This thesis investigates the time evolution of the entangled B0-B0-bar system by calculating the effects of disentanglement and decoherence. The disentanglement is implemented by inserting a factor ζ, which can be constant or time-dependent. This phenomenon changes the asymmetry of B0-B0-bar mixing by a phase shift and an amplitude decrease. This is similar to mistag in flavour tagging, so the consideration of this effect is needed to decrease systematic errors of TDCPV measurements. Decoherence can arise from the interaction of one particle with the environment, which results in a time-dependent damping of the oscillation amplitude. The different time propagations of |BH⟩ and |BL⟩, which are dependent on the mass difference, could be a reason for decoherence. The interaction of quantum black holes could also enhance the effect. Both disentanglement and decoherence are combined to form a detailed description of the time evolution of an entangled system. Furthermore, this work provides another approach of implementing disentanglement by using density matrices. Now, the system can be formulated as a combination of the entangled and the disentangled case, where ζ is the fraction. Moreover, it is shown that the CHSH inequality is violated, even when the oscillations are completely disentangled, because the B0-mesons do not oscillate fast enough due to their small mass difference and short mean lifetime.
This thesis investigates the time evolution of the entangled B0-B0-bar system by calculating the effects of disentanglement and decoherence. The disentanglement is implemented by inserting a factor ζ, which can be constant or time-dependent. This phenomenon changes the asymmetry of B0-B0-bar mixing by a phase shift and an amplitude decrease. This is similar to mistag in flavour tagging, so the consideration of this effect is needed to decrease systematic errors of TDCPV measurements. Decoherence can arise from the interaction of one particle with the environment, which results in a time-dependent damping of the oscillation amplitude. The different time propagations of |BH⟩ and |BL⟩, which are dependent on the mass difference, could be a reason for decoherence. The interaction of quantum black holes could also enhance the effect. Both disentanglement and decoherence are combined to form a detailed description of the time evolution of an entangled system. Furthermore, this work provides another approach of implementing disentanglement by using density matrices. Now, the system can be formulated as a combination of the entangled and the disentangled case, where ζ is the fraction. Moreover, it is shown that the CHSH inequality is violated, even when the oscillations are completely disentangled, because the B0-mesons do not oscillate fast enough due to their small mass difference and short mean lifetime.
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.
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.
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.
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.
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.
Due to the rapid development of research in the field of quantum physics and quantum information over the past decades, the need to study physical models that can effectively implement quantum computing has increased. An integral part of such models is the environment, which, on the one hand, leads to decoherence in the system, and on the other hand, generates interaction between spins, which in turn allows for the induction of entanglement, which is an integral part of many quantum algorithms. Therefore, it is essential to investigate the impact of the environment on the behavior of quantum systems, enabling the effective implementation of quantum information devices. Here, we consider the time evolution of two spins generated by the interaction through a bosonic environment. The behavior of negativity as a measure of entanglement between spins is studied for different models of environment. As a result, conditions on the parameters of the environment are obtained to achieve the maximum values of entanglement between spins. In this case, environmental models were obtained that minimize the decoherence of the system while maximizing its entanglement. It became possible to derive an effective unitary operator describing the corresponding evolution, since the influence of decoherence was negligibly small.