Weak Measurements and the quantum phase space

RENARD, Bryan

Harald Scherer, Paul Busch

Erkka Haapasalo, PEKKA J. LAHTI, Jussi Schultz

We generalize the concept of the weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory of sequential measurements. In particular, we show that the weak value can be obtained from a single measurement scheme. We then present a detailed analysis of the recent experiment [J. S. Lundeen et al., Nature (London) 474, 188 (2011)] concerning the reconstruction of the state of a photon using weak measurements. We compare their method with the reconstruction method through informationally complete phase space measurements. In particular, we show that unlike with phase space measurements, the reconstruction of a completely unknown state is not always possible using the method of weak measurements.

Jong Chan Lee, Hyang‐Tag Lim, Kang-Hee Hong +1 more

Allen Lobo, Carlos Alberto de Lima Ribeiro

We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring process on the entire phase space of the measuring system. By using coherent states, we go a step further than Jozsa in a recent paper and we present an example where the result of the measurement is symmetrical in the position and momentum observables and seems to be much better suited for quantum optical implementation.

M. Shioden