Experimental investigation of the uncertainty relations with coherent light

AbstractTaking advantage of coherent light beams, we experimentally investigate the variance-based uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system. Different from most of the experiments which devoted to record each individual quantum, we examine the uncertainty relations by measuring an ensemble of photons with two polarization degree of freedom characterized by the Stokes parameters which allow us to determine the polarization density matrix with high precision. The optimality of the recently proposed direct-sum majorization uncertainty relation is verified by measuring the Lorenz curves. Results show that the Lorenz curve method represents a faithful verification of the majorization uncertainty relation and the uncertainty relation is indeed an ensemble property of quantum system.

[1]  Arun Kumar Pati,et al.  Tighter Uncertainty and Reverse Uncertainty Relations , 2016, 1607.06712.

[2]  Xing Xiao,et al.  Implications and applications of the variance-based uncertainty equalities , 2015, 1503.00239.

[3]  H. Weyl.  Gruppentheorie und Quantenmechanik , 1928 .

[4]  P. Xue,et al.  Experimental test of a stronger multiobservable uncertainty relation , 2018, Physical Review A.

[5]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[6]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[7]  W. Heisenberg.  Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[8]  A. Pati,et al.  Stronger uncertainty relations for all incompatible observables. , 2014, Physical review letters.

[9]  M. S. Zubairy,et al.  Quantum optics: Frontmatter , 1997 .

[10]  E. H. Kennard.  Zur Quantenmechanik einfacher Bewegungstypen , 1927 .

[11]  Yunlong Xiao,et al.  Improved quantum entropic uncertainty relations , 2018, Physical Review A.

[12]  V. Dodonov.  Variance uncertainty relations without covariances for three and four observables , 2017, 1711.04037.

[13]  Yunlong Xiao,et al.  Experimental investigation of majorization uncertainty relations in the high-dimensional systems , 2019, 1901.00853.

[14]  S. Zozor,et al.  On a generalized entropic uncertainty relation in the case of the qubit , 2013, 1306.0409.

[15]  Xianqing Li-Jost,et al.  Weighted Uncertainty Relations , 2016, Scientific Reports.

[16]  P. Xue,et al.  Experimental investigation of the stronger uncertainty relations for all incompatible observables , 2016, 1604.05901.

[17]  C. Qiao,et al.  Equivalence theorem of uncertainty relations , 2015, 1512.02781.

[18]  S. Friedland,et al.  Universal uncertainty relations. , 2013, Physical review letters.

[19]  Patrick J. Coles,et al.  Entropic uncertainty relations and their applications , 2015, 1511.04857.

[20]  Qiu-Cheng Song,et al.  Stronger Schrödinger-like uncertainty relations , 2015, 1504.01137.

[21]  M. Teich,et al.  Fundamentals of Photonics , 1991 .

[22]  Zhi-Xin Chen,et al.  Tight N-observable uncertainty relations and their experimental demonstrations , 2018, Scientific Reports.

[23]  Chen Qian,et al.  State-independent uncertainty relations and entanglement detection , 2017, Quantum Inf. Process..

[24]  Markus P. Mueller,et al.  A Generalization of Majorization that Characterizes Shannon Entropy , 2015, IEEE Transactions on Information Theory.

[25]  D. Deutsch.  Uncertainty in Quantum Measurements , 1983 .

[26]  H. Fan,et al.  Experimental investigation of quantum entropic uncertainty relations for multiple measurements in pure diamond , 2017, Scientific Reports.

[27]  Bin Chen,et al.  Sum uncertainty relations for arbitrary N incompatible observables , 2015, Scientific Reports.

[28]  C. Branciard,et al.  Tight State-Independent Uncertainty Relations for Qubits , 2015, 1512.02383.

[29]  S. Fei,et al.  Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum. , 2016, Physical review letters.

[30]  Jun-Li Li,et al.  The Optimal Uncertainty Relation , 2019, Annalen der Physik.

[31]  Jun-Li Li,et al.  A Stronger Multi-observable Uncertainty Relation , 2017, Scientific Reports.

[32]  H. P. Robertson.  The Uncertainty Principle , 1929 .