量子信道的凸优化重建技术（英文）-豆柴文库

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量子信道的凸优化重建技术（英文）
Title:ConvexOptimizationTechniquesforQuantumChannelReconstruction
Abstract:
Quantumchannelsplayavitalroleinquantuminformationprocessingandcommunication.Theabilitytoaccuratelycharacterizeandreconstructquantumchannelsisofparamountimportance.Inrecentyears,convexoptimizationtechniqueshaveemergedaspowerfultoolsforthereconstructionofquantumchannels.Thispaperprovidesanoverviewofconvexoptimization-basedreconstructiontechniquesforquantumchannelsandhighlightstheiradvantages,applications,andchallenges.Thepaperalsodiscussesseveralrelevantalgorithms,suchasmaximumlikelihoodestimation,semidefiniteprogramming,andcompressivesensing,anddiscussestheirpotentialforimprovingchannelreconstructionaccuracyandefficiency.Finally,futuredirectionsandopenproblemsinthefieldofconvexoptimization-basedquantumchannelreconstructionareoutlined.
1.Introduction
Quantumchannelsaremathematicalrepresentationsofthephysicalprocessesthattransformquantumstates.Accuratelycharacterizingquantumchannelsiscrucialforvarioustasksinquantuminformationprocessing,includingquantumcommunication,quantumteleportation,quantumerrorcorrection,andquantumcomputation.Theprocessofreconstructingquantumchannelsfromexperimentaldataisknownasquantumchannelreconstruction.
2.ConvexOptimization-basedMethods
Convexoptimizationtechniquesprovideapowerfulframeworkforsolvingawiderangeofmathematicaloptimizationproblems.Thesetechniquesofferadvantagessuchasglobaloptimalityguarantees,robustnessagainstnoise,andscalabilitytolarge-scaleproblems.Inthecontextofquantumchannelreconstruction,convexoptimization-basedmethodsaimtofindthechannelthatbestmatchesagivensetofexperimentalmeasurements.
2.1MaximumLikelihoodEstimation
Onecommonlyusedconvexoptimizationapproachismaximumlikelihoodestimation(MLE).MLEaimstofindthequantumchannelthatmaximizesthelikelihoodofobtainingtheobservedmeasurementoutcomes.Thistechniqueisstatisticallyefficientandprovidesawell-foundedframeworkforestimatingquantumchannels.MLEcanbesolvedusingconvexoptimizationalgorithms,suc