Measurements of negative and complex joint probabilities in photon polarization

A weak measurement, which was proposed by Aharonov, et al. in 1988, is a quantum measurement leaving the coherence of the initial state intact and completely different from a fully projective measurement. It is also useful for a quantum state tomography, but it can provide non-classical correlation indicating non-positive statistics. The biggest problem is whether this strange statistics is essentially necessary or avoidable by utilizing other measurement theory, since the weak measurement is originally based on Von Neumann's measurement theory. Recently, we performed the quantum state tomography based on a sequential quantum measurement of non-commuting observables of photon polarization. This sequential measurement is realized by a variable strength measurement, which has capability of controlling a measurement strength from zero (no measurement) to fully projection (completely destructive measurement). We investigated the role of measurement uncertainties caused by the first measurement and estimated joint probabilities before the measurement without the use of quantum measurement theory or weak measurement theory. Consequently, the obtained joint probabilities of the initial state were consistent with negative or complex joint probabilities, which is called Kirkwood-Dirac pseudo-probability distribution. The result shows that the joint probabilities before the measurement are converted to the normal positive statistics due to influence of the measurement process. Therefore, it is highly probable that negative and complex probabilities show essential statistical properties of quantum systems. This result is deduced from the experimental results not only in weak regime, but also in strong regime without the use of weak measurement concept. In this seminar, I will introduce our experimental results and show possible reasons of the above interpretation. [slides]

Reference: Yutaro Suzuki, Masataka Iinuma, and Holger F. Hofmann, New Journal of Physics 14 (2012) 103022

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