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Russian Microelectronics

Investigating the effect of amplitude and phase relaxation on the quality of quantum information technologies

Yu. I. Bogdanov, B. I. Bantysh, Andrey Yu. Chernyavskiy, Vladimir F. Lukichev, Alexander A. Orlikovsky

Published Jul 1, 2015• 5 citations
Publisher

Abstract

In the formalism of quantum operations, we investigate the effect of the amplitude and phase relaxation on the evolution of quantum states. A model of the polarizing qubit, whose noises depend on the spectral degree of freedom that manifests itself in the process of light propagation in the anisotropic medium with dispersion, is discussed. An approximate analytical model is proposed for evaluating the effect of the phase plate on the polarizing state, taking into account the dispersion of light.

DOI
10.1134/s1063739715040022

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In the formalism of quantum operations, we investigate the effect of the amplitude and phase relaxation on the evolution of quantum states. A model of the polarizing qubit, whose noises depend on the spectral degree of freedom that manifests itself in the process of light propagation in the anisotropic medium with dispersion, is discussed. An approximate analytical model is proposed for evaluating the effect of the phase plate on the polarizing state, taking into account the dispersion of light.
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In this work we consider the Liouville equation; it describes the dynamics of the photon density matrix in the Schr\"odinger representation based on the Markov approximation in the channel without dispersion. The equation contains a relaxation superoperator dependent on the phenomenological parameters of the optical fiber. These parameters allow one to take into account the phenomena of birefringence and optical activity, isotropic absorption, and dichroism. We also present in our work that these parameters affect not only the polarization of the states but the length of the Stokes vector. Hence the developed technique describes the decoherence process in the polarization domain in the quantum case and allows one to analyze the dynamics of single-photon states in the quantum (depolarizing) channel more properly. We also present a visual illustration of polarization states' evolution in the polarization-coded quantum key distribution BB84 protocol as an example. We estimate quantum bit error rates' dependence on channel length. Also we examine maximal allowed channel length, dependent on various configurations of channel parameters.
The wave plate is a basic device for transforming and measuring the polarization states of light. It is known that the transformation of light by means of two wave plates makes it possible to measure the state of polarization in an arbitrary basis. The finite spectral width of the light, however, leads to a chromatic aberration of the polarization quantum transformation caused by the parasitic dispersion of the birefringence of the plate material. This causes systematic errors in the tomography of quantum polarization states and significantly reduces its accuracy. This study is a development of our work1, in which an adequate model for quantum measurements of polarization qubits under chromatic aberration was first formulated. This work includes a generalization of the results obtained earlier for the cases of two-qubit states. Along with examples of random states those uniformly distributed over the Haar measure are considered. Using a matrix of complete information, it is quantitatively traced how the presence of chromatic aberrations under conditions of a finite spectral width of light leads to the loss of information in quantum measurements. It is shown that the use of the developed model of fuzzy measurements instead of the model of standard projection measurements makes it possible to suppress systematic errors of quantum tomography even when using high-order wave plates. It turns out that the fuzzy measurement model can give a significant increase in the reconstruction accuracy compared to the standard measurement model.