Heisenberg uncertainty for qubit measurements (original) (raw)
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Experimental Test of Heisenberg's Measurement Uncertainty Relation Based on Statistical Distances
Physical review letters, 2016
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [P. Busch et al., Phys. Rev. Lett. 111, 160405 (2013); P. Busch et al., Phys. Rev. A 89, 012129 (2014)]. Here we reformulate their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible observables designed to approximate two incompatible observables on one qubit are measured simultaneously.
Heisenberg's error-disturbance uncertainty relation: Experimental study of competing approaches
Physical Review A, 2017
Over the past few years, Heisenberg's error-disturbance uncertainty relation has experienced increased attention since several experimental publications verified the theoretical findings of Ozawa predicting the violation and thus necessary reformulation of Heisenberg's relation. However, soon after their appearance, an alternative theory was presented by Busch and co-workers, which proclaimed the validity of Heisenberg's relation and thus gave rise to heated debates. Here, we present an experimental comparison of the competing approaches by applying them to the same neutron optical measurement apparatus. Empirical results for the different definitions of error and disturbance are presented for special input states and configurations of the apparatus to illustrate the opposing approaches. The inequalities restricting errors and disturbances are particularly emphasized. Despite the strong controversy, in the case of projectively measured qubit observables, both approaches lead to equal outcomes.
Towards a new uncertainty principle: quantum measurement noise
Physics Letters A, 1991
Two generalizations of a known approach to the joint measurement of position and momentum to the joint measurement of more general pairs of observables are compared. They weaken the restrictions on “noisy” measurements that prevented the above method from being more generally usable, in two different ways: additive object-dependent noise versus object-independent non-additive noise. In the latter approach a lower bound for the amount of noise in a joint measurement of incompatible observables is found, not as a consequence of the usual Heisenberg scatter principle, but of a new “inaccuracy principle”. Physically realizable examples are given.
Error and unsharpness in approximate joint measurements of position and momentum
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg’s famous but often challenged measurement uncertainty relation. This relation takes the form of a trade-off for the necessary errors in joint approximate measurements of position and momentum and other incompatible pairs of observables. Much work remains to be done to obtain a better understanding of the new error measures and their suitability. To this end we review here some of these error measures and associated measurement uncertainty relations. We investigate the properties and suitability of these measures, give examples to show how they can be computed in specific cases, and compare their relative strengths as criteria for “good” approximations.
Nature Physics, 2012
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics [1,. It was Heisenberg who used the famous gamma-ray microscope thought experiment to illustrate this indeterminacy . A lower bound was set for the product of the measurement error of an observable and the disturbance caused by the measurement. Later on, the uncertainty relation was reformulated in terms of standard deviations , which focuses solely on indeterminacy of predictions and neglects unavoidable recoil in measuring devices . A correct formulation of the error-disturbance relation, taking recoil into account, is essential for a deeper understanding of the uncertainty principle. However, the validity of Heisenberg's original error-disturbance uncertainty relation is justified only under limited circumstances . Another error-disturbance relation, derived by rigorous and general theoretical treatments of quantum measurements, is supposed to be universally valid . Here, we report a neutron optical experiment that records the error of a spin-component measurement as well as the disturbance caused on another spin-component measurement. The results confirm that both error and disturbance completely obey the new, more general relation but violate the old one in a wide range of an experimental parameter.
The Theory of Quantum Uncertainties and Quantum Measurements
- We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time ttt. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time t_0t_0t_0 under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove th...
Informatic error-disturbance relation in the qubit case
In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and the caused disturbance on another complementary observable. In the quantum theory, most of uncertainty relations are proposed to reveal the amount of unavoidable uncertainty in the measuring process. In this paper, we study the error-disturbance relation from the information viewpoint. We ask how much information, rather than how much uncertainty, can be obtained during the two sequential measurements. To achieve optimal information gain, we argue that the strategy for the "intelligent" prior apparatus is to clone the unknown state, and for the posterior one is to perform the swapping operation. We propose the coarse-grained random access code, and therein information causality as a physical principle can be exploited for deriving the upper-bound of information gain. Finally, we conjecture the information gain of measuring the position and momentum of a quantum object in the coarse-grained way.
Fortschritte Der Physik-progress of Physics, 2003
Common misconceptions on the Heisenberg principle are reviewed, and the original spirit of the principle is reestablished in terms of the trade-off between information retrieved by a measurement and disturbance on the measured system. After analyzing the possibility of probabilistically reversible measurements, along with erasure of information and undoing of disturbance, general information-disturbance trade-offs are presented, where the disturbance of the measurement is related to the possibility in principle of undoing its effect. *
Uncertainty characteristics of generalized quantum measurements
Physical Review A, 2003
The effects of any quantum measurement can be described by a collection of measurement operators ͕M m ͖ acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.