A1 Refereed original research article in a scientific journal
Weak versus approximate values in quantum state determination
Authors: Haapasalo E, Lahti P, Schultz J
Publisher: AMER PHYSICAL SOC
Publication year: 2011
Journal: Physical Review A
Journal name in source: PHYSICAL REVIEW A
Journal acronym: PHYS REV A
Article number: ARTN 052107
Number in series: 5
Volume: 84
Issue: 5
Number of pages: 7
ISSN: 1050-2947
DOI: https://doi.org/10.1103/PhysRevA.84.052107
Abstract
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.
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.
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