The physical interpretation of partial traces: Two nonstandard views

Mixed states are introduced in physics to express our ignorance about the actual state of a physical system and are represented in standard quantum mechanics by density operators. Such operators also appear if we consider a (pure) entangled state of a compound system Ω and take partial traces on the projection operator representing it. But because the coefficients in the convex sums expressing them never bear the ignorance interpretation in this case, they represent not mixed states (proper mixtures) but improper mixtures of the subsystems. Hence, states cannot be attributed to the subsystems of a compound physical system in an entangled state (the subentity problem). We discuss two alternative proposals that can be developed in the Brussels and the Lecce approaches. We firstly summarize the general framework provided by the Brussels approach, which suggests that improper mixtures can be regarded as new pure states. We then show that improper mixtures can also be regarded as true (but nonpure) states according to the Lecce approach. Despite their different terminologies, the two proposals seem compatible. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 248–264, August, 2007.     

On the first solution of a long standing problem: Uniqueness of the phaseless quantum inverse scattering problem in 3-d

After publishing his recent paper in SIAM J. Appl. Math. 74, 392–410, 2014 the author has realized that actually he has addressed in that paper, for the first time, a long standing open question being unaware about this. This question is about the uniqueness of a 3-d inverse scattering problem without the phase information. Thus, it makes sense in the current paper to explicitly make the latter statement and to formulate corresponding uniqueness theorems.