doi:10.1038/nindia.2017.98 Published online 1 August 2017
Theoretical physicists from the Harish-Chandra Research Institute (HRI) in Allahabad have derived a new kind of relation in quantum mechanics called the "Reverse Uncertainty Relation", that could find applications in various areas of quantum physics, quantum information and quantum technology1.
Debasis Mondal, Shrobona Bagchi and Arun Kumar Pati from HRI show, for the first time, that there is an upper limit to how accurately one can simultaneously measure the position and momentum of a particle.
The original uncertainty principle introduced in 1927 by Werner Heisenberg is a rule in quantum mechanics which sets a "lower" limit on the product of the "variances" of two "incompatible observables" (such as position and momentum), but it was not known if there is any "upper" limit.
"We show that there is indeed an upper limit," Pati, one of the authors, told Nature India. "The reverse uncertainty relation shows that there is a "spread" or "range" for both the sum and product of variances of two non-commuting observables," he said. In addition to the reverse uncertainty relation, the authors have proved a new and tighter uncertainty relation from which the Heisenberg uncertainty relation directly follows.
The new relation may be useful in setting an upper limit in "quantum metrology," which exploits quantum systems to reach unprecedented levels of precision in measurements. "Thus, this is not only of fundamental interest but can have applications in diverse areas of quantum physics," Pati said adding "the reverse uncertainty relation should open up a whole new direction of explorations in quantum mechanics which we have not thought of."
1. Mondal, D. et al. Tighter uncertainty and reverse uncertainty relations. Phys. Rev. A 95, 052117 (2017) doi: 10.1103/PhysRevA.95.052117