The Study Of Nonlocal Measurement And Its Applications

Measurement is one of the basic postulates of quantum mechanics.It Connects the quantum world and the classical world,which provides the main way to obtain informa-tion about microscopic particles.Many studies have explored quantum measurement both theoretically and experimentally.On the one hand,they are committed to reveal its physical nature,and on the other hand,they try to explore its technical applications.In recent years,with the development of weak measurement,people have become more and more interested in weak value.In the pre-and post-selected system weak value can be well defined which is related to the shift of pointer in weak measurement and has properties different from the eigenvalue.It's not only used to study the fundamental problems of quantum mechanics but also used to amplify weak signal and directly mea-sure the wave function and quantum process of the system.The neoclassical properties endowed by nonlocal systems are the main reason for the advantages of many quantum information tasks,so the explorations of some nonlocal quantities is helpful to promote the development of quantum information.As an important platform for quantum in-formation tasks,linear optical systems have their unique advantages,first photons can't interact with the environment easily,so the coherence of system can keep a long time;second the experimental technology is relatively mature,so most operations of pho-tons can be realized via linear optical elements;third do not need harsh experimental requirements,and most of the operations can be done in free space at room tempera-ture.Therefore,the author explored the nonlocal measurements and its corresponding applications based on the optical system,and completed relevant experimental demon-strations.This dissertation introduces the author's main achievements during her Phd career,as follows:1.Von Neumann measurement of nonlocal observablesThe causality of relativity restricts the implementation of quantum nonlocal mea-surement,study of which helps to reveal the connection between quantum mechanics and relativity.We demonstrate two methods of nonlocal measurement using local in-teraction and entangled probes.One is aimed at certain kind of nonlocal observables,while the other has a wider application with the help of teleportation and probabilistic quantum erasure.In both cases,the measurements have the properties attached to von Neumann measurement,namely,reliable,nondemolition and instantaneous.Therefore,it also allows subsequent measurements of the system to achieve more complex quantum information tasks.2.Direct Measurement of a nonlocal entangled quantum stateA quantum state can give all information about the quantum system.The measure-ment of the quantum state is inevitable in almost quantum information process.Using weak values to measure wave function directly can reduce resource consumption to a certain extent.We yield weak values of nonlocal projectors through extracting modular values with the help of entangled probes.For the first time,we give a feasible way ex-tending the direct measurement scheme to multi-body systems theoretically and realize the direct measurement of the two-photon entangled state experimentally.3.Directly Characterizing a Controlled-NOT GateThe characterization of quantum processes is helpful to the test and optimization of quantum information tasks and quantum networks.The weak value can be used to get each element of process matrix directly.We prove that local interactions are sufficient to realize the extraction of nonlocal sequential weak values,and then can realize the di-rect characterization of any bipartite unitary quantum process.We build the two-photon controlled NOT gate with a higher probability of success,and for the first time directly reconstructed it.There are fewer measurements are needed to quantify its process fi-delity.4.Experimental exchange of grins between quantum Cheshire catsWeak values can be an efficient tool for the studies of some quantum quantum paradox,like quantum Cheshire Cat,whose phenomenon can be directly exhibited by the mathematical description provided by weak values.We use the hyper-entangled source and select a specific final state with the help of second-order Franson interference.The required weak values can be obtained through non-unitary imaginary time evolution without introducing auxiliary pointers.We realize the first experimental observation of two Cheshire cats exchanging smiles without meeting each other,and unlike the previous experimental work our result cannot be described by classical theory.5.Counterfactual communication without traces in the transmission channelCounterfactual communication is a controversial topic,and therefore it catches much interest.We take a modified protocol to eliminate the trajectory of photons in the transmission channel by building a Michelson interferometer with an embedded Mach-Zehnder interferometer in one arm.We use the two-state vector formalism to define the trajectory of the particle.Photon's frequency is taken as the pointer in the weak mea-surement of the photon's trajectory,which is accomplished via EOM.The experimental results coincidence with our expectations,which can lead the conclusion that the pho-tons carrying the information do not appear in the channel.For the first time,we realize the truly counterfactual communication of two logical bits.