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Entanglement, decoherence and estimation in neutrino oscillations

Edson C. M. Nogueira

Published Aug 11, 2017• 0 citations
OpenAlex

Abstract

In this work, we studied entanglement and decoherence in neutrino oscillations from a quantum metrology perspective. A summary of the quantum eld theoretic description of neutrinos was done and the main quantum mechanical models were used to analyze the inuence of entanglement and decoherence on the quantum Fisher information related to the mixing angle. We have found that, although in a variety of physical settings there is a positive relationship between entanglement and the quantum Fisher information, this is not the case in the neutrino oscillations scenario. This shows that, at least in single-particle settings, entanglement is not directly related to the optimal estimation in metrological tasks.

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In this work, we studied entanglement and decoherence in neutrino oscillations from a quantum metrology perspective. A summary of the quantum eld theoretic description of neutrinos was done and the main quantum mechanical models were used to analyze the inuence of entanglement and decoherence on the quantum Fisher information related to the mixing angle. We have found that, although in a variety of physical settings there is a positive relationship between entanglement and the quantum Fisher information, this is not the case in the neutrino oscillations scenario. This shows that, at least in single-particle settings, entanglement is not directly related to the optimal estimation in metrological tasks.
Neutrino oscillations are at the forefront of advances in Physics beyond the Standard Model. Increasing accuracy in measurements of the neutrino mixing matrix is an important challenge in current experiments. It depends on parameters that do not directly correspond to observables of the neutrino system. This type of estimation problem is handled by Quantum Estimation Theory (QET) via the Fisher Information (FI) and the Quantum Fisher Information (QFI). In this work, we analyze two-flavor neutrino oscillations within the framework of QET. We compute the QFI for the mixing angle θθθ and show that mass measurements are the ones that achieve optimal precision. We also study the FI associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to θθθ. We study how these quantifiers relate to the single-particle, mode entanglement. We demonstrate that this form of entanglement does not enhance neither of them. In particular, this shows that in single-particle settings, entanglement is not directly connected with the optimal precision in metrological tasks.
In this work, we analyze two-flavor neutrino oscillations within the framework of quantum estimation theory (QET). We compute the quantum Fischer information (QFI) for the mixing angle [Formula: see text] and show that mass measurements are the ones that achieve optimal precision. We also study the Fischer information (FI) associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to [Formula: see text]. We investigate how these quantifiers relate to the single-particle, mode entanglement in neutrino oscillations. We demonstrate that this form of entanglement does not enhance either of them. In particular, our results show that in single-particle settings, entanglement is not directly connected with the enhancement of precision in metrological tasks.
The phenomena of particle mixing and flavor oscillations in elementary-particle physics can be addressed from the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and antineutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor ηpη_pηp​ to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For 0<P<10<P<10<P<1 and 0<ηm<10<η_m<10<ηm​<1, the QFIM in (P,χ,ηm)(P,χ,η_m)(P,χ,ηm​) is diagonal, with Hχχmode=Cηm2\mathcal{H}^{\rm mode}_{χχ}=C_{η_m}^2Hχχmode​=Cηm​2​ and Hξmξmmode=Cηm2/(1−ηm2)\mathcal{H}^{\rm mode}_{ξ_mξ_m}=C_{η_m}^2/(1-η_m^2)Hξm​ξm​mode​=Cηm​2​/(1−ηm2​), where ξm=−ln⁡ηmξ_m=-\lnη_mξm​=−lnηm​. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for (θ23,δCP,ξ31,g)(θ_{23},δ_{\rm CP},ξ_{31},g)(θ23​,δCP​,ξ31​,g) at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At Γ0=10−23 GeVΓ_0=10^{-23}\,\mathrm{GeV}Γ0​=10−23GeV, the fixed-coordinate ratio Fδδflav/Hδδ\mathcal{F}^{\rm flav}_{δδ}/\mathcal{H}_{δδ}Fδδflav​/Hδδ​ is approximately 0.0100.0100.010, 0.0130.0130.013, and 0.1050.1050.105, respectively; all three points show strong θ23θ_{23}θ23​--ξ31ξ_{31}ξ31​ incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.
Measurements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing parameters have entered a precision era, enabling increasingly stringent tests of neutrino oscillations. Within the framework of quantum estimation theory, we investigate whether flavor measurements, the only observables currently accessible experimentally, are optimal for extracting the oscillation parameters. We compute the Quantum Fisher Information (QFI) and the classical Fisher Information (FI) associated with ideal flavor projections for all oscillation parameters, considering accelerator muon (anti)neutrino and reactor electron antineutrino beams propagating in vacuum. Two main results emerge. First, flavor measurements saturate the QFI at the first oscillation maximum for θ13θ_{13}θ13​, θ23θ_{23}θ23​, and θ12θ_{12}θ12​, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for δCPδ_{CP}δCP​. In particular, only a small fraction of the available information on δCPδ_{CP}δCP​ is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESSνννSB, a planned facility. Second, the QFI associated with δCPδ_{CP}δCP​ is approximately one order of magnitude smaller than that of the mixing angles, indicating that the neutrino state intrinsically encodes less information about CP violation. Nevertheless, this quantum bound lies well below current experimental uncertainties, implying that the present precision on δCPδ_{CP}δCP​ is not fundamentally limited. Our results provide a quantitative framework to disentangle fundamental from practical limitations and establish a benchmark for optimizing future neutrino facilities.
As the lynchpin of all quantum correlations, quantum coherence is fundamental for distinguishing quantum systems from classical ones and is essential for realizing quantum advantages in areas such as computation, communication, and metrology. In this study, we investigate the relationship between quantum coherence and neutrino oscillations within the two and three flavor-mode qubit frameworks. Our analysis extends beyond the commonly used l 1 -norm and relative entropy of coherence to include all relevant measures of coherence such as robustness of coherence, coherence concurrence, trace-norm distance measure of coherence, coherence of formation, Schatten- p -norm-based functionals, geometric coherence and logarithmic coherence rank, each offering unique insights into the quantum correlations in these systems. Notably, while the l 1 -norm and relative entropy-based measures apply to general quantum states, the other measures are particularly relevant for entangled systems, highlighting the critical role of entanglement in neutrino oscillations. We present a detailed methodology for calculating coherence measures in both two-flavor and three-flavor mixing scenarios, contributing to a deeper understanding of how quantum coherence manifests and evolves in mode-entangled neutrino systems. Our findings emphasize the potential of these systems as robust candidates for quantum information tasks, facilitated by the weak interaction nature of neutrinos.