Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation

The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

[1]  K. Thorne,et al.  Quantum Nondemolition Measurements , 1980, Science.

[2]  H. M. Wiseman,et al.  Measuring measurement–disturbance relationships with weak values , 2010, 1007.3076.

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

[4]  H. Imai,et al.  Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures , 2008, 0809.1714.

[5]  Aephraim M. Steinberg,et al.  Violation of Heisenberg's measurement-disturbance relationship by weak measurements. , 2012, Physical review letters.

[6]  B. Englert,et al.  Quantum optical tests of complementarity , 1991, Nature.

[7]  H. M. Wiseman,et al.  Extending Heisenberg's Measurement-Disturbance Relation to the Twin-Slit Case , 1998 .

[8]  W. L. Cowley.  The Uncertainty Principle , 1949, Nature.

[9]  Masanao Ozawa,et al.  Quantum Limits of Measurements and Uncertainty Principle , 2015, 1505.05083.

[10]  K. Fujikawa.  Universally valid Heisenberg uncertainty relation , 2012, 1205.1360.

[11]  Masanao Ozawa.  Uncertainty relations for noise and disturbance in generalized quantum measurements , 2003 .

[12]  Masanao Ozawa,et al.  Physical content of Heisenberg's uncertainty relation: limitation and reformulation , 2003 .

[13]  M. Ozawa.  Universal uncertainty principle in the measurement operator formalism , 2005, quant-ph/0510083.

[14]  Takahiro Sagawa,et al.  Uncertainty relation revisited from quantum estimation theory , 2010, 1010.3571.

[15]  Aephraim M. Steinberg,et al.  A double-slit ‘which-way’ experiment on the complementarity–uncertainty debate , 2007, 0706.3966.

[16]  Masanao Ozawa,et al.  Realization of Measurement and the Standard Quantum Limit , 2015, 1505.01083.

[17]  Paul Busch,et al.  Approximate joint measurements of qubit observables , 2007, Quantum Inf. Comput..

[18]  Masanao Ozawa.  Position measuring interactions and the Heisenberg uncertainty principle , 2002 .

[19]  A. Messiah.  Quantum Mechanics , 1961 .

[20]  Ozawa.  Measurement breaking the standard quantum limit for free-mass position. , 1988, Physical review letters.

[21]  Goodman,et al.  Quantum correlations: A generalized Heisenberg uncertainty relation. , 1988, Physical review letters.

[22]  Shiro Ishikawa,et al.  Uncertainty relations in simultaneous measurements for arbitrary observables , 1991 .

[23]  J. Neumann.  Mathematische grundlagen der Quantenmechanik , 1935 .

[24]  Horace P. Yuen,et al.  Contractive states and the standard quantum limit for monitoring free-mass positions , 1983 .

[25]  So-Young Baek,et al.  Minimum-disturbance measurement without postselection , 2008, 0804.3127.

[26]  M. Ozawa,et al.  Experimental demonstration of a universally valid error–disturbance uncertainty relation in spin measurements , 2012, Nature Physics.

[27]  M. Ozawa.  Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement , 2002, quant-ph/0207121.

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

[29]  S. Lloyd,et al.  Quantum-Enhanced Measurements: Beating the Standard Quantum Limit , 2004, Science.

[30]  Reinhard F. Werner.  The uncertainty relation for joint measurement of position and momentum , 2004, Quantum Inf. Comput..

[31]  John Maddox.  Beating the quantum limits (cont'd) , 1988, Nature.