2021/03/31 by Marcos L. W. Basso, Jonas Maziero · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1016/j.physleta.2021.127875
published as Phys. Lett. A, 425, 127875 (2021) · 5 pages. arXiv admin note: substantial text overlap with arXiv:2012.14471
arxiv created 2021/12/06 · arxiv updated 2021/12/07
Distinguishability and predictability are part of complementarity relations which apply to two different kinds of interference experiments, with and without a path-detector, respectively. In [Opt. Comm. 179, 337 (2000)], Englert and Bergou pointed out the possible connection between distinguishability, predictability, and entanglement. They even conjectured that an entanglement measure was hidden between the measures of distinguishability and predictability. Here, we push forward this conjecture. We start defining a new entropic distinguishability measure and suggesting an entanglement measure as the difference between this entropic distinguishability and an entropic predictability measure already defined in the literature. Besides, we prove that it is possible to define an entanglement monotone from the largest value of the distinguishability and the corresponding predictability, provided that the predictability satisfy the criteria already established in the literature. Thus, this result formally connects an entanglement monotone with distinguishability and the corresponding predictability, without appealing to specific measures.