Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement

Abstract

We experimentally test the error-disturbance uncertainty relation (EDR) in generalized, strengthvariable measurement of a single photon polarization qubit, making use of weak measurement that keeps the initial signal state practically unchanged. We demonstrate that Heisenberg's EDR is violated, yet Ozawa's and Branciard's EDRs are valid throughout the range of our measurement strength.

Advantages of nonclassical pointer states in postselected weak measurements

“…Weak value has a nature of being a complex number, which lead the weak measurements to provide an ideal method to examine some fundamentals of quantum physics. Quantum paradoxes (Hardy's paradox [17][18][19] and the three-box paradox [20]), quantum correlation and quantum dynamics [21][22][23][24][25][26], quantum state tomography [27][28][29][30][31][32], violation of the generalized Leggett-Garg inequalities [33][34][35][36][37][38] and violation of the initial Heisenberg measurement-disturbance relationship [39,40] are just few examples. In these typ-ical examples, the small effects have been amplified due to the benefit of weak values.…”

Quantum measurement and uncertainty relations in photon polarization

“…To date, experimental evaluation of the measurement error and disturbance in qubit systems has been reported using neutron spin [20,35,36] and photon polarization [ 13,37,38,39,40]. Here, we review our experiments [13,39] in which the measurement error, disturbance and uncertainty relations were examined in generalized, strengthvariable measurement of a single photon polarization.…”

“…Here, we review our experiments [13,39] in which the measurement error, disturbance and uncertainty relations were examined in generalized, strengthvariable measurement of a single photon polarization.…”

“…At this point, the violation of Heisenberg's relation (69) is already apparent. In the experiment [39], we use the weak probe method to evaluate the measurement error and disturbance. The experimental setup is illustrated in Fig.…”

“…We see that the expected values (85) and (86) are dependent on the input signal state and thus the forming conditions (71) and (72) for Heisenberg's relation (69) are not fulfilled. The expected measurement error and disturbance defined in (46) are calculated to be [11,13,39] ǫ(A) = 2 sin θ, η(B) = 2 sin π 4 − θ .…”