Physicists Corrected Quantum Theory: Why It Matters 0 12

Physicists have managed to resolve a long-standing mathematical problem in one of the key theorems of quantum information theory — the generalized quantum Stein lemma. This theorem underpins modern understanding of how to distinguish quantum states and how 'quantum resources' can be transformed into one another. The work is published in the journal Nature Physics.

Quantum information theory studies ways to store and process data in systems governed by the laws of quantum mechanics. Within this field, so-called resource theories are developed — a formalism that describes what transformations are possible if only a limited set of operations is allowed. One of the cornerstones here is the generalized quantum Stein lemma, formulated in 2008, which describes how effectively one can distinguish one quantum state from a set of alternative states.

Several years ago, researchers discovered that there was a logical gap in the original proof of the theorem. This raised questions about the validity of a number of works that used this result. Attempts to close the gap had been made before, but all were incomplete.

Now, the authors of the new article have managed to rigorously restore the proof by introducing additional mathematical arguments and eliminating controversial assumptions. According to them, this allows the Stein lemma to be used again as a reliable tool in quantum information theory.

“The generalized quantum Stein lemma is a statement about the limiting capabilities of quantum hypothesis testing. The problem was that the previous proof did not take into account all the necessary conditions for the alternative set of states,” explained one of the authors of the work.

In the course of the research, the scientists showed that the transformation of quantum resources adheres to a universal law analogous to the second law of thermodynamics. This means that different types of quantum resources can be compared and converted into one another according to common rules, based on the speed of such transformations.

“In fact, we have managed to reaffirm the 'second law' for quantum resource theories,” noted the researchers. According to them, the result is important not only for fundamental physics but also for practical tasks: it provides a more reliable mathematical basis for assessing the capabilities of quantum computers and other quantum devices.

In the future, the authors plan to develop this approach to describe so-called dynamic quantum resources — processes and operations, not just states. This may help to better understand the limits of controlling quantum systems and bring closer the creation of more efficient quantum technologies.