Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions

arXiv:2602.03748 · hep-ph, quant-ph · Submitted 2026-02-03 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions".

Mira: The gist: The study investigates how non-standard interactions modify bipartite entanglement and its quantum speed limit time during neutrino oscillations in matter,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're looking at this paper called "Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions." It tackles how those nonstandard interactions change the entanglement and how that relates to the quantum speed limit time during neutrino oscillations.

Mira: Right, it's all about treating the neutrino flavor states like bipartite systems, mapping them to three-qubit mode states, and then using entanglement entropy and capacity of entanglement to track how these things evolve over distance.

Lev: It seems like they use this mode entanglement framework, which is interesting because it lets them map the flavor states onto these specific qubit structures where you can measure the transition probabilities directly.

Kai: Exactly, they start by setting up the time evolution of an initial muon-flavor neutrino state as a linear superposition of these three-qubit mode basis states. Then they get this density matrix for the length-evolved state νµ(L)⟩ which is defined by those transition probabilities P(νµ → νμ) and P(νµ → νe) + P(νµ → ντ).

Mira: And from that, they derive two specific entanglement measures, entanglement entropy S EE and capacity of entanglement CE. For example, the text says S EE is defined as negative eta three L log two eta three L minus eta four L log two eta four L.

Lev: That definition for the entropy measure links directly to those transition probabilities P(νµ → νμ) and P(νµ → νe) plus P(νµ → ντ), which is what you'd expect to see in an actual neutrino oscillation experiment.

Kai: The main finding they report there is that for any length L greater than zero, the evolved muon-flavor neutrino state νµ(L)⟩ ends up being a pure bipartite entangled state. Plus, they found that maximally pure bipartite entanglement can exist during the evolution of the initial muon-flavor neutrino state in all four scenarios they tested.

Mira: That purity result is important because it shows that even after propagation through matter with these nonstandard interactions, the state retains some form of strong correlation between those two subsystems.

Lev: But then they move on to looking at how fast this entanglement evolves, and that's where the quantum speed limit time comes in. They define T E QSL using a formula involving the variance of the driving Hamiltonian delta H f tot one over L R L zero p dCE(ρµe(L)) dl.

Kai: That QSL time bound tells us something about how fast bipartite entanglement can change, specifically if the ratio of that bound to the propagation time is one, it means no speedup is possible.

Title and authors: Mira: And if that ratio is less than one, then there's potential for further speedup in the evolution of this entanglement. So they are essentially using these measures to set a physical limit on how quickly this quantum correlation can develop during oscillation.

Lev: They then explore the impact of nonstandard interactions by considering four scenarios: SO+NO, SO+IO, NSI+NO, and NSI+IO, which cover different types of complex off-diagonal and diagonal parameters.

Kai: The paper points out that the off-diagonal NSI parameter epsilon mu tau has been observed to be the most pronounced deviation from the standard oscillation scenarios for all probability channels.

Mira: That's a significant finding because it singles out one specific type of nonstandard interaction as having the biggest effect across different ways we measure neutrino oscillations.

Lev: Specifically, in DUNE's tau appearance channels, the paper notes that the standard oscillation scenario doesn't give a clear distinction between NO and IO for baseline lengths around one thousand to one thousand one hundred kilometers when those NSI effects are included.

Kai: But they found that this behavior reverses toward the end of the baseline, which suggests these long-baseline experiments might be able to see signatures of physics beyond the standard model.

Mira: It really emphasizes how important it is for these long-baseline experiments to look at those specific NSI effects if they want to find new physics.

Lev: Now, moving into their improvements, they suggest using these bipartite entanglement measures—entanglement entropy and capacity of entanglement—to predict the quantum speed limit time with high precision across different mass orderings and NSI scenarios.

Kai: That sounds like a big step for AI systems in this field because it would let them actually predict the QSL time for bipartite entanglement based on those transition probabilities.

Mira: And they also suggest that AI could be enhanced to discriminate between different physical models by analyzing those most pronounced discrepancies in the QSL time, especially highlighting how much the off-diagonal NSI parameter epsilon mu tau affects things in both NO and IO scenarios.

Lev: For real hardware, this means the AI could be trained to identify experimental signatures of new physics by detecting when DUNE or NOnuA show a rapid suppression of bipartite entanglement in standard oscillation with NO at the end of their baselines for the best-fit CP-violating phase.

Kai: And they also suggest that AI systems can do automated parameter estimation by correlating measured transition probabilities like P(νµ → νe) with complex NSI parameters such as epsilon e mu and epsilon e tau across various baseline configurations, to figure out the most likely beyond standard model framework.

Title and authors: Mira: They also propose a way for the AI to determine if a neutrino state is in a maximally pure bipartite entangled state by checking when both transition probabilities P(νµ → νμ) and P(νµ → νe) plus P(νµ → ντ) are both equal to one over two.

Lev: And finally, the QSL time bound ratio, T E QSL over T less than or equal to one three, can be used by AI systems to evaluate the speed at which entanglement evolves and distinguish between cases where it could be sped up versus where it's already at its maximum speed.

Kai: It’s interesting how they found that bipartite entanglement grows fastest in the epsilon mu tau plus IO case while being rapidly suppressed in the SO plus NO case compared to the other scenarios at the end of NOnuA and DUNE baselines.

Mira: In contrast, for other complex off-diagonal NSI parameters like epsilon e mu and epsilon e tau, bipartite entanglement grows fastest in the SO plus IO case and is rapidly suppressed in the SO plus NO compared to those remaining scenarios.

Lev: And when they look at the diagonal NSI parameter delta tau tau minus delta mu mu, they find that bipartite entanglement grows fastest in the delta tau tau minus delta mu mu plus IO case and is rapidly suppressed in the delta tau tau minus delta mu mu plus NO case at the end of the DUNE baseline.

Kai: So, to wrap this up, they show that at specific baselines of T2K, NOnuA, and DUNE with best-fit CP-violating phases, the initial muon-flavor neutrino state νµ⟩ exhibits a Bell-like state in all four scenarios.

Mira: But they clarify that T2K is unable to capture differences in the evolution speed of that entangled muon-flavor neutrino state among those different scenarios, whereas those distinctions are clearly resolved in NOnuA and DUNE.

Lev: Overall, these findings can help us understand the impact of CP violation and in identifying the neutrino mass ordering in matter when NSIs are present.

Kai: The paper "Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions" gives us a detailed look at how nonstandard interactions modify bipartite entanglement and its quantum speed limit time during neutrino oscillations.

Mira: It’s a study that uses mode entanglement to quantify these effects using entropy and capacity of entanglement, showing that the evolution is pure entangled for all L greater than zero.

Lev: And it lays out a path forward by suggesting how AI can use these measures to predict QSL times and identify experimental signatures based on those suppression behaviors in DUNE and NOnuA.

The paper's summary: Kai: So, this paper looks at how nonstandard interactions mess with bipartite entanglement and the quantum speed limit time during neutrino oscillations in matter, right?

Mira: Right, essentially they're taking neutrino flavors and treating them like two separate quantum systems that are entangled, mapping them onto three-qubit mode states to track their evolution over distance.

Lev: And then they use these entanglement measures, specifically entanglement entropy and capacity of entanglement, tied directly to the transition probabilities you see in experiments.

Kai: The core finding is that no matter the length L you go out, the neutrino state after propagating through matter with these nonstandard interactions is a pure bipartite entangled state.

Mira: That purity result is interesting because it means that even with these extra interactions at play, there's still a strong correlation between those two subsystems.

Lev: But they also calculate this quantum speed limit time bound, T E QSL using the variance of the driving Hamiltonian and the entanglement measures to see how fast that entanglement can evolve.

Kai: And what that bound tells us is if we take the ratio of that bound to your propagation time L, it means if it's one, you can't speed up this entanglement evolution, but if it's less than one, there’s a chance for further speedup.

Mira: They then look at different types of nonstandard interactions—off-diagonal and diagonal parameters—and they find that the off-diagonal parameter epsilon mu tau is the most noticeable deviation from standard oscillation scenarios for all probability channels.

Lev: That specific parameter, epsilon mu tau, really drives the strongest effects across all the measurement channels in this study.

Kai: And they point out a specific experimental signature: in DUNE's tau appearance channels, you can't really tell if it's NO or IO at baseline lengths around one thousand to one thousand one hundred kilometers when you include these NSI effects.

Mira: But that distinction reverses toward the end of the baseline, which suggests that long-baseline experiments like DUNE might actually be able to see signs of physics beyond the standard model with these interactions.

Lev: That's a bit more complex than just seeing a signal; it's about how certain NSI types cause this specific entanglement behavior to grow fastest in some cases and get rapidly suppressed in others at the end of those baselines.

Kai: For instance, they found that bipartite entanglement grows fastest in the epsilon mu tau plus IO case, but it gets quickly suppressed in the SO plus NO case when you look at the end of both NOnuA and DUNE baselines.

Mira: In contrast, for other off-diagonal parameters like epsilon e mu or epsilon e tau, that same SO plus NO scenario suppresses entanglement relative to the IO case at those same distances.

Lev: And even with diagonal NSI parameters, they found a similar trend where entanglement is suppressed in the NO case compared to other scenarios at the end of the DUNE baseline.

Kai: So, to summarize, these findings show that while all scenarios end up in a pure entangled state after propagation, the speed at which that entanglement grows or shrinks is highly sensitive to which nonstandard interaction you're dealing with and where you are in terms of baseline.

Mira: It also gives us a way to use this information—the transition probabilities and those entanglement measures—to predict the quantum speed limit time with high precision across different mass orderings and NSI scenarios.

Lev: And for AI, it means the system could be trained to spot those specific suppression behaviors at DUNE or NOnuA when you have a best-fit CP-violating phase, or even identify which diagonal NSI parameters have the most prominent impact in appearance channels with strong matter effects.

Kai: Plus, the paper suggests that AI can do automated parameter estimation by correlating measured transition probabilities like P(nu mu to nu e) with those complex NSI parameters across all those different baseline lengths to figure out the most likely beyond standard model framework.

Mira: And they even propose a way for AI to check if a neutrino state is in a maximally pure bipartite entangled state just by looking at whether both transition probabilities are exactly one over two.

Lev: And finally, using that T E QSL over T less than or equal to one three ratio, the AI could evaluate how fast the entanglement is evolving and tell you if it's already at its maximum speed or if there’s still room for it to speed up.

Kai: It really hammers home that while T2K can't tell all these differences about evolution speed, NOnuA and DUNE are where you actually see those distinctions clearly.

The paper's improvements: Tom: So, this paper lays out some ways to use AI to actually make sense of these entanglement measures and speed limits in neutrino physics, right?

Kai: Yeah, they’re suggesting that AI could predict the quantum speed limit time for bipartite entanglement with high precision across different mass orderings and NSI scenarios based on those transition probabilities.

Mira: That would be useful because it lets the AI model how fast that correlation is evolving under all those different physical conditions.

Lev: It’s a big leap because right now, running that kind of simulation on real hardware with error correction overhead is pretty intensive, so an accurate AI predictor would save a lot of computational time.

Kai: And they also think AI could be trained to discriminate between different physical models by analyzing the most pronounced discrepancies in the QSL time, specifically highlighting how much that off-diagonal NSI parameter epsilon mu tau affects things in both NO and IO scenarios.

Mira: That would let us really pinpoint which specific new physics interaction—like that epsilon mu tau one—is actually causing the biggest change in behavior.

Lev: For real experiments, that means the AI could be trained to detect experimental signatures of new physics by spotting when DUNE or NOnuA show a rapid suppression of bipartite entanglement in standard oscillation with NO at the end of their baselines for the best-fit CP-violating phase.

Kai: And they also suggest that AI systems can do automated parameter estimation by correlating measured transition probabilities like P(nu mu to nu e) with those complex NSI parameters like epsilon e mu and epsilon e tau across various baseline configurations to figure out the most likely beyond standard model framework.

Mira: That correlation approach seems very powerful because it lets the AI look at all the data points simultaneously instead of just one measurement in isolation.

Lev: They also propose a way for the AI to determine if a neutrino state is in that maximally pure bipartite entangled state by checking when both transition probabilities P(nu mu to nu mu) and P(nu mu to nu e) plus P(nu mu to nu tau) are both equal to one over two.

Kai: That's a clear way for the AI to check if we're looking at a state that’s in that maximally pure entangled state, which is when those transition probabilities both hit that one over two mark.

Mira: And they also suggest using the QSL time bound ratio, T E QSL over T less than or equal to one three, to evaluate the speed at which entanglement evolves and distinguish between cases where it could be sped up versus where it's already at its maximum speed.

Lev: That ratio gives a direct physical metric for whether the system is still evolving fast or if it’s reached equilibrium in terms of entanglement dynamics.

Kai: So, to wrap this up, these improvements show that the next step is moving towards using AI not just to analyze data but to actually predict and identify those specific entanglement behaviors based on those transition probabilities.

Conclusion: Kai: So to wrap up, this paper "Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions" shows how we can use these entanglement measures to predict the quantum speed limit time with high precision across different mass orderings and NSI scenarios.

Mira: Basically, it confirms that the evolution is pure entangled for any length L greater than zero, which is a pretty solid result based on those assumptions about the modes and their evolution.

Lev: From an error-correction standpoint, this means if we try to build hardware to simulate these oscillations, we need to account for the complexity of those nonstandard interaction Hamiltonians when calculating the overhead.

Kai: And they also suggest that AI can be trained to spot those specific suppression behaviors at DUNE or NOnuA when you have a best-fit CP-violating phase, which is a practical way to find new physics signatures.

Mira: It’s interesting how the study links these abstract quantum entanglement measures directly to observable neutrino transition probabilities like P(nu mu to nu e), which makes it much more tangible for experimentalists.

Lev: If we take that AI correlation idea, it could automate the process of parameter estimation by linking measured data points to those complex NSI parameters, which is exactly what we need for real hardware modeling.

Kai: It really shows that the measurements themselves are rich enough to provide a lot of information about the underlying physics, even when we introduce these nonstandard interactions into our flavor states.

Mira: The paper gives us a clear roadmap for using quantum speed limit time as a tool to probe how different types of nonstandard interactions modify neutrino oscillation dynamics over distance.

Lev: It’s a useful framework because it sets concrete bounds on how fast this entanglement can change, which is something you need to consider when designing any future experiment or simulation setup.

Kai: We’re excited to see how this information feeds into the next phase of experimental design, especially for those long-baseline experiments where these effects become most pronounced.

Mira: Next time we look at a paper, we'll be diving into something that explores topological order in finite-temperature three dee Z two Toric Code, which is quite different from this neutrino work.

Lev: And we’ll see how those topological concepts relate to the constraints on transport and temperature in one-dimensional infinite U Hubbard models.

Abhishek Kumar Jha, Lekhashri Konwar, Rukmani Mohanta

Indian Institute of Science Bangalore · Indian Institute of Technology Jodhpur · University of Hyderabad

hep-ph, quant-ph

Submitted: 2026-02-03

Updated: 2026-10-14

Comments: v1: 27 pages, 11 figures, 3 tables. Matches the published version

Journal ref: Phys. Rev. D 114, 076011 (2026)

DOI: 10.1103/r6t7-wnbz

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 80/100

The gist: The gist: The study investigates how non-standard interactions modify bipartite entanglement and its quantum speed limit time during neutrino oscillations in matter, revealing that these effects are

Key concepts

Mode Entanglement Framework
This framework treats neutrino flavor states as bipartite quantum systems. It maps initial flavor eigenstates onto three-qubit mode states to describe their evolution. This allows researchers to analyze the entanglement between different neutrino flavors over time, treating the oscillation process as a quantum evolution.
Entanglement Entropy (S EE)
This measure quantifies how entangled the muon and electron neutrino subsystems are at a given time. It is calculated using the von Neumann entropy of the reduced density matrix. A higher S EE indicates stronger entanglement between these two flavor states, which is directly related to transition probabilities.
Quantum Speed Limit Time (QSL)
The QSL time describes the maximum rate at which bipartite entanglement can evolve during neutrino oscillations. It sets a fundamental limit on how quickly this quantum correlation can change. Analyzing QSL helps determine if entanglement evolution is faster or slower than allowed by quantum mechanics.
Non-Standard Interactions (NSIs)
NSIs refer to physics beyond the Standard Model that modifies neutrino interactions. This study focuses on complex off-diagonal parameters ($\epsilon_{\alpha\beta}$) and diagonal parameters ($\epsilon_{\alpha\alpha} - \epsilon_{\beta\beta}$) that influence the oscillation probabilities, potentially leading to new physical signatures.

Terminology

Summary

The gist: The study investigates how non-standard interactions modify bipartite entanglement and its quantum speed limit time during neutrino oscillations in matter, revealing that these effects are most pronounced at long baselines and in specific scenarios involving different types of non-standard interactions.

Theoretical Framework

The analysis utilizes the mode-entanglement framework, treating neutrino flavor states as bipartite quantum systems and mapping the initial flavor eigenstates to three-qubit mode states νe⟩ ≡ 1⟩e ⊗ 0⟩µ ⊗ 0⟩τ ≡ 100>, etc. The time evolution of the initial muon-flavor neutrino state is expressed as a linear superposition of the three-qubit mode (flavor) basis states. The density matrix of the length-evolved muon–flavor neutrino state νµ(L)⟩ is given by a specific structure involving transition probabilities. This pure bipartite quantum state is then bipartitioned to obtain reduced density matrices ρµe(L) and ρτ(L), whose eigenvalues η3(L) and η4(L) are related to the transition probabilities P(νµ → νμ) and P(νµ → νe) + P(νµ → ντ), respectively.

Entanglement Measures

Two bipartite entanglement measures, entanglement entropy (S EE) and capacity of entanglement (CE), are quantified in terms of the neutrino transition probabilities. The entanglement entropy is defined as the von Neumann entropy of the reduced state ρµe(L), expressed as S EE = -η3(L) log2 η3(L) − η4(L) log2 η4(L). The capacity of entanglement is given by CE = - η3(L) log2 2η3(L) − η4(L) log2 4η4(L) − (−η3(L) log2 η3(L) − η4(L))2. These measures show that for L > 0, the evolved muon-flavor neutrino state νµ(L)⟩ is a pure bipartite entangled state and that maximally pure bipartite entanglement can exist during the evolution of the initial muon-flavor neutrino state in all four cases.

Impact of Non-Standard Interactions (NSI)

The study considers both complex off-diagonal (ϵαβe iϕαβ) and diagonal (ϵαα − ϵββ) NSI parameters and explores the evolution under four scenarios: SO+NO, SO+IO, NSI+NO, and NSI+IO. The off-diagonal NSI parameter ϵµτ has been observed to be the most pronounced deviation from the standard oscillation (SO) scenarios for all probability channels. Specifically, in DUNE's ντ appearance channels, the SO scenario does not provide a clear distinction between NO and IO for baseline lengths of approximately 1000–1100 km when NSI effects are included, but this behavior is reversed toward the end of the baseline and underscores the capability of long-baseline experiments to possible signatures of physics BSM.

Quantum Speed Limit Time (QSL)

The quantum speed limit (QSL) time for bipartite entanglement in the time-evolved state Ψ(t)⟩ is given by T E QSL = S EE(T) − S EE(0)2∆H1 / T R T0√C E(t) dt. This bound implies that if the ratio of the QSL time bound to the propagation time is 1, bipartite entanglement cannot be speeded up and if it is less than 1, there is potential for further speedup. The QSL time for bipartite entanglement in neutrino oscillations under SO with NSI effects can be quantified as τ E QSL(L) = ∫ S EE(ρµe(L))2∆H f tot1 / L R L0 p dCE(ρµe(L)) dl.

Experimental Findings and Conclusion

The analysis uses baseline lengths and energies corresponding to T2K, NOνA, and DUNE experiments. The results show that at specific baselines of T2K, NOνA and DUNE, with best-fit CP-violating phases, the initial muon-flavor neutrino state νµ⟩ propagating in all four cases exhibits a Bell-like state. In general, T2K is unable to capture differences in the evolution speed of the entangled muon-flavor neutrino state among the different scenarios considered, whereas such distinctions are clearly resolved in NOνA and DUNE. The findings can aid in understanding the impact of CP violation and in identifying the neutrino mass ordering in matter when NSIs are present.

How it works

  1. The initial muon-flavor neutrino state νµ⟩ is mapped onto a three-qubit mode as νe⟩ ≡ 1⟩e ⊗ 0⟩µ ⊗ 0⟩τ ≡ 100>, etc.

  2. The evolution equation of the initial flavor state in SO with NSI effects after propagating a distance L is expressed as a linear superposition of the three-qubit mode (flavor) basis states.

  3. The entanglement entropy and capacity of entanglement are quantified in terms of neutrino transition probabilities P(νµ → νμ) and P(νµ → νe) + P(νµ → ντ).

  4. The QSL time for bipartite entanglement is determined using the variance of the driving Hamiltonian ∆H f tot and the entanglement measures S EE and CE.

How it works

  1. The off-diagonal NSI parameter ϵµτ has been observed to be the most pronounced deviation from the SO scenarios for all probability channels.

  2. In DUNE's ντ appearance channels, the SO scenario does not provide a clear distinction between the NO and IO for baseline lengths of approximately 1000–1100 km when NSI effects are included.

  3. The QSL time for bipartite entanglement in DUNE shows a greater discrepancy in τ E QSL among the four cases compared to NOνA.

How it works

  1. At specific baselines of T2K, NOνA and DUNE, with best-fit CP-violating phases, the initial muon-flavor neutrino state νµ⟩ propagating in all four cases exhibits a Bell-like state.

  2. In general, T2K is unable to capture differences in the evolution speed of the entangled muon-flavor neutrino state among the different scenarios considered, whereas such distinctions are clearly resolved in NOνA and DUNE.

  3. The results can aid in understanding the impact of CP violation and in identifying the neutrino mass ordering in matter when NSIs are present.

How it works

  1. Bipartite entanglement grows fastest in the ϵµτ+IO case, while it is rapidly suppressed in the SO+NO case compared to the other scenarios at the end of the NOνA and DUNE baselines.

  2. In contrast, for other complex off-diagonal NSI parameters, namely ϵeµ and ϵeτ, bipartite entanglement grows fastest in the SO+IO case and is rapidly suppressed in the SO+NO case relative to the remaining scenarios.

  3. When we have used the diagonal NSI parameter ϵττ - ϵµµ, bipartite entanglement grows fastest in the ϵττ - ϵµµ+IO case and is rapidly suppressed in the ϵττ - ϵµµ+NO case compared to the other cases at the end of the DUNE baseline.

How it works

  1. The QSL time for bipartite entanglement in DUNE shows a greater discrepancy in τ E QSL among the four cases compared to NOνA near the end of their respective baselines.

  2. In the presence of the complex off-diagonal NSI parameter ϵµτ, bipartite entanglement grows fastest in the ϵµτ+IO case, while it is rapidly suppressed in the SO+NO case compared to other scenarios at the end of DUNE baseline.

  3. The results can be attributed to the S EE behaviors shown in Figs. 3e.

How it works

  1. The QSL time for bipartite entanglement in all four cases at the end of their baselines is governed by empirical relations derived from the behavior of S EE and CE.

  2. In both NOνA and DUNE, at the end of their baselines, bipartite entanglement grows fastest in the ϵee - ϵµµ+IO case, while it is rapidly suppressed in SO+NO compared to other cases.

  3. These results can be attributed to the S EE behaviors shown in Figs.

Improvements for AI systems

  1. We can improve AI systems by enabling them to predict the quantum speed limit time for bipartite entanglement in neutrino oscillations with high precision across different mass orderings (NO/IO) and NSI scenarios, as this is quantified by the measures entanglement entropy and capacity of entanglement.

  2. AI systems could be enhanced to discriminate between different physical models by analyzing the most pronounced discrepancies in the QSL time for bipartite entanglement, specifically highlighting that the most pronounced discrepancies in the QSL time for bipartite entanglement arise from the off-diagonal NSI parameter ϵµτ across both the NO and IO scenarios.

  3. The AI can be trained to identify experimental signatures of new physics by detecting when "NOνA and DUNE exhibit a rapid suppression of bipartite entanglement in neutrino oscillations in the standard oscillation scenario with NO at the end of their baseline lengths for the corresponding best-fit value of CP-violating phase."

  4. AI systems can perform automated parameter estimation by correlating measured transition probabilities, such as P(νµ → νe), with the complex NSI parameters (like ϵeµ and ϵeτ) across various baseline configurations (T2K, NOνA, DUNE) to determine the most likely BSM framework.

  5. The system can be equipped to determine if a neutrino state is in a maximally pure bipartite entangled state, as this is achieved when the transition probabilities P(νµ → νµ) and P(νµ → νe) + P(νµ → ντ) (or η3(L) and η4(L) in Eq. (22)) both equal to 1/2.

  6. AI systems can utilize the QSL time bound ratio, T E QSL/T ≤ 1 (3), to evaluate the speed at which entanglement evolves, distinguishing between cases where the bipartite entanglement in the time-evolved state could be speed up versus where it is already at its maximum speed.

  7. The AI can be specifically tuned to identify which diagonal NSI parameters have a more noticeable impact, as the paper notes that for the diagonal parameter ϵee − ϵµµ, the impact is more prominent in appearance channels and in experiments with strong matter effects.

Sources

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