Maximum Violation Of KCBS Inequality For Continuous Variable Systems

This thesis is based on the study of quantum contextuality in continuous variable systems.Quantum contextuality means that in a quantum system larger than two dimensions,the value of any observable is related to other observable measurements that are compatible with it.Quantum contextuality is the essential difference between quantum measurement and classical measurement.With the development of quantum information science,quantum contextuality can be applied as an important quantum resource in various types of quantum information processing.At the same time,quantum contextuality is an important resource for fault-tolerant quantum computing,which can accelerate the speed of fault-tolerant quantum computing.The study of quantum contextuality can deepen people's understanding of the quantum world and provide theoretical support for the application of quantum contextuality.Most of the concepts of quantum information were originally proposed and developed in the separation variable system.In recent years,quantum teleportation,quantum error correction,quantum computation,entanglement purification and cloning have also been proposed in continuous variable systems,so the intertextuality of continuous variable systems is studied.Therefore,it is of great significance and value to study the intertextuality of continuous variable systems.The paper discusses the quantum intertextuality of continuous variable systems with the coherent state as the light source.The reason is that coherent states are an important concept in modern physics.In theoretical research,the coherent state is the quantum state closest to the classical electromagnetic field,and is a completely coherent quantum state,so it has important significance in the study of classical and quantum boundaries.In application,the coherent state as a continuous variable quantum state has potential value in quantum dense coding,quantum key distribution,and remote quantum communication.Therefore,whether in the basic quantum theory research or practical level,the coherent state has significant research significance and representativeness.Quantum contextuality is usually proved by proving the violation of the KS inequality.This thesis mainly chooses the KCBS inequality to study the quantum contextuality of continuous variable systems.The reason is that the KCBS inequality only requires five observables in the three-dimensional Hilbert space to prove quantum contextuality.It is the simplest KS proof scheme currently known.At the same time,KCBS inequality satisfies all non-contextual variable models,so it is also the most basic KS inequality.The main innovation of this thesis is that the five cyclic vertical measurement directions required by KCBS inequality are constructed,and the coherent state is used as the measured state.Two conclusions are obtained:First,for any coherent state,a set of measurement schemes can always be found to achieve maximum violate to the KCBS inequality,and a unitary transformation is satisfied between these measurement schemes.Second,a set of single measurement schemes is found such that when ?>2.16,the coherent state is robust to the maximum violate of the KCBS inequality.