We investigate the importance of going beyond the mean-field approximation in the dynamics of collective neutrino oscillations. To expand our understanding of the coherent neutrino oscillation problem, we apply concepts from many-body physics and quantum information theory. Specifically, we use measures of nontrivial correlations (otherwise known as entanglement) between the constituent neutrinos of the many-body system, such as the entanglement entropy and the Bloch vector of the reduced density matrix. The relevance of going beyond the mean field is demonstrated by comparisons between the evolution of the neutrino state in the many-body picture vs the mean-field limit, for different initial conditions.We investigate the importance of going beyond the mean-field approximation in the dynamics of collective neutrino oscillations. To expand our understanding of the coherent neutrino oscillation problem, we apply concepts from many-body physics and quantum information theory. Specifically, we use measures of nontrivial correlations (otherwise known as entanglement) between the constituent neutrinos of the many-body system, such as the entanglement entropy and the Bloch vector of the reduced density matrix. The relevance of going beyond the mean field is demonstrated by comparisons between the evolution of the neutrino state in the many-body picture vs the mean-field limit, for different initial conditions.

Aug 9, 20190 citations

Entanglement and many-body effects in collective neutrino oscillations

Alessandro Roggero

Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in the mean-field approximation show evidence for collective oscillations occurring at timescales much shorter than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using matrix product states and show how collective bipolar oscillations can be triggered by many-body correlations if appropriate initial conditions are present. We find entanglement entropies scaling at most logarithmically in the system size suggesting that classical tensor network methods could be efficient in describing collective neutrino dynamics more generally. These observation provide a clear path forward, not only to increase the accuracy of current simulations, but also to elucidate the mechanism behind collective flavor oscillations without resorting to the mean-field approximation.Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in the mean-field approximation show evidence for collective oscillations occurring at timescales much shorter than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using matrix product states and show how collective bipolar oscillations can be triggered by many-body correlations if appropriate initial conditions are present. We find entanglement entropies scaling at most logarithmically in the system size suggesting that classical tensor network methods could be efficient in describing collective neutrino dynamics more generally. These observation provide a clear path forward, not only to increase the accuracy of current simulations, but also to elucidate the mechanism behind collective flavor oscillations without resorting to the mean-field approximation.

arXiv:2102.10188Physical review. D/Physical review. D.Nov 10, 202157 citations

Many-body neutrino flavor entanglement in a simple dynamic model

Martin, Joshua D., A. Roggero, Huaiyu Duan +1 more

Dense neutrino gases form in extreme astrophysical sites, and the flavor content of the neutrinos likely has an important impact on the subsequent dynamical evolution of their environment. Through coherent forward scattering among neutrinos, the flavor content of the gas evolves under a time-dependent potential which can be modeled in a quantum many-body formalism as an all-to-all coupled spin-spin interaction. This two-body potential generically introduces entanglement and greatly complicates the study of these systems. In this work we study the evolution of the quantum many-body problem as well as the typically employed mean-field approximation to it for a small number of neutrinos ( $N = 16$ ). We consider randomly chosen one- and two-body couplings in the Hamiltonian, and the resulting evolution of several initial product states. We subsequently compare many-body and mean-field predictions for one-body observables, and we consider one- and two-body entanglement to assess under what conditions the many-body and mean-field predictions are likely to disagree. Except for a special category of prototypical initial conditions, we find that the typically employed mean-field approximation is insufficient to capture the evolution of one-body operators in the systems we consider. We also observe a loss of coherence in one- and two-body trace-reduced subsystems which suggests that the evolution may be well approximated as a classical mixture of separable states.Dense neutrino gases form in extreme astrophysical sites, and the flavor content of the neutrinos likely has an important impact on the subsequent dynamical evolution of their environment. Through coherent forward scattering among neutrinos, the flavor content of the gas evolves under a time-dependent potential which can be modeled in a quantum many-body formalism as an all-to-all coupled spin-spin interaction. This two-body potential generically introduces entanglement and greatly complicates the study of these systems. In this work we study the evolution of the quantum many-body problem as well as the typically employed mean-field approximation to it for a small number of neutrinos ($N = 16$). We consider randomly chosen one- and two-body couplings in the Hamiltonian, and the resulting evolution of several initial product states. We subsequently compare many-body and mean-field predictions for one-body observables, and we consider one- and two-body entanglement to assess under what conditions the many-body and mean-field predictions are likely to disagree. Except for a special category of prototypical initial conditions, we find that the typically employed mean-field approximation is insufficient to capture the evolution of one-body operators in the systems we consider. We also observe a loss of coherence in one- and two-body trace-reduced subsystems which suggests that the evolution may be well approximated as a classical mixture of separable states.

arXiv:2301.07049Jan 17, 20231 citation

Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems

Marc Illa, Martin J. Savage A

The time evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum's H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle rescalings are found to converge for large system sizes, signaling the presence of genuine multi-neutrino entanglement.The time evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum's H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle rescalings are found to converge for large system sizes, signaling the presence of genuine multi-neutrino entanglement.

arXiv:2210.08656Physical Review LettersMay 31, 202342 citations

Coherent dynamics of flavor mode entangled neutrinos

Ashutosh Kumar Alok, Massimo Blasone A, Trambak Jyoti Chall +2 more

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.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.

Nuclear Physics BJul 27, 20261 citation

Collective neutrino oscillations with tensor networks using a time-dependent variational principle

Michael J. Cervia, Pooja Siwach, Amol V. Patwardhan +3 more

If a system of flavor-oscillating neutrinos is at high enough densities that neutrino-neutrino coherent forward scatterings are non-negligible, the system becomes a time-dependent many-body problem. An important and open question is whether the flavor evolution is sufficiently described by a mean-field approach or can be strongly affected by correlations arising from two-body interactions in the neutrino Hamiltonian, as measured by nontrivial quantum entanglement. Numerical computations of the time evolution of many-body quantum systems are challenging because the size of the Hilbert space scales exponentially with the number of particles $N$ in the system. Thus, it is important to investigate approximate but beyond-mean-field numerical treatments at larger values of $N$ . Here we investigate the efficacy of tensor network methods to calculate the time evolution of interacting neutrinos at larger values of $N$ than are possible with conventional methods. In particular, we introduce the use of time-dependent variational principle methods to address the long-range (in momentum space) interactions of the neutrino Hamiltonian when including many distinct vacuum oscillation frequencies. We also define new error measures based upon the instantaneously conserved charge operators known for this Hamiltonian to determine validity of large- $N$ tensor network calculations.If a system of flavor-oscillating neutrinos is at high enough densities that neutrino-neutrino coherent forward scatterings are non-negligible, the system becomes a time-dependent many-body problem. An important and open question is whether the flavor evolution is sufficiently described by a mean-field approach or can be strongly affected by correlations arising from two-body interactions in the neutrino Hamiltonian, as measured by nontrivial quantum entanglement. Numerical computations of the time evolution of many-body quantum systems are challenging because the size of the Hilbert space scales exponentially with the number of particles $N$ in the system. Thus, it is important to investigate approximate but beyond-mean-field numerical treatments at larger values of $N$. Here we investigate the efficacy of tensor network methods to calculate the time evolution of interacting neutrinos at larger values of $N$ than are possible with conventional methods. In particular, we introduce the use of time-dependent variational principle methods to address the long-range (in momentum space) interactions of the neutrino Hamiltonian when including many distinct vacuum oscillation frequencies. We also define new error measures based upon the instantaneously conserved charge operators known for this Hamiltonian to determine validity of large-$N$ tensor network calculations.

arXiv:2202.01865Physical review. D/Physical review. D.Jun 22, 202235 citations

N = 16

). We consider randomly chosen one- and two-body couplings in the Hamiltonian, and the resulting evolution of several initial product states. We subsequently compare many-body and mean-field predictions for one-body observables, and we consider one- and two-body entanglement to assess under what conditions the many-body and mean-field predictions are likely to disagree. Except for a special category of prototypical initial conditions, we find that the typically employed mean-field approximation is insufficient to capture the evolution of one-body operators in the systems we consider. We also observe a loss of coherence in one- and two-body trace-reduced subsystems which suggests that the evolution may be well approximated as a classical mixture of separable states.

N

in the system. Thus, it is important to investigate approximate but beyond-mean-field numerical treatments at larger values of

N

. Here we investigate the efficacy of tensor network methods to calculate the time evolution of interacting neutrinos at larger values of

N

than are possible with conventional methods. In particular, we introduce the use of time-dependent variational principle methods to address the long-range (in momentum space) interactions of the neutrino Hamiltonian when including many distinct vacuum oscillation frequencies. We also define new error measures based upon the instantaneously conserved charge operators known for this Hamiltonian to determine validity of large-

N

tensor network calculations.