Is the Heisenberg uncertainty relation really violated?

Bell's Theorem: a new Derivation that Preserves Heisenberg and Locality

By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time depend…

Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements

Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of measuring apparatuses. Here, Heisenberg's uncertainty relation is generalized to a relation that holds for all the possible quantum measurements, from which conditions are obtained for measuring apparatuses to satisfy Heisenberg's relation. In particular, every apparatus with the noise and the disturbance statistically independent from the measured object is p…

Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements

Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.

Does consciousness really collapse the wave function? A possible objective biophysical resolution of the measurement problem

An analysis has been performed of the theories and postulates advanced by von Neumann, London and Bauer, and Wigner, concerning the role that consciousness might play in the collapse of the wave function, which has become known as the measurement problem. This reveals that an error may have been made by them in the area of biology and its interface with quantum mechanics, when they called for the reduction of any superposition states in the brain through the mind or consciousness. Many years later Wigner changed his mind to reflect a simpler and more realistic objective position, expanded upon…

Experimental test of error-disturbance uncertainty relation with continuous variables

Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for Gaussian states. Two conjugate continuous-variable observables, amplitude and phase quadratures of an optical mode, are measured simultaneously by using a heterodyne measurement system. The EDR with continuous variables for a coherent state, a squeezed state and a thermal state are verified experimentally. Our experimental results demonstrate that Heisenberg…

Error-disturbance uncertainty relations in Faraday measurements

We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate the error and disturbance of the model and examine the uncertainty relations. We found that for the coherent light meter in pure polarization, both the error and disturbance behave the cyclic oscillations due to the Faraday rotation in both the light and spin polarizations. We also examine a class of polarization squeezed light meter, where we apply the phase-…

超导量子处理器中的误差-扰动不确定性关系

Error-disturbance uncertainty relations in a superconducting quantum processor

本文在NISQ超导量子处理器上通过顺序弱测量实验检验误差-扰动不确定性关系，发现Heisenberg EDR被违反而Ozawa和Branciard EDR在整个测量强度范围内均成立，验证了普适EDR在含噪量子处理器中的有效性。

How well can we guess the outcome of measurements of non-commuting observables?

According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily large factor if one aims, instead, to guess the unknown value of a past measurement. For experiments on a single quantum system, the precise assignment of past position and momentum measurement outcomes is accompanied by large uncertainty about their linear combinations, while we show that entanglement with an ancillary system permits accurate retrodiction of an…

Equivalence principle violation from large scale structure

We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances. Specifically, we observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched. To obtain the above result, spinor and scalar fields are separately analyzed by considering the non-relativist…

Linear simultaneous measurements of position and momentum with minimum error-trade-off in each minimum uncertainty state

So-called quantum limits and their achievement are important themes in physics. Heisenberg's uncertainty relations are the most famous of them but are not universally valid and violated in general. In recent years, the reformulation of uncertainty relations is actively studied, and several universally valid uncertainty relations are derived. On the other hand, several measuring models, in particular, spin-1/2 measurements, are constructed and quantitatively examined. However, there are not so many studies on simultaneous measurements of position and momentum despite their importance. Here we s…

基于盒中粒子动量新概念的反弹波包、Ehrenfest 定理与不确定关系

Bouncing Wave Packets, Ehrenfest Theorem, and Uncertainty Relation based upon a new Concept for the Momentum of a Particle in a Box

针对盒中粒子动量算符非自伴导致 Ehrenfest 定理失效的问题，本文采用新型自伴动量算符，证明该定理对所有物理边界条件成立，并用反弹波包加以阐释，同时给出 HRS 不确定关系的简洁形式及物理解释。