Measurements of Negative Joint Probabilities in Optical Quantum System

Abstract

Quantum information science is based on the superposition principle and the non-local quantum correlation of quantum states. These non-classical properties are still mysterious and inadequately understood as physical phenomena. The biggest reason to un-resolving such problems is that we can directly not get all bare information of the quantum states since an action by any measurement absolutely changes the quantum states. Recently, we realized a variable strength measurement of photon polarization, which is capable of controlling the measurement strength from zero (no measurement) to fully projection (completely destructive measurement). This apparatus makes it possible to perform a sequential measurement of two non-commuting observables with an error and the back-action effects produced by the measurement, which never gives exact values simultaneously. We investigated the role of measurement uncertainties of the first variable strength measurement. The experimentally-obtained joint probabilities can be recognized as statistical mixture obtained by random polarization flips arising the measurement uncertainties from an intrinsic joint probability distribution. This natural assumption provided a removal of the back-action effect from the experimental probabilities and the obtained intrinsic probabilities resulted in negative. This analysis also shows how the negative probabilities are converted to observable positive statistics by variable combinations of resolution and back-action uncertainties.