Classical physics allows the constellation of the planets, for example, to be calculated precisely and can thus forecast, among other things, when there will be a solar or lunar eclipse. A comparable operation on an atomic scale is possible only to a limited extent. At least this is the implication of Heisenberg’s uncertainty principle, which says that in quantum mechanics, for example, the position and momentum (velocity multiplied by its mass) of an electron relative to its atomic nucleus cannot be determined with any desired degree of precision. A collaborating group of physicists from ETH Zurich, the University of Munich and the University of Darmstadt have now developed a theory and described in mathematical formulae how this uncertainty principle can almost be set aside under certain conditions, namely if the data to simulate a particular problem are recorded “quantum mechanically” and processed further via a quantum computer.

More valuable quantum information

Heisenberg’s uncertainty principle applies wherever predictions about measured quantum mechanical variables are made on the basis of classical data. It arises due to the fact that, in quantum mechanics, there are no clearly defined 0 and 1 states like those of a bit in a classical computer, and instead several alternative possibilities can exist simultaneously. “If we collect the available information about a particle in a quantum memory, this makes this information more valuable than information gathered in a classical way,” says Renato Renner, Assistant Professor at the Institute for Theoretical Physics of ETH Zurich and co-author of the paper. These quantum data then theoretically allow measured variables to be predicted with any desired precision, and the Heisenberg uncertainty becomes arbitrarily small.

The fact that such a procedure might be possible has already been shown by a paper in 2004, in which a quantum memory for light was built experimentally. Renner says it is entirely possible that this could make a quantum memory and data recorded quantum mechanically a reality: “Our formula then allows quantification of the size of the remaining uncertainty in this case.”

The scientists – including Matthias Christandl, who previously took part in the study from Munich and began a Swiss National Research Council professorship at ETH Zurich in June – are convinced that this method has a wide variety of applications, especially in quantum cryptography. In fact, Heisenberg’s uncertainty principle is often used to justify the security of quantum cryptography. However, this justification is no longer valid if, for example, an attacker uses a quantum computer himself. Renner is convinced that the new results will allow this loophole to be closed.

Predicting “quantum components”

Quantum scientists could also use the formula in the future to test the properties of quantum-mechanical components such as transistors, for example. In fact, up to now it has been difficult to prove that such components, which will perhaps one day enable the construction of a quantum computer, really do satisfy the conditions for a “quantum component”. The formula now enables the scientists almost to turn the tables. This means that if such a module allows measured variables to be predicted with a precision that is unachievable according to Heisenberg’s principle, the component must necessarily be quantum mechanical.

Literature reference:

Berta M, Christandl M, Colbeck R, Renes JM & Renner R: The uncertainty principle in the presence of quantum memory, Nature Physics advance online Publication 35. July 2010, DOI: 10.1038/NPHYS1734