复旦量子力学讲义qmapter7.ppt

Chapter 7Quantum Entanglement and Quantum Information,7.1 Pure states and mixed states,Introduction:Quantum entanglement describes the coherence of two or many quantum states according to the superposition principle of quantum states.Energy:interactions,conservation laws,workEntropy:information,order and disorderEntanglement:coherence,teleportation,Pure state,7.1 Pure states and mixed states,System A:,Systems A+B:,Pure state,7.1 Pure states and mixed states,Density matrix:,In the base of the representation O,7.1 Pure states and mixed states,The average value of a quantity F:,7.1 Pure states and mixed states,Mixed state:the non-coherent mixture of two or many pure states,System A:,7.1 Pure states and mixed states,In the base of the representation O,7.1 Pure states and mixed states,Systems A+B:the reduced density matrix,If is a observable quantity of system A,its average value:,is a unit operator of system B.,7.1 Pure states and mixed states,is called the reduced density matrix.,7.1 Pure states and mixed states,The properties of measurement,7.1 Pure states and mixed states,For a s=1/2 particle:,Pure State:,Mixed State:,The superposition state and its mixed state:,7.1 Pure states and mixed states,The measurement of:,Pure State:,Mixed State:,7.1 Pure states and mixed states,7.2 Entangled states and Bell basis,Entangled state:non-entangled state:Schmit theorem:A two particles pure state can be expressed as,7.2 Entangled states and Bell basis,Prove:,are the orthogonal basis of hillbert space.,7.2 Entangled states and Bell basis,7.2 Entangled states and Bell basis,Bell basis:,7.2 Entangled states and Bell basis,The density matrix of particle A for the state:,Mixed state.,7.2 Entangled states and Bell basis,For the state:,Mixed state.,For the non-entangled state:,Pure state.,7.2 Entangled states and Bell basis,We can make two new entangled states:,Bell basis:,7.2 Entangled states and Bell basis,Therefore,Bell basis are the common eigen states of,7.3 Schordinger cat and which way experiments,Schordinger catrecent experimentsWhich way experiments,7.3 Schordinger cat and which way experiments,7.3 Schordinger cat and which way experiments,7.3 Schordinger cat and which way experiments,7.4 Measurement and decoherence,Measurement,Wave packet collapse,Quantum decoherence,The non-diagonal terms of density matrix disappear,7.4 Measurement and decoherence,System A is at the state,while B is at the state.,7.5 Quantum teleporation,7.5 Quantum teleporation,MotivationProcedure,The particle 1 with its spin at Alice.,7.5 Quantum teleporation,The particle 2,3 with its spin are at the entangled state,EPR pair:,In the Bell basis,7.5 Quantum teleporation,If Alice obtain,the particle 3 measured by Bob is,7.5 Quantum teleporation,