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arXiv:quant-ph/0305069 · Journal of Physics A Mathematical and General

Reply to the Comment on On the uncertainty relations and squeezed states for the quantum mechanics on a circle

K. Kowalski, J Rembieli ski

Published May 8, 2003• 12 citations
arXivHTMLPDF

Abstract

In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently proposed uncertainty relations for a quantum particle on a circle. He states that (i) the quantity $Δ^2(\hatϕ)$ introduced by us representing the uncertainty of the angle is not a proper measure of the position uncertainty and therefore the proposed inequalities can hardly be qualified as a relevant uncertainty relations on a circle; and that (ii) the most suitable uncertainty relations on a circle are those based on the Gram-Robertson matrix. It is shown by examples that both points are erroneous.

DOI
10.1088/0305-4470/36/20/323

Related papers

Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"

D. A. Trifonov

It is shown by examples that the position uncertainty on a circle, proposed recently by Kowalski and Rembieli\\'nski [J. Phys. A 35 (2002) 1405] is not consistent with the state localization. We argue that the relevant uncertainties and uncertainty relations (UR's) on a circle are that based on the Gram-Robertson matrix. Several of these generalized UR's are displayed and related criterions for squeezed states are discussed.

•Sep 4, 2002•7 citations

Comment on On the uncertainty relations and squeezed states for the quantum mechanics on a circle

D A Trifonov

It is shown by examples that the position uncertainty on a circle, proposed recently by Kowalski and Rembieliński (2002 J. Phys. A:Math. Gen. 35 1405 ) is not consistent with the state localization. We argue that the relevant uncertainties and uncertainty relations (URs) on a circle are those based on the Gram–Robertson matrix. Several of these generalized URs are displayed and related criteria for squeezed states are discussed.

arXiv:quant-ph/0209032•Journal of Physics A Mathematical and General•Feb 12, 2003•8 citations

Comment on `On the uncertainty relations and squeezed states for the quantum mechanics on a circle'

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Errors were introduced at typesetting stage to equations (11) and (12) on page 2201. Please see the pdf for the corrected formulas.

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On the uncertainty relations and squeezed states for the quantum mechanics on a circle

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The disputed question of uncertainty relations (UR) on a circle is regarded as a particular element of a more general problem which refers to the quantum description of angular observables $L_z$ and $ϕ$. The improvised $L_z-ϕ$ UR are found to be affected by unsourmontable shortcomings. Also in contradiction with a largely accepted belief it is proved that the usual procedures of quantum mechanics are accurately applicable for the $L_z-ϕ$ pair. The applicability regards both the known circular motions and the less known non-circular rotational motions. The presented facts contribute as arguments to the following indubitable conclusions: (i) the traditional interpretation of UR must be denied as an incorrect doctrine, (ii) for a natural physical consideration of the the $L_z-ϕ$ pair the results from the usual quantum mechanics are sufficient while the improvised $L_z-ϕ$ UR must be rejected as senseless formulas and (iii) the descriptions of quantum measurements have to be done in a framework which is distinct and additional in respect with the usual quantum mechanics.

arXiv:quant-ph/0206009•Jun 3, 2002•4 citations

Comment on "Uncertainty Relations for Positive Operator Valued Measures"

Alexey E. Rastegin

The principal aim of this Comment is to correct those entropic uncertainty relations that are presented in a paper by Massar [arXiv:quant-ph/0703036v2 (current version)], concerning two approaches to a study of the noise produced by POVM's. It is next emphasized that the first of the entropic bounds for POVM obtained by the above author has been already presented in Ref. [8]. Some exposition obscurity with equation (14) of the commented paper is elucidated. Finally, some more specific remarks on the paper content are given.

arXiv:0810.0083•Oct 1, 2008•1 citation
In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently proposed uncertainty relations for a quantum particle on a circle. He states that (i) the quantity Δ2(ϕ^)Δ^2(\hatϕ)Δ2(ϕ^​) introduced by us representing the uncertainty of the angle is not a proper measure of the position uncertainty and therefore the proposed inequalities can hardly be qualified as a relevant uncertainty relations on a circle; and that (ii) the most suitable uncertainty relations on a circle are those based on the Gram-Robertson matrix. It is shown by examples that both points are erroneous.
The disputed question of uncertainty relations (UR) on a circle is regarded as a particular element of a more general problem which refers to the quantum description of angular observables LzL_zLz​ and ϕϕϕ. The improvised Lz−ϕL_z-ϕLz​−ϕ UR are found to be affected by unsourmontable shortcomings. Also in contradiction with a largely accepted belief it is proved that the usual procedures of quantum mechanics are accurately applicable for the Lz−ϕL_z-ϕLz​−ϕ pair. The applicability regards both the known circular motions and the less known non-circular rotational motions. The presented facts contribute as arguments to the following indubitable conclusions: (i) the traditional interpretation of UR must be denied as an incorrect doctrine, (ii) for a natural physical consideration of the the Lz−ϕL_z-ϕLz​−ϕ pair the results from the usual quantum mechanics are sufficient while the improvised Lz−ϕL_z-ϕLz​−ϕ UR must be rejected as senseless formulas and (iii) the descriptions of quantum measurements have to be done in a framework which is distinct and additional in respect with the usual quantum mechanics.
The principal aim of this Comment is to correct those entropic uncertainty relations that are presented in a paper by Massar [arXiv:quant-ph/0703036v2 (current version)], concerning two approaches to a study of the noise produced by POVM's. It is next emphasized that the first of the entropic bounds for POVM obtained by the above author has been already presented in Ref. [8]. Some exposition obscurity with equation (14) of the commented paper is elucidated. Finally, some more specific remarks on the paper content are given.