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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Analysis of errors in an optical Controlled-NOT gate with a high-precision testing bed

Tomohisa Nagata, Ryo Okamoto, Holger Friedrich Hofmann, Shigeki Takeuchi, Keiji Sasaki

Published Jun 1, 2007• 0 citations
Publisher

Abstract

In our paper, we report the analysis of errors in the C-NOT gate using a high-precision test-bed. From the result of previous experiment, we have identified two main causes of errors: one is the mismatch between optical modes, and the other is the un-intentional phase shift between two polarization, horizontal polarizations and vertical polarization. To evaluate these factors more precisely, we construct a test-bed setup in which piezo-electric stages are used to avoid mode mismatch, and the extinction ratio of polarization is kept below 10-3. In the poster, we will report the experimental results with the test-bed and the analysis of errors in detail.

DOI
10.1109/cleoe-iqec.2007.4386920

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In our paper, we report the analysis of errors in the C-NOT gate using a high-precision test-bed. From the result of previous experiment, we have identified two main causes of errors: one is the mismatch between optical modes, and the other is the un-intentional phase shift between two polarization, horizontal polarizations and vertical polarization. To evaluate these factors more precisely, we construct a test-bed setup in which piezo-electric stages are used to avoid mode mismatch, and the extinction ratio of polarization is kept below 10-3. In the poster, we will report the experimental results with the test-bed and the analysis of errors in detail.
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The errors in linear optics controlled not (C-NOT) gates are analyzed considering the polarization-dependent phase sifts, in addition to the incorrectness of the beam splitting ratios. It is shown that the phase sifts at the optical components is as crucial as other error sources discussed in the previous studies. Such a phase shift unintentionally changes the linearly-polarized photons into a elliptically polarized ones. The operators for a beam splitting device and the process matrix of the C-NOT operation including such errors are also given.
Possible error sources in an experimentally realized linear-optics controlled-Z gate[1] are analyzed by considering the deviations of the beam splitting ratios from the ideal values (δRH,δRV), the polarization-dependent phase shift (birefringence) of the optical components (δφ) and the mode mismatch of input photons (δξ). It is found that the error rate is linearly dependent on δRV and δξ , while the dependence on δRH and δφ is approximately quadratic. As a practical result, the gate is much more sensitive to small errors in RV than in RH. Specifically, the reflectivity error for vertical polarization must be less than 0.1% to realize a gate with an error of less than 0.1%, whereas the reflectivity error for horizontal polarization can be up to 1%. It is also shown that the effects of different error sources are not independent of each other (linear error model). Under certain conditions, the deviation from the linear error model exceeds 10% of the total error. The method of analysis used illustrates the basic features of errors in general linear optics quantum gates and circuits, and can easily be adapted to any other device of this type.
Silica Planar Lightwave Circuit Based Integrated 1 ×\times× 4 Polarization Beam Splitter Module for Free-Space BB84 Quantum Key Distribution
We have developed an integrated polarization beam splitter (PBS) module with silica planar lightwave circuit technology for use in BB84 quantum key distribution (QKD). The PBS module is designed to operate on four linear polarizations of the horizontal/vertical/diagonal/antidiagonal direction, and shows the minimum polarization extinction ratio of 17.6 dB. When the module is loaded on the free-space BB84 QKD test-bed, quantum bit error rate and sifted key rate are 2.81% and 415 kb/s at clock rate of 100 MHz, respectively.
We experimentally demonstrate optical Mach-Zehnder interferometer utilizing displaced Sagnac configuration to enhance its phase stability. The interferometer with footprint of 27×40 cm offers individually accessible paths and shows phase deviation less than 0.4° during a 250 s long measurement. The phase drift, evaluated by means of Allan deviation, stays below 3° or 7 nm for 1.5 h without any active stabilization. The polarization insensitive design is verified by measuring interference visibility as a function of input polarization. For both interferometer's output ports and all tested polarization states the visibility stays above 93%. The discrepancy in visibility for horizontal and vertical polarization about 3.5% is caused mainly by undesired polarization dependence of splitting ratio of the beam splitter used. The presented interferometer device is suitable for quantum-information and other sensitive applications where active stabilization is complicated and common-mode interferometer is not an option as both the interferometer arms have to be accessible individually.