Studies On Estimation And Manipulation Of Quantum Coherence

A physical state can be in a coherent superposition state,which is one characteristic feature that marks the departure of quantum physics from classical physics.The superposition of quantum states can be explored,for instance,in quantum key distribution and quantum algorithms.With the development of quantum information science,quantum coherence plays a vital role in many emerging fields,such as quantum thermodynamics and quantum biology.Recently,researchers began to understand quantum coherence from a quantitative point of view and established a quantifying framework based on quantum resource theory.Previous research indicates that the amount of quantum coherence directly determines whether quantum systems can accomplish specific quantum information processing tasks.Since any quantum system inevitably interacts with its environment,such an interaction generally spoils the coherence of the quantum state and weakens the ability of quantum states to perform QIP tasks.Therefore,the estimation of coherence is necessary to determine whether the quantum system can accomplish QIP tasks.Further,the manipulation of coherence can effectively promote the use of coherence in QIP tasks.In this thesis,we focus on the estimation and manipulation of quantum coherence.The main results are as follows.First,we propose an effective estimation method for the quantum coherence of multipartite quantum states.Using the stabilizer formalism,we develop a measurement selection method in spectrum estimation,which significantly improves the applicability of spectrum estimation for multipartite quantum states.Further,we establish the connection between various coherence measures and spectrum estimation.Based on these results,we can effectively estimate the spectrum information of quantum states using a small number of measurements and then characterize the lower bounds of coherence for various coherence measures.In addition,we prove the constraint relationship of coherence for the quantum states with the same diagonal elements and propose an estimation method for the upper bound of coherence,which only needs one measurement and can be applied to all coherence measures.Second,we verify the experimental feasibility of our proposed coherence estimation method.We experimentally prepare various multi-qubit entangled states,including the Greenberger-Horne-Zeilinger state,the cluster state,and the W state,and show how to infer their coherence by measuring a few observable efficiently.Our results show that the upper and lower bounds of coherence can be effectively estimated at most of the 5 measurements for all experimentally prepared quantum states.In addition,for some vital quantum states,we find that the spectrum-estimation-based method significantly improves the accuracy of coherence estimation compared to the fidelity-based method and the witness-based method for the same experimental data.Third,we prove two no-go theorems for the deterministic purification and the probabilistic enhancement of coherence.Specifically,we define a coherence measure and prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of incoherent and coherent states.Moreover,we give an easy-to-verified condition to determine whether a state can be probabilistically enhanced via stochastic strictly incoherent operation.These results can be regarded as the complementary theories of deterministic purification and the probabilistic enhancement of coherence.They also provide a theoretical criterion of feasibility for coherence manipulation in some QIP tasks.