Experimental Study Of Quantum State Tomography And Dynamics Time-Correlation In Nuclear Magnetic Resonance Systems

Quantum computing as an interdisciplinary research has attracted extensive attentions.It is based on quantum mechanics which is totally different from classical principle and has some special properties including no-cloning theorem and quantum superposition.There are lots of well-developed quantum systems for realizing quantum computing and being a candidate to be an universal quantum computer in the future.One of them is Nuclear Magnetic Resonance(NMR).In NMR,spin-1/2 nuclei in a chemical molecule are considered as qubits.Radio-frequency pulses can realize arbitrary single-qubit rotations on spins.Two-qubit quantum gates can be realized via the interaction between different nuclei.As a controlled quantum system based on nuclear spins,NMR has a lot of wide applications in quantum algorithm,quantum simulations and developments of quantum control techniques.The thesis focus on some research about quantum state tomography,simulations of open quantum systems and quantum mechanics completeness in NMR,and we obtain five research achievements as follows.We study the possibility of the global quantum state being reconstructed using its local density matrices(2-RDMs),and firstly present a family of states which are merely uniquely determined(UD)by their 2-RDMs assuming that the state is pure.As a result,we can classify quantum states into three classes according to UD properties.In experiments,we further test the feasibility and stability of reconstructing the global state using its 2-RDMs for each class.This discovery will efficiently decrease the complexity of quantum state tomography.Time-correlation functions can be used to compute the magnetic susceptibility of spin systems under a family of perturbations.We experimentally realize quantum algorithm of measuring n-time correlation functions in NMR.In detail,we demonstrate 2-time correlation functions for arbitrary times and measure time correlation functions at fixed times up to 10 th order.Considering that any non-unitary operations can be decomposed into a linear combination of unitary ones,we proposed a quantum algorithm for the simualtion of quantum channels.Experimentally,we realized the simulations of three single-qubit quantum channels including phase damping,amplitude damping and depolarizing channels.We re-study the possibility of measuring entanglement without quantum state tomography by merely using single-copy observables.We propose a theorem claiming that there is no any non-adaptive scheme to measure entanglement without state tomography by only employing single-copy measurements.We also realize a previous experiment [Phys.Rev.Lett.105,230404(2010)]which said entanglement can be detected without state tomography via adaptive singlecopy measurements.Our simulation and experiments both show the opposite conclusion that the scheme actually leads to full state tomography.By the way,we also propose a scheme to realize quantum filters with the assist of ancillary qubits,which can be directly extended to other systems.We firstly present an experimental demonstration of an entanglement-assisted quantum delayed-choice scheme in NMR.This experiment is from the proposed scheme [Nat.Comms.5:3997(2014)].Our results not only show the continuous change of a particle between wave-like and particle-like behaviour,but also show that Hidden variable theory based on wave-particle objectivity,determinism and independence fails to explain experimental results.