Despite being very influential on both foundations and applications of quantum mechanics, weak values are still somewhat controversial. Although there are some indications that weak values are physical properties of a single quantum system, the common way weak values are presented is statistical: it is commonly believed that for measuring weak values one has to perform many weak measurements over a large ensemble of pre- and postselected particles. Other debates surround the anomalous nature of weak value and even their quantumness. To address these issues, we present some preliminary data showing that anomalous weak values can be measured using just a single detection, i.e. with no statistics. In our experiment, a single click of a detector indicates the weak value as a single photon property, which moreover lies well beyond the range of eigenvelues of the measured operator. Importantly, the uncertainty with which the weak values is measured is smaller than the difference between the weak value and the closet eigenvalue. This is the first experimental realization of robust weak measurements.
Counterfactual communication, transferring bits and even qubits without particle travelling in the transmission channel is a bizarre quantum effect. It is also a very controversial topic. Here I will try to clarify the meaning of various “counterfactual" quantum protocols.
In quantum mechanics, the eigenvalues and their corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property related to large ensembles of particles. In contrast to this paradigm, we demonstrate a unique method allowing to extract the expectation value of a single particle, namely, the polarisation of a single protected photon, with a single experiment. This is the first realisation of quantum protective measurements.
It is shown, under the assumption of possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously. The measurement is based on teleportation method. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.