Study Of Quantum-memory-assisted Entropic Uncertainty Relation And Ultra-entropic Squeezing

The uncertainty principle is one of the fundamental and most important con-cepts in quantum theory.This principle sets limits on the precise prediction of the outcomes of two incompatible quantum measurements on a particle.The un-certainty principle reveals the essential distinction of quantum mechanics from the classical mechanics.The uncertainty principle can be expressed in different mathematic forms.Entropy-version uncertainty relation is the best form for char-acterizing the uncertainty.Recently,based on the quantum entanglement,the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)is improved and has attracted wide attentions.QMA-EUR is not.only a generalization and extension of the original uncertainty relations,but also more convenient for appli-cation in developing quantum technologies,such as quantum measures,quantum cryptography,and witnessing entanglement,which is the one of the hot issues in the quantum information processing.However,the decoherence or dissipation due to irreversible interactions with the extern environment will cause degradation of the quantum correlation between the entangled system.One of the natural consequences of the interaction between the system and its environment is decoherence and destroying entanglement,which can be viewed as the loss of information of the system and thus increases system's entropic uncertainty.In this thesis,we focus on the Maassen-Uffink's entropic un-certainty of the single qubit system and the quantum-memory-assisted entropic uncertainty(QMA-EU)of the two-qubit system in the amplitude damping(AD),Markovian and non-Markovian environments.The controlling scheme via weak measurement and is reversal is proposed to reduce the QMA-EU;We have inves-tigated features of QMA-EU in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinski-Moriya interaction under decoherence conditions including dephas-ing and noisy environments;We have investigated the entropic squeezing effects of two-level atom trapped in an imperfective single-mode cavity and proposed a scheme for controlling entropic squeezing by means of another external cavity interacting with the imperfective single-mode cavity.The main contents are as follows:In Chapter 1,a research background and status of uncertainty relations are introduced.In Chapter 2,the mathematical expressions and physical mechanism of vari-ance uncertainty relations,entropic uncertainty relation and QMA-EUR are intro-duced in brief,and the derivations and proofs of several lower bound of QMA-EUR are introduced as well.We introduced the theoretical foundation of Heisenberg XYZ spin chain model briefly,and the reduced densities of two-qubit Heisenberg XYZ spin chain model with DM interactions along x,y,Z directions are obtained.We also measured the correlations of the XYZ spin chain model by means of mu-tual information.The concepts of entropic squeezing and ultra-entropic squeezing are introduced briefly.In Chapter 3,we have investigated the dynamical features of OMA-EU and its lower bound in the AD noise channel in the case of the initial state shared between Alice and Bob is extended Werner-like state.It is found that the entropic uncertainty of observables ?x and ?z increases at first and then decreases to an asymptotic value over the damping time,Furthermore,the entropic uncertainty is not always inversely proportional to the concurrence of the two-qubit system.To reduce the entropic uncertainty,the controlling scheme via.weak measurement and is reversal is proposed.It is showed that the prior weak measurement can effectively reduce the entropic uncertainty in AD channel.Furthermore.we also numerically illustrated that the amount of entropic uncertainty can be reduced by weak measurement reversal after the quantum entangled state bypassing the AD channel,but the poster weak measurement cannot reduce it.In Chapter 4,we have investigated the dynamical features of Maassen-Uffink's entropic uncertainty of the single qubit system and QMA-EU of the two-qubit sys-tem in the Markovian and non-Markovian environments in the case of the initial state shared between Alice and Bob is extended Werner-like state.To reduce the amount of entropic uncertainty of Pauli observables in non-Markovian envi-ronment,we have presented two schemes by means of prior weak measurement and posterior weak measurement reversal.It is shown that the value of entropic uncertainty of the single qubit system increases from 1 and then decreases to 1 monotonically in Markovian environment,but oscillates in non-Markovian envi-ronment.For QMA-EU of the two-qubit system,the value of entropic uncertainty of the single qubit system increases from 0 and then decreases to 1 monotonically in Markovian environment,but decreases with oscillation tendency in non-Markovian environment.Furthermore,the strong interaction of non-Markovian environment has benefit of keeping the amount of entropic uncertainty at a lower value.It is also shown that the prior weak measurement can effectively reduce the peak values of the QMA-EU dynamical process in dissipative environment for long periods of time but it is ineffectual on the wave minima of dynamical process,while the posterior weak measurement reversal can effectively reduce the wave minima values of the QMA-EU dynamical process but it is ineffectual on the peak of dynamical process.Some explanations about these phenomenons are given from aspects of physical mechanics of weak measurement and weak measurement reversal operations.In Chapter 5,we have investigated the effects of equilibrium temperature,DM interactions and spin-spin interaction along x,y,z directions on the QMA-EU for a pair of Puali observables in the two-qubit Heisenberg XYZ spin chain model.It is found that in the non-zero temperature condition the entropic uncertainty closes to zero at very low temperature,starts to increase with temperature after a threshold,and generally constant at a fixed value.The DM interaction and the spin interaction along x,y,z directions can efficiently suppressing the entropic un-certainty.We also verified the entropic uncertainty about measurement outcomes is anticorrelated with the sum of the accessible information of observer.Further-more,in the noisy environment,the behaviors of entropic uncertainty and its lower bound monotonically increase with the time.The behavior of QMA-EU and its lower bound at infinite time stable at value 2 quickly.In the dephasing environ-ment,the evolutions of QMA-EU and its lower bound oscillate with the time and saturate at a finite value,and this value is varied with the purity parameter.In Chapter 6,we have investigated the effects of the atom entropic squeez-ing of a two-level atom trapping in an imperfective optical cavity and discussed the controlling scheme of entropic squeezing effects by means of external cavity architecture.The results show that due to the dissipation of the imperfective cav-ity,the entropic squeezing effect decays with time.The tendency of the decays is Markovian in the regime of weak coupling between two-level atom and cavity,and it is non-Markovian in the regime of strong coupling.Meanwhile,the decays performance with Markovian and non-Markovian can be switched by the coupling manipulation by means of external cavity architecture.It is important the this coupling manipulation based external cavity architecture can effectively protected the atom entropic squeezing effects in the regime of weak and strong coupling.Furthermore,the performance of protecting is without relation of dissipation fac-tor of external cavity at initial time,but in the long time,the smaller of dissipation factor is,the better of protecting performance is.In Chapter 7,the summary and outlook are presented.