Learning to Detect Entanglement

This paper introduces the forest algorithm, an algorithm that can detect entanglement through the use of decision trees generated by machine learning. Tests against similar tomography-based detection algorithms using experimental data and numerical simulations indicate that, once trained, the proposed algorithm outperforms previous approaches. The results identify entanglement detection as another area of quantum information where machine learning can play a helpful role.

[1]  A. Winter,et al.  Aspects of Generic Entanglement , 2004, quant-ph/0407049.

[2]  Thomas Alexander,et al.  QInfer: Statistical inference software for quantum applications , 2016, 1610.00336.

[3]  Trevor Hastie,et al.  An Introduction to Statistical Learning , 2013, Springer Texts in Statistics.

[4]  C. Schwemmer,et al.  Optimized state-independent entanglement detection based on a geometrical threshold criterion , 2013, 1308.6441.

[5]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[6]  G. Tóth,et al.  Entanglement detection , 2008, 0811.2803.

[7]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[8]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[9]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[10]  F. Petruccione,et al.  An introduction to quantum machine learning , 2014, Contemporary Physics.

[11]  Marek Zukowski,et al.  Experimentally friendly geometrical criteria for entanglement. , 2007, Physical review letters.

[12]  T. Paterek,et al.  Correlation complementarity yields bell monogamy relations. , 2010, Physical review letters.

[13]  M. Ledoux The concentration of measure phenomenon , 2001 .

[14]  C. Schwemmer,et al.  Experimental Schmidt decomposition and state independent entanglement detection. , 2011, Physical review letters.

[15]  M. Horodecki,et al.  Quantum entanglement , 2007, quant-ph/0702225.

[16]  Jacob biamonte,et al.  Quantum machine learning , 2016, Nature.

[17]  Christopher Granade,et al.  Practical Bayesian tomography , 2015, 1509.03770.

[18]  Robin Blume-Kohout,et al.  Entanglement verification with finite data. , 2010, Physical review letters.