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International Conference on Micro- and Nano-Electronics (ICMNE)

Measurement of polarization quantum states under chromatic aberration conditions

Yu. I. Bogdanov, Boris I. Buntysh, Nadezhda A. Bogdanova, Marat I. Shakirov, Vladimir F. Lukichev

Published Jan 31, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2624247

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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.
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.
Abstract In this work we present an algorithm of building an adequate model of polarizing quantum state measurement. This model takes into account chromatic aberration of the basis change transformation caused by the parasitic dispersion of the wave plates crystal and finite radiation spectral bandwidth. We show that the chromatic aberration reduces the amount of information in the measurements results. Using the information matrix approach we estimate the impact of this effect on the qubit state reconstruction fidelity for different values of sample size and spectral bandwidth. We also demonstrate that our model outperforms the standard model of projective measurements as it could suppress systematic errors of quantum tomography even when one performs the measurements using wave plates of high order.
Systematic errors are inevitable in most measurements performed in real life because of imperfect measurement devices. Reducing systematic errors is crucial to ensuring the accuracy and reliability of measurement results. To this end, delicate error-compensation designs are often necessary in addition to device calibration to reduce the dependence of the systematic error on the imperfection of the devices. The art of error-compensation designs is well appreciated in nuclear magnetic resonance systems by using composite pulses. In contrast, there are few works on reducing systematic errors in quantum optical systems. Here we propose an error-compensation design applicable to reducing the systematic error in projective measurements on ensembles of both single and multiqubit systems. This design can significantly decrease the systematic error due to dominant error sources in typical optical experiments. In particular, it can reduce the systematic error to the second order of the phase errors of both the half-wave plate (HWP) and the quarter-wave plate as well as the angle error of the HWP. Its power in reducing the systematic error was verified experimentally on qubit state tomography and numerically on two-qubit state tomography. Our study may find applications in high-precision tasks in polarization optics and quantum optics.
Abstract A model for calculating quantum tomography protocols of ionic qudits is proposed, which allows taking into account errors in setting transformation parameters during measurements. The fidelity of ionic qudit tomography under errors in specifying transformation parameters is compared between the standard method and the method of fuzzy quantum measurements. A radical advantage of the fuzzy quantum measurement model over the standard model is demonstrated. It is shown that the developed model makes it possible to obtain a set of two-level of quantum state transformations of qudits that ensures the implementation of the given quantum measurement protocol.
The report presents a general approach for estimating quantum information technologies by means of fuzzy quantum measurements. The developed methods are used for precision reconstruction of quantum states under conditions of significant influence of decoherence and quantum noise. Monitoring of the amount of information about quantum states and their parameters, including the loss of information caused by the effect of quantum noise, is considered. Examples of the developed approach as applied to readout errors and phase relaxation are presented.
The report presents a general approach for estimating quantum information technologies by means of fuzzy quantum measurements. The developed methods are used for precision reconstruction of quantum states under conditions of significant influence of decoherence and quantum noise. Monitoring of the amount of information about quantum states and their parameters, including the loss of information caused by the effect of quantum noise, is considered. Examples of the developed approach as applied to readout errors and phase relaxation are presented.