Assisted Distillation Of Coherence In Multipartite Quantum System

Quantum coherence,as the most fundamental resource in quantum mechanics,is widely used in quantum information processing,quantum computing,quantum algorithms and quantum thermodynamics.Its existence is the main reason why the quantum world differs from the classical world.In quantum information processing tasks,quantum coherence is an important quantum resource to complete such tasks,and its centralized conversion is of great significance to improve the efficiency of quantum tasks.Quantum coherent distillation is such an important operation related to the transfer and concentration of quantum coherent resources.With the development of quantum science and technology,the multipartite system often has a broader application prospect than the single quantum system.Therefore,the coherent distillation in the multipartite system is worth studying,which is also the starting point of this paper.In this paper,the proof of the measure of the assisted coherence distillation will be given first.Then we propose a relatively simple and operable framework of the assisted coherence distillation in the asymptotic limit,which is called coordinately assisted distillation of quantum coherence.We investigate the problem of assisted distillation of quantum coherence in multipartite system,and further,we demonstrate it experimentally using a linear optical platform.In addtion,we derive the relaionship between the robustness measures of coherent and the assisted distillation of quantum coherence,which link the two quantum coherence measures by operational implications.As a unique and beautiful phenomenon in the quantum world,the quantum uncertainty relation plays an important role in quantum information processing,which is essentially derived from the noncommutability of observables in the quantum world.The noncommutability of such operators also plays an important role in quantum resource theory.The quantum uncertainty relation can be used as the criterion inequality for quantum entanglement,and it can also be used as the criterion inequality for quantum coherence.We consider the following question:Can quantum uncertainty relations also exist in the same way that quantum resources exist in both local and global distribution?We answer this question by giving two types of uncertain relations for multiple observables,in which the standard deviations of the observables are found to depend not only on the noncommutability of each pair of observables,but also on the noncommutability between the multiple observables.Then,based on a linear optical platform,we experimentally check the uncertainty relations.The specific research content of this dissertation is as follows:1.Proof of upper bound reachability of assisted coherent distillation rate of multipartite system under different operating frames.For assisted coherent distillation of mixed quantum systems,a variety of operational frameworks have been proposed,such as:Separate framework,that is,the operations of two parties are separate,and there is no classical communication between them;Local quantum-incoherent operation operation and classical communication(LQICC)framework(the original definition framework of assisted coherent distillation).We first use the law of large numbers Shannon information compression theory,typical sequence theory,typical subspace theory to prove the upper bound reachabability of assisted coherent distillation under protected quantum-incoherent(PQI)framework.Then,we prove that the operation proposed in this work is PQI operation,and the upper bound of the assisted distillable coherence in quantum mixed states can be perfectly reachable under the PQI protocol.2.Research on the distribution of multipartite system assisted coherence distillation.In a multipartite system,we study the distribution law of assisted coherence distillation in this system.By using some mathematical properties of quantum relative entropy,we reveal the law of inequality during the assisted coherence distillation process in multipartite systems when one of the subsystems acts as the assistant system.3.Coordinately assisted distillation of quantum coherence We investigate a class of assisted coherent distillation in a coordinate framework,and give the analytic results in the asymptotic limit.We also give two types of the distribution inequalities in the coordinately assisted coherence distillation.We experimentally demonstrate the inequalities in the GHZ and W states by using a linear optical setup.By comparing with some genuine multipartite entanglement measures and genuine multipartite correlation measures,the inequality given by us can be used to detect the multipartite quantum correlations.4.The uncertainty relation of multiple observables and its experimental demonstration.Based on the expansions of the expected value of the product of the observables,we give the product form uncertain relation and the weighted summation form uncertain relation.We extend a class of Cauchy-Schwartz inequality and define a type of multiple commutator.Based on the inequalities given by us,one can find that the product and the summation of the standard deviations of the multiple observables depend not only on the noncommutation between each pair of observables,but also on the noncommutation between the multiple observables.In addition,we experimentally demonstrate the uncertainty relation on a linear optical platform.