Heisenberg’s uncertainty principle is without any doubt one of the cornerstones of modern quantum physics. However, several formulations coexist which address different physical scenarios. Heisenberg’s uncertainty principle in a formulation of standard deviations, i.e., uncertainties intrinsic to any quantum system, is uncontroversial and demonstrated in various quantum systems. Probably it’s most well-known formulation, as the product of the position and momentum standard deviations given by . However, uncertainty relations in terms of standard deviations describe the limitation of preparing quantum objects and have no direct relevance to the limitation of measurements on single systems, as originally suggested by Heisenberg. His starting point is a relation between the precision (mean error) of a position measurement and the disturbance it induces on a subsequent momentum measurement of a particle – more precisely of an electron. This is beautifully captured in the famous γ-ray microscope thought experiment, which is solely based on the Compton-effect.
The indeterminacy inherent in quantum measurements is an outstanding character of quantum theory, which manifests itself typically in the uncertainty principle. In the last decade, several universally valid forms of error-disturbance uncertainty relations were derived for completely general quantum measurements for arbitrary states. An optimal form for spin measurements for some pure states was established recently. However, the bound in his inequality is not stringent for mixed states. Masanao Ozawa derived a new bound tight in the corresponding mixed state case, which was tested by our group. We experimentally observed the attainability of the new bound.
Information is a key quantity in science and plays a significant role in many economic sectors such as communication technologies, cryptography, or data storage. In quantum communication and information technology the transfer and encryption of information is studied; in the quantum regime phenomena such as the Heisenberg uncertainty principle have to be taken into account as well. By using the so-called information entropy, we precisely analyze uncertainty in terms of “knowledge” and “predictability” and established a trade-off relation between them. These concepts play a central role in the theory of communication, engineering and computer science.
Heisenberg’s uncertainty principle. is certainly one of the most famous foundations of quantum physics. According to this principle, not all properties of a quantum particle are determined with arbitrary accuracy. In the early days of quantum theory, this has often been justified by the notion that every measurement inevitably recoils the quantum particle, which disturbs the results of any further measurements. This, however, turns out to be an oversimplification. In our neutron polarimetric experiment different sources of quantum uncertainty could now be distinguished, validating theoretical results of an error-disturbance uncertainty relation proposed by Masanao Ozawa and a new tight inequality.