Weak measurements are universal

Details Weak measurements are universal Weak measurements are universal

2005-03-02

arxiv.org/abs/quant-ph/0503017v4

Phys. Rev. Lett. 95, 110409 (2005)

Physics

Quantum Physics

4 pages, RevTeX format, essentially the published version, reference updated

Scientific paper

10.1103/PhysRevLett.95.110409

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.

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