Proof of Heisenberg's error-disturbance relation.

@article{Busch2013ProofOH,
  title={Proof of Heisenberg's error-disturbance relation.},
  author={Paul Busch and Pekka Lahti and Reinhard F. Werner},
  journal={Physical review letters},
  year={2013},
  volume={111 16},
  pages={
          160405
        }
}
While the slogan "no measurement without disturbance" has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [L. Rozema et al, Phys. Rev… 

Figures from this paper

Quantum rms error and Heisenberg's error-disturbance relation

Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8 , 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109 , 100404 (2012)] include claims of a violation of

Soundness and completeness of quantum root-mean-square errors

  • M. Ozawa
  • Physics
    npj Quantum Information
  • 2019
Defining and measuring the error of a measurement is one of the most fundamental activities in experimental science. However, quantum theory shows a peculiar difficulty in extending the classical

Heisenberg Uncertainty Relations: An Operational Approach

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal

Quantum uncertainty switches on or off the error-disturbance tradeoff

It is demonstrated both theoretically and experimentally that there is no tradeoff if the outcome of measuring B is more uncertain than that of A, and the tradeoff will be switched on and well characterized by the Jensen-Shannon divergence.

Disturbance-Disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance

The Heisenberg uncertainty principle, which underlies many quantum key features, is under close scrutiny regarding its applicability to new scenarios. Using both the Bell-Kochen-Specker theorem

Verifying Heisenberg’s error-disturbance relation using a single trapped ion

An experimental test of one of the new Heisenberg’s uncertainty relations using a single 40Ca+ ion trapped in a harmonic potential is reported, providing the first evidence confirming the BLW-formulated uncertainty at a single-spin level.

Colloquium: Quantum root-mean-square error and measurement uncertainty relations

Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement

Error-disturbance relation in Stern-Gerlach measurements

Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic uncertainties in quantum states, Heisenberg's error-disturbance relation (EDR) has been

Uncertainty from Heisenberg to Today

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 developed later. We recount the

Disproving Heisenberg's error-disturbance relation

Recently, Busch, Lahti, and Werner (arXiv:1306.1565v1 [quant-ph]) claimed that Heisenberg's error-disturbance relation can be proved in its original form with new formulations of error and
...

References

SHOWING 1-10 OF 29 REFERENCES

Probabilistic and Statistical Aspects of Quantum Theory

Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV.

Quant

  • Inform. Comput. 4, 546
  • 2004

Gruppentheorie und Quantenmechanik (Hirzel, Leipzig, 1928)

  • 1928

Quantum Inf

  • Comput. 4, 546
  • 2004

Zeitschrift für Physik 44

  • 326
  • 1927

Zeitschr

  • Phys. 44, 326
  • 1927

Phys

  • Rev. 34, 163
  • 1929

43