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arXiv:quant-ph/9801028 · Physical Review A

Reply to “Loss-error compensation in quantum-state measurements”

T. Kiss, Ulrike Herzog, Ulf Leonhardt

Published Apr 1, 1998• 18 citations
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Abstract

The authors of the preceding Comment [G. M. D'Ariano and C. Macchiavello, preceding paper, Phys. Rev. A 57, 3131 (1998)] tried to reestablish a $0.5$ efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].

DOI
10.1103/physreva.57.3134

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In the two papers [T. Kiss, U. Herzog, and U. Leonhardt, Phys. Rev. A 52, 2433 (1995); U. Herzog, Phys. Rev. A 53, 1245 (1996)] with titles similar to the one given above, the authors assert that in some cases it is possible to compensate a quantum efficiency $\ensuremath{\eta}<~1/2$ in quantum-state measurements, violating the lower bound $1/2$ proved in a preceding paper [G. M. D'Ariano, U. Leonhardt, and H. Paul, Phys. Rev. A 52, R1801 (1995)]. Here we reestablish the bound for homodyning any quantum state, and show how the proposed loss-compensation method would fail in a real measurement outside the $\ensuremath{\eta}>1/2$ regime.

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The authors of the preceding Comment [G. M. D'Ariano and C. Macchiavello, preceding paper, Phys. Rev. A 57, 3131 (1998)] tried to reestablish a 0.50.50.5 efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].
In the two papers [T. Kiss, U. Herzog, and U. Leonhardt, Phys. Rev. A 52, 2433 (1995); U. Herzog, Phys. Rev. A 53, 1245 (1996)] with titles similar to the one given above, the authors assert that in some cases it is possible to compensate a quantum efficiency $\ensuremath{\eta}<~1/2$ in quantum-state measurements, violating the lower bound 1/21/21/2 proved in a preceding paper [G. M. D'Ariano, U. Leonhardt, and H. Paul, Phys. Rev. A 52, R1801 (1995)]. Here we reestablish the bound for homodyning any quantum state, and show how the proposed loss-compensation method would fail in a real measurement outside the $\ensuremath{\eta}>1/2$ regime.
The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.