Quantum information analysis says neutrinos carry more δ-CP data than detectors extract

Neutrinos carry enough quantum information to constrain the CP-violating phase δ-CP to within roughly 3° for a sample of about 1000 neutrino and antineutrino events — a precision floor several times sharper than the 7–18° uncertainty projected for the Deep Underground Neutrino Experiment (DUNE) when it starts operating in 2028.

That is the central result of a study by researchers in Italy, accepted in Physical Review Letters, led by Michela Ignoti, a PhD student at the University of Milan, with theoretical physicist Claudia Frugiuele. Their finding implies that much of the uncertainty in current and planned measurements of δ-CP stems not from the physics encoded in the particles themselves but from how experiments read them out.

Why δ-CP matters

Neutrinos oscillate between three flavours as they travel. Experiments such as T2K in Japan fire neutrino beams at distant detectors and count how often each flavour arrives. The open question is whether neutrinos and antineutrinos oscillate differently. A difference would violate charge-parity (CP) symmetry — the symmetry between matter and antimatter — with consequences for why the universe contains more of one than the other.

"A CP-violating phase is connected to the matter-antimatter imbalance in the universe," Ignoti said. "That's one of the reasons why we're interested in measuring it precisely."

The phase δ-CP is an angle between 0° and 360°. Values of 0° and 180° imply no intrinsic CP violation; 90° and 270° would indicate maximal violation. DUNE, in the US, aims to measure it, but projections put its eventual uncertainty at 7–18°, depending on the parameter's true value.

What did the Milan group actually calculate?

The team applied quantum information theory — the framework that quantifies how much information a quantum system can carry — to compute the theoretical maximum precision available in a neutrino sample. For the equivalent of around 1000 neutrino and antineutrino events, the quantum information content alone could pin δ-CP to about 3°. That is sharp enough to distinguish competing theories of how neutrinos violate CP symmetry.

The gap between 3° and 7–18° has a structural cause. Flavour-detection probability rises and falls in a repeating pattern as neutrinos travel. T2K and its planned successor Hyper-Kamiokande measure near the first peak, where the probability of flavour change is highest and event counts are strongest. Measurements near the second peak, however, are more sensitive to δ-CP, because small changes in the angle shift the flavour-change probability there much more strongly.

Why experiments do not simply move to the second peak

One planned facility, the European Spallation Source neutrino Super Beam (ESSνSB), is designed around the second oscillation peak. But Patrick Huber, a neutrino physicist at Virginia Tech who was not involved in the study, identified two costs. First, the second peak demands a longer source-to-detector baseline, so fewer neutrinos arrive.

"If you keep everything else in the experiment the same, the event rates in the second oscillation maximum are much, much smaller," Huber said. "About 10 times smaller at least."

Second, longer baselines mean more travel through matter. Matter interactions affect neutrinos and antineutrinos differently, and separating those effects from genuine CP violation becomes harder. For these reasons, Huber does not expect the result to send current experiment designers back to the drawing board, and Frugiuele agrees with that reading of the practical limits. "What reactor experiments are doing right now is pretty much the best that can be done," she said.

Where the framework gets tested next

Both Huber and the Milan team see a growing role for quantum information calculations as experiments improve. A near-term test bed already exists: China's Jiangmen Underground Neutrino Observatory, which began its first data run last year, can extract information from the first and tenth oscillation peaks.

The researchers plan to extend the method to other oscillation parameters and to build in more realistic experimental conditions. "We want to study astrophysical neutrinos and make the framework more realistic for experiments, including by accounting for matter effects," Ignoti said.