Uncertainty relations for general phase spaces

Werner, R. F.

doi:10.1007/s11467-016-0558-5

Cited by 21 publications

(41 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Of the two metrics we only demand translation invariance d(x + z, y + z) = d(x, y), which makes sense because the domain is a group. We claim [51] that in all these cases the uncertainty regions for measurement and preparation coincide. The crucial step is to consider a special type of joint measurement, called a covariant phase space measurement.…”

Section: Results On Measurement and Preparation Uncertaintymentioning

confidence: 72%

Uncertainty from Heisenberg to Today

Werner

Farrelly

2019

Found Phys

Self Cite

View full text Add to dashboard Cite

We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit", visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg's programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg's work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between shaky arguments and overarching claims. Nevertheless, the main message can be taken into the new quantum theory, and can be brought into the form of general theorems. They come in two kinds, not distinguished by Heisenberg. These are, on one hand, constraints on preparations, like the usual textbook uncertainty relation, and, on the other, constraints on joint measurability, including trade-offs between accuracy and disturbance.

show abstract

Section: Results On Measurement and Preparation Uncertaintymentioning

confidence: 72%

Uncertainty from Heisenberg to Today

Werner

Farrelly

2019

Found Phys

Self Cite

View full text Add to dashboard Cite

show abstract

“…There are also variants, in which the sharpness of a distribution is measured by other quantities than the usual variance [10][11][12][13], for instance entropies [14,15], or where more than two observables are considered simultaneously [16,17]. Quite different methods [18] are needed for optimal measurement uncertainty relations [10], or information-disturbance bounds [10], so we will not consider these aspects here.…”

Section: Introductionmentioning

confidence: 99%

State-Independent Uncertainty Relations and Entanglement Detection in Noisy Systems

2017

Self Cite

View full text Add to dashboard Cite

Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal state-independent lower bound for the sum of the variances for any set of two or more measurements. The bounds come with a guaranteed error estimate, so results of preassigned accuracy can be obtained straightforwardly. Our method also works for postive-operator-valued measurements. Therefore, it can be used for detecting entanglement in noisy environments, even in cases where conventional spin squeezing criteria fail because of detector noise.

show abstract

“…Moreover, we identify the class of the approximate joint measurements with the class of the joint POVMs satisfying the same symmetry properties of their target position and momentum observables [3,23]. We are supported in this assumption by the fact that, in the discrete case [41], simmetry covariant measurements turn out to be the best approximations without any hypothesis (see also [17,19,20,29,32] for a similar appearance of covariance within MURs for different uncertainty measures).…”

Section: Introductionmentioning

confidence: 84%

“…A very rich literature on this topic flourished in the last 20 years, and various kinds of MURs have been proposed, based on distances between probability distributions, noise quantifications, conditional entropy, etc. [12,[14][15][16][17][18][19][20][21][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation

Barchielli

Gregoratti

Toigo

2017

Entropy

View full text Add to dashboard Cite

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be quantified in various ways. The relative entropy is the natural theoretical quantifier of the information loss when a 'true' probability distribution is replaced by an approximating one. In this paper, we provide a lower bound for the amount of information that is lost by replacing the distributions of the sharp position and momentum observables, as they could be obtained with two separate experiments, by the marginals of any smeared joint measurement. The bound is obtained by introducing an entropic error function, and optimizing it over a suitable class of covariant approximate joint measurements. We fully exploit two cases of target observables: (1) n-dimensional position and momentum vectors; (2) two components of position and momentum along different directions. In (1), we connect the quantum bound to the dimension n; in (2), going from parallel to orthogonal directions, we show the transition from highly incompatible observables to compatible ones. For simplicity, we develop the theory only for Gaussian states and measurements.

show abstract

Uncertainty relations for general phase spaces

Cited by 21 publications

References 18 publications

Uncertainty from Heisenberg to Today

Uncertainty from Heisenberg to Today

State-Independent Uncertainty Relations and Entanglement Detection in Noisy Systems

Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation

Contact Info

Product

Resources

About