Are there some (simple) rules or conditions which dictate whether a physical process will lead to a state of quantum entanglement of two or more particles or systems? Given the relevance of the entangled state for the development of quantum technologies, it would be useful to know the conditions which can lead to this strange state of matter. I’m sure much of this may be buried within existing mathematics of quantum mechanics. Nevertheless, to enable a wider understanding and appreciation of entanglement, it would be helpful to have some simple rules (in words) which can state whether or not a process will lead to an entangled state.
thank you, Neil
Take two qubits: the first one is in the superpositional state (|0> + |1>), and the second one in the ground state |0>.
Apply the Control-Not gate to these qubits, and you will get the entangled state (|00> + |11>). (I have omitted the normalization constant.)
It’s not that simple. For example, atoms are trapped in an optical cavity composed of two mirrors. When a “squeezing” laser is set through the cavity, the atoms are entangled, and will have the same oscillation frequency .
Of course there are. Entanglement means that the state isn't a product, but a sum of products. So it's sufficient-and necessary-that the states of interest not be eigenstates of the Hamiltonian (or the evolution operator). A typical example is that of localized magnetic moments, that aren't eigenstates of a Hamiltonian that describes an exchange interaction, whose eigenstates are superpositions of product states.
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