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

Abstract

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.

Optimized entropic uncertainty for successive projective measurements

“…A new form of EUR for successive measurements is proposed in view of Heisenberg's 1927 statement [1] that "it is impossible to measure position without disturbing momentum". Much debate and effort has been expended on formalising its underlying meaning, while more recently, experiments have found different ways of demonstrating it [24][25][26][27]. A stateindependent information theoretic error-disturbance relation has also been proposed [15], which shows a tradeoff relation between error and disturbance.…”

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.…”

“…The optical implementation of the generalized measurement described above is shown in Fig. 3, which we call a variable polarization beamsplitter (VPBS) [12,13]. Here, the signal to be measured is the single photon polarization qubit, and the probe is the path qubit, i.e, the use of path degrees of freedom (|+1 and |−1 ) of the photon, the roles of which are the same as those of a PBS.…”

“…Thus, it is not difficult to prepare these states in experiments. In practice, the three-state method was used to evaluate the error and disturbance in the measurement of neutron spin [20] and photon polarization [13]. However, in general cases, it is difficult to implement the operation I ±Â or even in practical experiments, and thus the applicability of (49) …”

“…The quantum circuit model of this Figure 3. (a) Generalized polarization measurement using a variable polarizing beamsplitter (VPBS) [12,13]. PBS and HWP stand for polarization beamsplitters and half-wave plates, respectively.…”