arXiv:1403.0368

Comment on "Noise and Disturbance in Quantum Measurements: An Information-Theoretic Approach"

Paul Busch, PEKKA J. LAHTI, Reinhard F. Werner

Published Mar 3, 2014• 1 citation

Abstract

In this comment on the work of F. Buscemi, M.J.W. Hall, M. Ozawa and M.M. Wilde [PRL 112, 050401, 2014, arXiv:1310.6603], we point out a misrepresentation of measures of error and disturbance introduced in our recent work [PRL 111, 160405, 2013, arXiv:1306.1565] as being "purely formal, with no operational counterparts". We also exhibit an tension in the authors' message, in that their main result is an error-disturbance relation for state-independent measures, but its importance is declared to be limited to discrete variables. In contrast, we point out the separate roles played by such relations for either state-dependent or state-independent measures of error and disturbance.

DOI: 10.48550/arxiv.1403.0368

Related papers

Comment on "Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement"

Paul Busch, PEKKA J. LAHTI, Reinhard F. Werner

In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since it is based on the choice of unsuitable and operationally problematical quantifications of measurement error and disturbance. As we have shown elsewhere [PRL 111, 160405, 2013], for appropriate choices of operational measures of error and disturbance, Heisenberg's heuristic relation can be turned into a precise inequality which is a rigorous consequence of quantum mechanics.

arXiv:1403.0367Mar 3, 20141 citation

Measurement Uncertainty: Reply to Critics

Paul Busch, PEKKA J. LAHTI, Reinhard F. Werner

In a recent publication [PRL 111, 160405 (2013)] we proved a version of Heisenberg's error-disturbance tradeoff. This result was in apparent contradiction to claims by Ozawa of having refuted these ideas of Heisenberg. In a direct reaction [arXiv:1308.3540] Ozawa has called our work groundless, and has claimed to have found both a counterexample and an error in our proof. Here we answer to these allegations. We also comment on the submission [arXiv:1307.3604] by Rozema et al, in which our approach is unfavourably compared to that of Ozawa.

arXiv:1402.3102Feb 13, 20145 citations

Noise and disturbance of qubit measurements: An information-theoretic characterization

Alastair A. Abbott, Cyril Branciard

Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These definitions are invariant under relabeling of measurement outcomes, and lend themselves readily to the formulation of state-independent uncertainty relations both for the joint estimate of observables (noise-noise relations) and the noise-disturbance tradeoff. Here we derive such relations for incompatible qubit observables, which we prove to be tight in the case of joint estimates, and present progress towards fully characterizing the noise-disturbance tradeoff. In doing so, we show that the set of obtainable noise-noise values for such observables is convex, whereas the conjectured form for the set of obtainable noise-disturbance values is not. Furthermore, projective measurements are not optimal with respect to the joint-measurement noise or noise-disturbance tradeoffs. Interestingly, it seems that four-outcome measurements are needed in the former case, whereas three-outcome measurements are optimal in the latter.

arXiv:1607.00261Physical Review ADec 12, 201613 citations

Noise and disturbance in quantum measurements and operations

Masanao Ozawa

Heisenberg's uncertainty principle has been understood to set a limitation on measurements, whereas the long standing mathematical formulation does not allow such an interpretation. Recently, a new relation was found by the present author to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing. Here, we discuss the state-dependent notion of precise measurements of a given observable, and consider a perfect distance such that zero distance implies the perfect correlation. Then, we shall show that even in the perfect error notions both the position measuring noise and the momentum disturbance can be arbitrarily small. We also show that it is possible to generalize the new noise-disturbance uncertainty relation to perfect error distances.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 5, 20068 citations

Determining measurement errors: where the good meet the bad

Paul Busch, Neil Stevens

Recently there have been claims of experimental violations of Heisenberg's error-disturbance relation [Rozema et al, PRL 109, 200404 (2012), Erhard et al, Nature Phys. 8, 185 (2012)]. These claims were contradicted by a proof of a form of such relations [Busch et al, PRL 111, 160405 (2013)], showing that the validity of any formalization of Heisenberg's principle depends on the choice of appropriate measures of error and disturbance. While the error quantity underlying the experiments was shown to be conceptually problematic in general, it turns out to coincide, in the qubit experiments in question, with the alternative error measure used by Busch et al. Here we analyze this coincidence and discover a technique, hitherto deemed unavailable, for determining the disturbance measure. We show that this procedure reflects directly the operational meaning of the disturbance measure, in contrast to the weak-value method used in the experiments of Rozema et al and several other groups. The latter is thus not fundamental for an understanding of the quantum mechanical error-disturbance trade-off. The strong scheme is also shown to be applicable to a wider class of joint measurement scenarios.

Jul 29, 20140 citations

A Note on Different Definitions of Momentum Disturbance

Lee A. Rozema, Dylan H. Mahler, Alex Hayat +1 more

In [1], Busch et al. showed that it is possible to construct an error-disturbance relation having the same form as Heisenberg's original heuristic definition[2], in contrast to the theory proposed by Ozawa[3] which we and others recently confirmed experimentally[4,5]. With Ozawa's definitions of measurement error and disturbance, a relation of Heisenberg's form is not in general valid, and a new error-disturbance relationship can be derived. Here we explain the different physical significance of the two definitions, and suggest that Ozawa's definition better corresponds to the usual understanding of the disturbance that Heisenberg discussed.

arXiv:1307.3604Jul 13, 20135 citations