a⟩ ∈ H A and | b⟩ ∈ H B. It is entangled otherwise.
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Bruβ, D. (2009). Creation and Detection of Entanglement. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_44
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