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Physical Review A

Compensation of losses in photodetection and in quantum-state measurements

T. Kiss, Ulrike Herzog, Ulf Leonhardt

Published Sep 1, 1995• 104 citations
Publisher

Abstract

We show how losses in photodetection and in quantum-state measurements can be numerically compensated after the measurements have been performed. When the overall efficiency exceeds 1/2, our recipe works for all quantum states. For smaller efficiencies, however, the convergence of the compensation procedure depends on the quantum state under investigation.

DOI
10.1103/physreva.52.2433

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Compensation of detection losses in quantum state reconstruction

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We show how losses in photodetection and in quantum-state measurements can be numerically compensated after the measurements have been performed. When the overall efficiency exceeds 1/2, our recipe works for all quantum states. For smaller efficiencies, however, the convergence of the compensation procedure depends on the quantum state under investigation.
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 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)].
Polarization-dependent loss (PDL) is a serious problem that hinders the transfer of polarization qubits through quantum networks. Recently it has been shown that the detrimental effects of PDL on qubit fidelity can be compensated for with the introduction of an additional passive PDL element that rebalances the polarization modes of the transmitted qubit. This procedure works extremely well when the output of the system is postselected on photon detection. However, in cases where the qubit might be needed for further analysis this procedure introduces unwanted vacuum terms into the state. Here we present procedures for the compensation of the effects of PDL using noiseless amplification and attenuation. Each of these techniques introduces a heralding signal into the correction procedure that significantly reduces the vacuum terms in the final state. When detector inefficiency and dark counts are included in the analysis noiseless amplification remains superior, in terms of the fidelity of the final state, to both noiseless attenuation and passive PDL compensation for detector efficiencies greater than 40%.