Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

Abstract

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurementdisturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum mechanics.The Heisenberg Uncertainty Principle is one of the cornerstones of quantum mechanics. In his original paper on the subject, Heisenberg wrote "At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position" [1]. Here Heisenberg was following Einstein's example and attempting to base a new physical theory only on observable quantities, that is, on the results of measurements. The modern version of the uncertainty principle proved in our textbooks today, however, deals not with the precision of a measurement and the disturbance it introduces, but with the intrinsic uncertainty any quantum state must possess, regardless of what measurement (if any) is performed [2][3][4]. These two readings of the uncertainty principle are typically taught side-by-side, although only the modern one is given rigorous proof. It has been shown that the original formulation is not only less general than the modern one -it is in fact mathematically incorrect [5]. Recently, Ozawa proved a revised, universally valid, relationship between precision and disturbance [6], which was indirectly validated in [7]. Here, using tools developed for linear-optical quantum computing to implement a proposal due to Lund and Wiseman [8], we provide the first direct experimental characterization of the precision and disturbance arising from a measurement, violating Heisenberg's original relationship.In general, measuring one observable (such as position, q) will, according to quantum mechanics, induce a random disturbance in the complementary observable (in this case momentum, p). Heisenberg proposed, and it is widely believed, that the product of the measurement precision, (q), and the magnitude of the induced disturbance, η(p), must satisfy (q)η(p) ≈ h, where h is Planck's constant. This idea was at the crux of the FIG. 1. Schematic of the weak measurement proposal. a) A general meth...

Spin–orbit coupling in surface plasmon scattering by nanostructures

“…The consideration of polarization degree of freedom in electromagnetic waves paves the way for a variety of novel optical effects, like optomechanical forces 15 and mimicking spintronics 16 and spin-based electronic circuits 17 , where additional (spinor) degree of freedom extends the space of scalar wavefunctions to vectorial variables. An optical analogue of the inverse SHE described here in scattering of highly confined plasmonic waves on metal-dielectric interface, capable of carrying transverse spin, may ultimately serve as the platform for conventional or quantum electromagnetic signal processing, providing, among others, an integrated source of LCP/RCP-entangled photons 18,19 , orbital angular momentum entanglement 20,21 and platforms for testing fundamental laws of nature 22 . Being a fundamental optical effect, it also brings crossdisciplinary similarities, for example, spin-current injections and related effects in solid-state electronic devices.…”

Fundamental Features of Quantum Dynamics Studied in Matter-Wave Interferometry—Spin Weak Values and the Quantum Cheshire-Cat

“…Our results clearly show that the determined weak values are of quantum-mechanical origin, no classical (wave) theory can describe the weak values observed in our experiment. A full determination of the weak value can be used to characterize the evolution of the neutron's wave-function inside an interferometer, just like in a report of a photonic double-slit experiment [53]. Moreover, our measurement scheme with a neutron interferometer is applied to demonstrate a fundamental phenomenon of quantum mechanics, namely the quantum Cheshire Cat.…”

“…The weak value's property of allowing information to be extracted from a quantum system with minimal disturbance is applied as a new method for estimation of quantum states [47][48][49][50] (see [51] for a recent review). This particular property of the weak value is also utilized in experimental tests of a reformulation of Heisenberg's uncertainty principle [52][53][54][55] (an overview of different viewpoints of that topic can be found in [56]). In addition, the weak value and weak measurements have been successfully applied to quantum paradoxes such as the three-box problem [57] and Hardy's paradox [58][59][60].…”

Quantum Inverse Measurement Theory Contributing to the Birth of Interpretation System of Quantum Mechanics of Local-Realism and Determinism

“…Lee Rozema in the quantum optics research group of the University of Toronto has designed a device for measuring object properties. The results of the study are published in September 7, 2012 in the Physical Review Letters [4].…”