Experimental Violation of Heisenberg's Precision Limit by Weak Measurements

Along with the uncertainty principle, Heisenberg postulated another set of relations, which set a lower limit on the disturbance caused by a measurement [1]. These relations were shown by Ozawa to be inaccurate [2], shedding doubt on widely accepted bounds on the information left in a system after a measurement, and offering new insights into the foundations of quantum physics and quantum information. A theoretical scheme for testing Ozawa's precision-disturbance relations was proposed [3]. In this proposal the hurdle of destructive measurements is addressed by the weak value approach [4]. This scheme is based on a 3-qubit quantum circuit that requires two CNOT gates of variable strength with a common control qubit. Here, we present an experimental realization of Heisenberg's precision limit violation based on weak value measurements. We implement a technique inspired by the one-way quantum computing using entanglement as the substrate for quantum gates. In this way, we demonstrate a violation of Heisenberg's relation for measurement disturbance, confirming the revised bound due to Ozawa. \\[4pt] [1] Z. Phys. 43 172(1927); [2] Ann. Phys. NY 311 350(2004); [3] New J. Phys. 12 093011(2010); [4] Phys. Rev. Lett. 60 1351(1988)