Proper and Improper Separability
نویسندگان
چکیده
The distinction between proper and improper mixtures is a staple of the discussion of foundational questions in quantum mechanics. Here we note an analogous distinction in the context of the theory of entanglement. The terminology of ‘proper’ versus ‘improper’ separability is proposed to mark the distinction. 1 Proper and Improper mixtures In many discussions of the measurement problem in quantum mechanics, it has proved essential to distinguish between density operators which can be given an ‘ignorance’ interpretation; and those which cannot. In the former case, the system whose state the density operator represents is in some definite quantum state from a specified set — say a pure state |ψi〉 — but we don’t know which. Our ignorance of the actual state can be represented by a probability distribution {pj} over the different (not necessarily orthogonal) possibilities {|ψj〉}, and the density operator may be written as
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