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arXiv:1607.00529 · New Journal of Physics

Quantum walks as simulators of neutrino oscillations in a vacuum and matter

Giuseppe Di Molfetta, Armando Pérez

Published Oct 21, 2016• 72 citations
arXivHTMLPDF

Abstract

We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae.

DOI
10.1088/1367-2630/18/10/103038

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We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae.
We simulate three-flavor neutrino oscillations on two-qubit quantum circuits. The flavor space is embedded as ∣00⟩=νe\ket{00}=ν_e∣00⟩=νe​, ∣01⟩=νμ\ket{01}=ν_μ∣01⟩=νμ​, ∣10⟩=ντ\ket{10}=ν_τ∣10⟩=ντ​ with the ∣11⟩\ket{11}∣11⟩ channel kept inert, and the input mixing parameters (NuFIT~5.3, normal ordering, with SK-atm) follow the global fit. We verify three physical settings against analytic or exact references: vacuum propagation, reproduced by a mass-eigenstate phase circuit to ∼10−16\sim 10^{-16}∼10−16; constant-density Mikheev--Smirnov--Wolfenstein (MSW) matter effects, showing resonant flavor conversion when the matter potential AAA crosses Δm312Δm^2_{31}Δm312​; and varying-density (supernova shock-shell) propagation by slicing plus second-order Suzuki--Trotter splitting, with per-slice Trotter error ∼10−6\sim 10^{-6}∼10−6 and total accuracy ∼10−4\sim 10^{-4}∼10−4 against the continuous profile. We report a Suzuki--Trotter precision--resource calibration varying order, step number, and matrix/probability error. It delimits brute-force Trotterization on solar baselines: we quantify both standard alternatives, coherence averaging and adiabatic MSW. We also compute quantum-information diagnostics from the same model parameters, namely mode entanglement and the CP asymmetry. Finally, we extend the framework to open quantum systems via a Lindblad master equation with dephasing and absorptive channels. These results provide a reproducible link between low-energy oscillation observables and quantum-information measures.
Quantum simulation is an important way to study the Dirac particles in a general situation. Discrete quantum walk (DQW), is a powerful quantum simulation scheme, and implementable in well controllable table-top set-ups. We first identify that the conventional DQW can't exactly simulate Dirac Cellular Automaton (DCA), a discretized theory of free Dirac Hamiltonian (DH). We found some choice of coin parameters of the split-step (SS) DQW, a generalization of DQW can fully simulate single-particle DCA. Next we question whether the same SS-DQW can simulate dynamics of free Dirac particle with extra degrees of freedom like colors, flavors besides the spin or chirality. One such example is Neutrino oscillation. By moving from the U(2) coined SS-DQW to the U(6) coined SS-DQW we have simulated the exact probability profile of Neutrino flavor transitions. We further probe towards simulating single particle massive DH in presence of background potentials and space-time curvature. By using a SS-DQW with position-time dependent coin parameters, and we realize that it will give us an unbounded effective Hamiltonian, at the continuum limit of position-time. So we have introduced a modified version of SS-DQW which will produce a bounded effective Hamiltonian. This modified SS-DQW with U(2) coin operations produces single-particle massive DH in presence of abelian gauge potentials and space-time curvature. Introducing higher dimensional---U(N) coin operations in the modified SS-DQW we can include non-abelian potentials in the same DH. In order to simulate two-particle DH in presence of curved space-time and external potentials, we have used two particle modified SS-DQW, where the shift operations act separately on each particle, the coin operations which act simultaneously on both particles contain all kinds of interactions.
Here we present neutrino oscillation in the framework of quantum walks. Starting from a one spatial dimensional discrete-time quantum walk we present a scheme of evolutions that will simulate neutrino oscillation. The set of quantum walk parameters which is required to reproduce the oscillation probability profile obtained in both, long range and short range neutrino experiment is explicitly presented. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental set-up with access to control a single six-level system, a multiparticle three-qubit or a qubit–qutrit system. We also present the entanglement between spins and position space, during neutrino propagation that will quantify the wave function delocalization around instantaneous average position of the neutrino. This work will contribute towards understanding neutrino oscillation in the framework of the quantum information perspective.
Considering the neutrino state like an open quantum system, we analyze its propagation in vacuum or in matter. After defining what can be called decoherence and relaxation effects, we show that in general the probabilities in vacuum and in constant matter can be written in a similar way, which is not an obvious result in this approach. From this result, we analyze the situation where neutrinos evolution satisfies the adiabatic limit and use this formalim to study solar neutrinos. We show that the decoherence effect may not be bounded by the solar neutrino data and review some results in the literature. We discuss the current results where solar neutrinos were used to put bounds on decoherence effects through a model-dependent approach. We conclude explaining how and why this models are not general and we reinterpret these constraints.
In this paper, we investigate the entanglement entropy associated with neutrino oscillations in matter, employing the framework of Von Neumann entropy. Our study focuses on two-flavor neutrino oscillations, both in vacuum and in matter. We statistically analyze how the entanglement entropy evolves over successive oscillation periods, depending on the oscillation length at various energy scales. Our findings provide new insights into the role of entanglement entropy in characterizing the quantum behavior of neutrino oscillations in matter.
Abstract Quantum simulation of particle phenomena is a rapidly advancing field of research. With the widespread availability of quantum simulators, a given quantum system can be simulated in numerous ways, offering flexibility in implementation and exploration. Here, we perform quantum simulation of neutrino propagation in matter, a phenomenon that plays a crucial role in neutrino oscillations. We present quantum circuits with novel gate arrangements to simulate neutrino propagation in both constant and varying matter density profiles. The oscillation probabilities are determined by encoding and measuring the qubit states in the neutrino flavor basis, showing excellent agreement with theoretical predictions.