In this thesis we study the robustness of entanglement in the B0 meson pairs at the Belle II and if andhow different quantum states can be distinguished. The first objective is to quantitatively analyse the influence of CP violation and ∆Γ ̸= 0 on concurrence, which is used to measure entanglement, of the quantum states |ψ−⟩ =1/√2 (|B0B ̄0 − |B ̄0B0⟩⟩) and |ψ⟩ = 1/2 [(|B0B ̄0⟩ − |B ̄0B0⟩) + i(|B0B ̄0⟩ + |B ̄0B0⟩)]. For the first state it remains constanteven for CP violation but for the second it is possible to see the effects of the parameters in discussion. Furthermore we study scattering among the B mesons in vacuum, scattering with matter and finally radiative emission at Υ(5S), the first scenario is rather trivial due to the simplified assumptions, such as only strong/electromagnetic interactions. As result one observes no change in the concurrence, which is therefore concluded to be affected only by weak interaction (mixing). The second and third scenarios are investigated with the help of open quantum systems and for both the concurrence decreases after the application of the quantum channels built with Kraus operators. At the last part of the thesis the relations between entanglement and the measurement basis are studied introducing an arbitrary phase φ in the Bloch sphere representation. One finds that |ψ(φ)⟩ can violate CHSH or not depending on φ and the choice of the measurement basis. The distinction of states on the equator of the Bloch sphere is possible using the correlation function Ef1,f2(t1,t2) constructed for flavor and CP tags. Further it is also possible to distinguish entangled states of the family |ψ(φ)⟩ from some separable states also using the correlation function and choosing the flavor-CP tag. A distinction of any kind using only flavor tags on both arms of the correlation function is shown not to be possible. Finally we show that the CP-violating parameter Cf and Sf , used to measure CP violation, are biased if a wrong assumption on the nature of the quantum state is made.
In this thesis we study the robustness of entanglement in the B0 meson pairs at the Belle II and if andhow different quantum states can be distinguished. The first objective is to quantitatively analyse the influence of CP violation and ∆Γ ̸= 0 on concurrence, which is used to measure entanglement, of the quantum states |ψ−⟩ =1/√2 (|B0B ̄0 − |B ̄0B0⟩⟩) and |ψ⟩ = 1/2 [(|B0B ̄0⟩ − |B ̄0B0⟩) + i(|B0B ̄0⟩ + |B ̄0B0⟩)]. For the first state it remains constanteven for CP violation but for the second it is possible to see the effects of the parameters in discussion. Furthermore we study scattering among the B mesons in vacuum, scattering with matter and finally radiative emission at Υ(5S), the first scenario is rather trivial due to the simplified assumptions, such as only strong/electromagnetic interactions. As result one observes no change in the concurrence, which is therefore concluded to be affected only by weak interaction (mixing). The second and third scenarios are investigated with the help of open quantum systems and for both the concurrence decreases after the application of the quantum channels built with Kraus operators. At the last part of the thesis the relations between entanglement and the measurement basis are studied introducing an arbitrary phase φ in the Bloch sphere representation. One finds that |ψ(φ)⟩ can violate CHSH or not depending on φ and the choice of the measurement basis. The distinction of states on the equator of the Bloch sphere is possible using the correlation function Ef1,f2(t1,t2) constructed for flavor and CP tags. Further it is also possible to distinguish entangled states of the family |ψ(φ)⟩ from some separable states also using the correlation function and choosing the flavor-CP tag. A distinction of any kind using only flavor tags on both arms of the correlation function is shown not to be possible. Finally we show that the CP-violating parameter Cf and Sf , used to measure CP violation, are biased if a wrong assumption on the nature of the quantum state is made.
In this thesis, we study the quantum entanglement of neutral B-mesons from the decay of the Υ(5S). The experiment which provided real data for this decay is the Belle experiment which ran from 1999 to 2010 and gathered about 121fb−1 of data for the Υ(5S). The decay of the Υ(5S) particle is expected to produce entangled pairs of neutral B-mesons, therefore any deviations of the theoretical predictions for such entangled pairs to the measured data can be attributed to an effect called Quantum Decoherence (QD). QD is a more general term for the loss of the quantum properties of a system. In this thesis QD will refer specifically to the loss of entanglement (=ˆ disentanglement). To start with, we will briefly go over the basics of the flavor physics of the neutral meson system and study effects of mixing and the time dependence of the flavor states for B0 mesons. Then we will use this framework to calculate the theoretical probability density of measuring possible states for these entangled systems and compare them to the disentangled system. We will further analyse how QD can manifest by considering the entanglement of formation, which refers to a system that consists of multiple entangled states. It will be shown how disentanglement can arise in such systems and then apply this theory directly to the B0-meson systems we expect from the Υ(5S) decay. In the end, there is a brief introduction to the experimental uncertainties of the Belle detector, which is captured by the resolution function, and its impact on the theoretical prediction.
In this work, we study the entanglement of the B mesons produced in Upsilon(5S) decays into the final states each with C = ±1 eigenvalue Upsilon(5S) to B0B0-bar (C = -1), Upsilon(5S) to B0B0-bar* + c.c. (C = +1), Upsilon(5S) to B0*B0-bar* (C = -1). For this purpose, we use Belle Monte Carlo data. The B mesons are reconstructed from hadronic decays: B0 to D-pi+, with D- to K+pi-pi- B0 to D*-pi+, with D*- to D0-bar pi_s- and D0-bar to K+pi-, B0 to D*-pi+, with D*- to D0-bar pi_s- and D0-bar to K+pi-pi+pi-. We then determine the decay–time difference of the B meson pairs to investigate the time depen- dence of their quantum entanglement. Since an entanglement analysis has never been performed for Upsilon(5S) decays, this thesis establishes the foundation for such a study. This includes deriving the theoretical framework of entanglement at the Upsilon(5S), performing the necessary kinematic consider- ations for the decaytime calculation, and developing new time and flavor variables for the analysis, since the Belle II software framework is only partially applicable to the Upsilon(5S)) case. In addition, we generate Signal Monte Carlo samples of 1 x 10^6 B0(*)B0-bar(*) events to increase statistical precision. In the Upsilon(5S) system, it is possible to obtain two different types of entanglement. When these two types are mixed, one obtains a disentangled state, with the degree of disentanglement being equal to the mixing ratio of the two entangled states. By applying the model of partial spontaneous disentanglement (PSD), which introduces a fraction zeta, we can measure this disentanglement frac- tion when mixing the states and thereby validate the theoretical prediction. To achieve this, we implemented the PSD framework for the Upsilon(5S) case. We verified that, when mixing the two en- tangled states in equal proportions, the expected disentanglement fraction of 100% is successfully reproduced.
We establish the precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the neutral meson B d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-Factory of entangled states. Genuine asymmetry parameters in the time distribution of the asymmetries are identified and their measurability analysed, disentangling genuine and possible fake terms. The nine asymmetry parameters – three different observables for each one of the three symmetries – are expressed in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled B d -meson states and we obtain a global fit to their values from the BaBar Collaboration experimental results. The possible fake terms are all compatible with zero. The information content of the nine asymmetry parameters is indeed different. The non-vanishing and are impressive separate direct evidence of Time-Reversal-Violation and CP-Violation in these transitions (and compatible with Standard Model expectations). A 2σ effect for the Re(θ) parameter responsible of CPT-Violation appears; interpreted as an upper limit, it leads to eV at 95% C.L. for the diagonal flavour terms of the mass matrix. Finally, we consider scenarios where, in the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the ω -effect. The analysis is extended to identify how to probe the complex ω when the connection between the Intensities for the two time-ordered decays ( f, g ) and ( g, f ) is lost ( f flavour and g CP eigenstate decay channels), and how the ω -effect is disentangled from CPT violation in the evolution Hamiltonian.
Studies of Quantum Entanglement in the Υ(4S)→B0Bˉ0 system at Belle II using B0→D(∗)−π+ decays
This thesis presents a study of quantum entanglement in the Υ(4S)→B0Bˉ0 system using the hadronic B0→D(∗)−π+. As it is the first study of such kind at Belle II, this work is focused on establishing an analysis framework, which enables testing disentanglement in hadronic B0 modes. A novel event generator model has been implemented within basf2 to create a Signal MC samples with 1 Mio. BBˉ events, corresponding to an integrated luminosity of 1 ab^-1 which are reconstructed in B0→D(∗)−π+ decays. The model of partial spontaneous disentanglement is implemented, where a fraction ζ of B0Bˉ0 pairs disentangle right at production. The implementation is proven to be successful, as the model is sensitive to such entanglement effects. Fits to Δt distributions for different values of ζgen in Signal MC samples return consistently the correct values for free parameter ζ within uncertainties. A subsequent Toy Monte Carlo study once more shows the model's and fitting processes' suitability for disentanglement studies, although some biased behavior for parameter ζ could not be fully resolved. However, this thesis provides a proof-of-concept for future probes of entanglement at Belle II. The question, whether unaccounted disentanglement effects introduce a bias in time-dependent CP violation measurements at Belle II is answered. Such effects in the region of ζ∼O(1−10%) is absorbed in form of a bias of 1-2% in wrong tag parameters. However, slight biases in these parameters do in general not translate to a shift in parameters ACP and SCP, thus the worry of an unaccounted systematic effect is for now mitigated.
Study of Quantum Decoherence in Neutral B Meson pairs produced at the Υ(5S) Resonance
This thesis presents the development and validation of an analysis framework to study quantum decoherence in neutral B-meson pairs produced at the Υ(5S) resonance, using Monte Carlo simulated data from the Belle experiment. Unlike the Υ(4S), the Υ(5S) provides access to both antisymmetric (C=−1) and symmetric (C=+1) quantum states through the channels B0Bˉ0, B0∗Bˉ0+c.c., and B0∗Bˉ0∗. Decoherence effects are studied with the Partial Spontaneous Disentanglement model, which introduces a fraction ζ of B0∗Bˉ∗0 pairs disentangled at production. The analysis exploits the decay times of both neutral B mesons, for which time-dependent probability density functions are derived and extended to include detector-resolution effects. The framework is first validated on Signal Monte Carlo samples, where one-dimensional fits to Σt successfully recover the expected decoherence values for both entangled and disentangled configurations. Fits to Generic Monte Carlo samples, which include realistic backgrounds and event compositions, reveal strong correlations between the decoherence parameter and flavour-tagging wrong-tag fractions, particularly in the C=−1 channels. The results from these fits show significant deviations from expected ζ values and large uncertainties. Pure Toy Monte Carlo studies confirm that the fitter behaves linearly with respect to the injected decoherence parameter and show only small biases consistent with those observed in the nominal fits, but too small to fully explain them. To address the limitations of the single fits, a two-dimensional analysis in (Δt,Σt) is developed. By exploiting the full time-dependent information, the two-dimensional fit significantly reduces the statistical uncertainty on the decoherence parameter from ∼O(10%) to ∼O(4%) and mitigates correlations with the flavour-tagging parameters. This work constitutes a proof of concept for future analyses on Belle data and demonstrates the potential of the Υ(5S) system for studying quantum entanglement and decoherence in neutral B mesons.
A bstract With the advent of Belle II and the LHCb upgrade, the precision measurements of various B-Physics observables are on cards. This holds significant potential for delving into physics beyond the standard model of electroweak interactions. These measurements can also serve as means to establish limits on phenomena occurring at much finer length scales, such as quantum decoherence, which may arise due to potential discreteness in space-time or non-trivial topological effects. In this work, we set up the formalism to investigate the impact of quantum decoherence on several potential observables in B meson systems. The approach employs the trace-preserving Kraus operator formalism, extending unitary evolution to non-unitary dynamics while maintaining complete positivity. In this formalism, the decoherence effects are parametrized in terms of a single parameter. Through the analysis of purely leptonic, semileptonic, and non-leptonic decays of B mesons, we identify observables that could, in principle, be influenced by decoherence. The theoretical expressions are provided without neglecting the impact of decay width difference (∆Γ) and CP violation in mixing. Considering that many of these observables can be measured with high precision using the abundant data collected by LHCb and Belle II, our formalism can be applied to establish constraints on the decoherence parameter through multiple decay channels. This offers an alternative set-up for such studies, which, at present, are predominantly conducted in the neutrino sector.