Weak Measurements Are Universal
Abstract
It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.
 Publication:

Physical Review Letters
 Pub Date:
 September 2005
 DOI:
 10.1103/PhysRevLett.95.110409
 arXiv:
 arXiv:quantph/0503017
 Bibcode:
 2005PhRvL..95k0409O
 Keywords:

 03.65.Ta;
 03.65.Ca;
 03.67.Mn;
 Foundations of quantum mechanics;
 measurement theory;
 Formalism;
 Entanglement production characterization and manipulation;
 Quantum Physics
 EPrint:
 4 pages, RevTeX format, essentially the published version, reference updated