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arXiv:1510.06761 · Europhysics Letters (EPL)

Flavor entanglement in neutrino oscillations in the wave packet description

Massimo Blasone A, Fabio Dell’Anno, Silvio De Siena, Fabrizio Illuminati

Published Oct 1, 2015• 42 citations
arXivHTMLPDF

Abstract

The wave packet approach to neutrino oscillations provides an enlightening description of quantum decoherence induced, during propagation, by localization effects. Within this approach, we show that a deeper insight into the dynamical aspects of particle mixing can be obtained if one investigates the behavior of quantum correlations associated to flavor oscillations. By identifying the neutrino three-flavor modes with (suitably defined) three-qubit modes, the exploitation of tools of quantum information theory for mixed states allows a detailed analysis of the dynamical behavior of flavor entanglement during free propagation. This provides further elements leading to a more complete understanding of the phenomenon of neutrino oscillations, and a basis for possible applicative implementations. The analysis is carried out by studying the distribution of the flavor entanglement; to this aim, we perform combined investigations of the behaviors of the two-flavor concurrence and of the logarithmic negativities associated with specific bipartitions of the three flavors.

DOI
10.1209/0295-5075/112/20007

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The wave packet approach to neutrino oscillations provides an enlightening description of quantum decoherence induced, during propagation, by localization effects. Within this approach, we show that a deeper insight into the dynamical aspects of particle mixing can be obtained if one investigates the behavior of quantum correlations associated to flavor oscillations. By identifying the neutrino three-flavor modes with (suitably defined) three-qubit modes, the exploitation of tools of quantum information theory for mixed states allows a detailed analysis of the dynamical behavior of flavor entanglement during free propagation. This provides further elements leading to a more complete understanding of the phenomenon of neutrino oscillations, and a basis for possible applicative implementations. The analysis is carried out by studying the distribution of the flavor entanglement; to this aim, we perform combined investigations of the behaviors of the two-flavor concurrence and of the logarithmic negativities associated with specific bipartitions of the three flavors.
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.
We investigate wave–particle–entanglement complementarity in three-flavor neutrino oscillations within a quantum information–theoretic framework. By considering three-flavor oscillation along with the possible entanglement between the detector and the propagation states, we extend beyond the usual wave-particle duality and arrive at a more complete triality description involving predictability, visibility, and entanglement. Using reduced density matrices and considering I-concurrence as an entanglement measure, we show that the total information carried by the system is conserved and naturally organized through the relation P 2 + V 2 + E 2 = 1 . While predictability and visibility exhibit the expected complementary behavior, we show that entanglement encodes additional wave-like information that is not captured by visibility alone. We apply our formalism to realistic long-baseline neutrino experiments, namely DUNE and T2K , and find that at the first oscillation maximum, a simultaneous characterization of the particle-like and wave-like nature of neutrinos becomes possible through the combined measurement of predictability and entanglement. Our results provide a unified operational interpretation of neutrino oscillations and highlight the role of quantum correlations in extending wave–particle duality to multipartite systems.
Tools of quantum information theory can be exploited to provide a convenient description of the phenomena of particle mixing and flavor oscillations in terms of entanglement, a fundamental quantum resource. We extend such a picture to the domain of quantum field theory where, due to the nontrivial nature of flavor neutrino states, the presence of antiparticles provides additional contributions to flavor entanglement. We use a suitable entanglement measure, the concurrence, that allows extracting the two-mode (flavor) entanglement from the full multimode, multiparticle flavor neutrino states.
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three- qubit modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signatures exhibited by flavor transition probabilities as an effective averaging of the oscillating terms are then explained as owing to loss of entanglement between mass modes involved in the relativistic propagation.
In the physics of flavor mixing, the flavor states are given by superpositions of mass eigenstates. By using the occupation number to define a multiqubit space, the flavor states can be interpreted as multipartite mode-entangled states. By exploiting a suitable global measure of entanglement, based on the entropies related to all possible bipartitions of the system, we analyze the correlation properties of such states in the instances of three- and four-flavor mixing. Depending on the mixing parameters, and, in particular, on the values taken by the free phases, responsible for the CPCPCP-violation, entanglement concentrates in certain bipartitions. We quantify in detail the amount and the distribution of entanglement in the physically relevant cases of flavor mixing in quark and neutrino systems. By using the wave packet description for localized particles, we use the global measure of entanglement, suitably adapted for the instance of multipartite mixed states, to analyze the decoherence, induced by the free evolution dynamics, on the quantum correlations of stationary neutrino beams. We define a decoherence length as the distance associated with the vanishing of the coherent interference effects among massive neutrino states. We investigate the role of the CPCPCP-violating phase in the decoherence process.
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.