Experimental Study Of Efficient Multi-parameter Quantum Estimation

Quantum estimation of a single parameter in quantum metrology has been studied extensively.Practical applications,like simultaneous estimation of a multidimensional field,typically involve multiple parameters,for which the ultimate precision is much less understood.Multi-parameter quantum estimation focuses on simultaneous estima-tion of multiple unknown parameters beyond shot-noise limit with the aid of quantum resources such as quantum entanglement and quantum control.In the multi-parameter estimation scenario,the precision limit of each parameter cannot be saturated simultane-ously by designing optimal estimation schemes for each parameter one by one given the same amount of resources.It is also a waste of time and quantum resources.However,the strategy to simultaneously estimate all of the parameters and reach the precision limits will also fail in most cases due to the incompatibilities in the probe states,quan-tum measurements,or quantum channels.To realize efficient multi-parameter quantumestimation,these incompatibilities must be suppressed or even counteracted.Firstly,to maximize the precision of parameter estimation,it is essential to se-lect a quantum probe state that is sensitive to parameter variation.However,in multi-parameter quantum estimation,the optimal probe states corresponding to different pa-rameters are not always the same.Or the optimal probe state given by the multi-parameter optimization process is not an achievable quantum state.This is the incom-patibility in the probe state.Secondly,the incompatibility in quantum measurements means that the optimal measurements of different parameters are not commuting and cannot be realized at the same time.Finally,the incompatibility in the quantum chan-nel refers to the non-commutativity in dynamics of the system evolution,so that the accumulation of information of different parameters does not increase linearly with time.It may even make the performance worse than the shot-noise limit.Solutions to deal with these incompatibility issues are currently limited to theoretical research.In order to promote efficient multi-parameter quantum estimation towards practical ap-plications,we have experimentally developed collective measurement techniques and quantum control-enhanced sequential multi-parameter estimation strategy.In addition,to improve the scalability of multi-parameter quantum estimation,we have given so-lutions about the implementation of multi-pass technology and the efficient quantum process reconstruction algorithm.The following are the main experimental work com-pleted during my PhD:1.To reduce the incompatibility in quantum measurements,the inseparable collec-tive measurement technique on the multiple copies of the quantum state is developed.We apply the technique to the realization of the entangling measurements,which is used in the demonstration of quantum orienteering.Specifically,we experimentally realize the optimal orienteering protocols based on parallel spins and antiparallel spins,respec-tively.The optimal entangling measurements for decoding the direction information from parallel spins and antiparallel spins are realized using photonic quantum walks.Our experiments clearly demonstrate the advantage of antiparallel spins over parallel spins in orienteering.In addition,entangling measurements can extract more informa-tion than local measurements even if no entanglement is present in the quantum states.2.Using quantum control to regulate quantum channels is a feasible solution to counteract the incompatibilities in the probe states,quantum measurements,and quan-tum channels.In the work of experimental realization of the control-enhanced sequen-tial multi-parameter estimation,by relating the precision limit directly to the Heisen-berg uncertainty relation,we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously.Guided by this insight,we experimentally demonstrate an optimally controlled multi-pass scheme,which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2)operators.With eight controls,we achieve a 13.27 dB im-provement in terms of the variance(6.63 dB for the SD)over the classical scheme with the same loss.As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters,our work marks an important step in multi-parameter quantum metrology with wide implications.3.In the previous work,the sequential scheme is difficult to scale up.In order to improve the scalability of the scheme,one solution is to realize an actively controlled multi-pass cavity,the core structure of which is an optical switch that does not destroy the quantum states encoded on each degree of freedom of the photon.To construct the optical switch,we realized a low-loss and polarization-independent coherent interface between temporal and spatial degrees of freedom,specifically the time-bin and path modes.The experimental loss is 0.2 dB,and the fidelity of the conversion process is found by tomography to be 0.970(0.947)without(with)considering the polarization DOF.As an application,our interface transforms a time-bin qubit output from an entan-glement distribution channel to a path qubit,which allows postselection-loophole-free measurement of the Bell inequality.4.To alleviate the exponential growth of the computational complexity of the parameter reconstruction algorithm in large-scale multi-parameter estimation,we have designed a new estimation algorithm-self-guided quantum process tomography algo-rithm,which can be used for efficient realization of multi-parameter estimation prob-lems such as quantum process tomography.The conventional method uses standard quantum process tomography,which requires O(d2)input states and O(d4)quantum measurements for a d-dimensional Hilbert space.These experimental requirements are compounded by the complexity of processing the collected data,which can take several orders of magnitude longer than the experiment itself.In this paper we propose an al-ternative self-guided algorithm for quantum process tomography,tuned for the task of finding an unknown unitary process.Our algorithm is a fully automated and adaptive process characterization technique.The advantages of our algorithm are:inherent ro-bustness to both statistical and technical noise;requires less space and time since there is no post-processing of the data;requires only a single input state and measurement;and,provides on-the-fly diagnostic information while the experiment is running.Nu-merical results show our algorithm achieves the same 1/n scaling as standard quantum process tomography when n uses of the unknown process are used.We also present experimental results wherein the algorithm,and its advantages,are realized for the task of finding an element of SU(2).