Neutrino flavor-mass uncertainty relations and an entanglement-assisted determination of the PMNS matrix

Abstract:

As a result of a nontrivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton side which is determined by the PMNS matrix. The parameters of the latter, including the $CP$-violating phase $\delta$, can be obtained by guessing them and improving the guess by minimizing the remaining oscillations.

S. Floerchinger, J.-M. Schwind, “Neutrino flavor-mass uncertainty relations and an entanglementassisted determination of the PMNS matrix”, Phys. Rev. D 102, 093001 (2020).

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.093001

Related to Project C06, A06*