New Quantum State Distinguishability Measure Proposed

Recent research by Adrian A. Budini, Ruynet L. de Matos Filho, and Marcelo F. Santos introduces a new approach to measuring the distinguishability of quantum states. Their paper, titled "Quantum distinguishability measures: projectors vs. states maximization," proposes an alternative definition of distinguishability that relies on maximizing over normalized states, or density matrices, rather than the traditional method that uses measurement projectors.

The authors argue that this new method leads to a distance measure based on an infinite-norm, contrasting with the conventional 1-norm approach. This shift in perspective not only fulfills important properties such as convexity and monotonicity but also maintains invariance under unitary transformations. The research establishes equivalent operational implementations that utilize classical probabilities and hypothesis testing scenarios.

One significant implication of this work is its potential to enhance the understanding of quantum systems, particularly in the context of completely positive transformations. The findings suggest that contractivity is only guaranteed for unital maps, which allows for the introduction of a measure of the quantumness of non-unital maps. This measure corresponds to the maximum possible deviation from contractivity, providing a new tool for researchers in quantum physics.

The paper includes specific examples that support its main conclusions, indicating practical applications for the proposed distinguishability measure. This research could pave the way for advancements in quantum information processing and quantum computing, where understanding the nuances of quantum state distinguishability is crucial.

For further details, the paper can be accessed at arXiv:2409.00198.