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European Conference on Optical Communication

Quantum theory of noise in stokes vector receivers and application to bit error rate analysis

Kazuro Kikuchi

Published Jan 1, 2019• 2 citations
Publisher

Abstract

Polarization-modulated optical signals can be demodulated via direct detection of Stokes vectors. In this article, we develop a quantum theory of noise in the Stokes vector receiver. Examining the conditions that enable simultaneous measurement of three elements of the Stokes vector, we demonstrate that an optical pre-amplifier in front of the Stokes vector receiver can reduce the power penalty associated with simultaneous measurements, down to the quantum limit of 3 dB. Then, the 3-D Gaussian noise model for the shot noise and optical pre-amplifier noise is discussed. Subsequently, based on the noise analyses, we derive bit error rate formulae for the cubic-lattice polarization modulation format and evaluate the sensitivity of the Stokes vector receiver.

DOI
10.1049/cp.2019.1042

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Polarization-modulated optical signals can be demodulated via direct detection of Stokes vectors. In this article, we develop a quantum theory of noise in the Stokes vector receiver. Examining the conditions that enable simultaneous measurement of three elements of the Stokes vector, we demonstrate that an optical pre-amplifier in front of the Stokes vector receiver can reduce the power penalty associated with simultaneous measurements, down to the quantum limit of 3 dB. Then, the 3-D Gaussian noise model for the shot noise and optical pre-amplifier noise is discussed. Subsequently, based on the noise analyses, we derive bit error rate formulae for the cubic-lattice polarization modulation format and evaluate the sensitivity of the Stokes vector receiver.
We study the limits that quantum mechanics imposes on the accuracy of the measurement of the Stokes polarization-vector in the case of classical states. Using the apparatus of the conventional Stokes receiver, we propose an estimation method that allows not only to exceed the signal-to-noise limit that is achieved by a heterodyne measurement or after ideal phase-insensitive amplification, but also to achieve the quantum SNR limit for the measurement of classical light. We refer to this receiver scheme as the enhanced Stokes receiver.
Two schemes for interferometric optical phase measurement, with sensitivity limited only by quantum noise in the light, are analyzed. Direct detection is applicable to signals at modulation frequencies away from the technical noise of the light, so that quantum noise dominates the measurement. Alternatively signals otherwise obscured by classical optical noise may be recovered with a phase-modulation technique that shifts the signals to a quantum-noise-limited region of the photocurrent spectrum. The analysis is tested experimentally by using a polarimetric electric-field sensor. In the direct-detection scheme quantum-noise-limited performance produced a phase sensitivity of 0.25 µrad. The indirect scheme allowed subkilohertz signals to be extracted from classical noise 67 dB greater with sensitivity approaching the quantum noise limit.
Optical direct detection usually operates far above the quantum limit, due to the high thermal noise level of PIN photodiodes. For signal energy at the quantum level, the thermal effects in photon counters are also a strong limitation. The optical amplification or the heterodyne detection of the 2 quadratures of the field, widely used in high bit rate and long haul optical systems, overcome this limitation at the expense of a minimum 3db noise figure. By allowing a noise free mixing gain, as well as single quadrature measurements, the balanced homodyne receiver is allowed to reach quantum noise limited operation. The aim of this paper is to review the different quantum receiver implementations and to compare the minimum signal energy required to achieve a given bit error rate, or a given bit erasure rate, in high bit rate communications and quantum communications. Application to quantum cryptography will be also addressed.
In this paper, we consider the influence of a divergence of polarization of a quantum signal transmitted through an optical fiber channel on the quantum bit error rate of the subcarrier wave quantum key distribution protocol. Firstly, we investigate the dependence of the optical power of the signal on the modulation indices' difference after the second phase modulation of the signal. Then we consider the Liouville equation with regard to relaxation in order to develop expressions of the dynamics of the Stokes parameters. As a result, we propose a model that describes quantum bit error rate for the subcarrier wave quantum key distribution depending on the characteristics of the optical fiber. Finally, we propose several methods for minimizing quantum bit error rate.