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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum security in homodyne reception using weak coherent states

E. García, Josué Aarón López-Leyva, Francisco Javier Mendieta, A. Arvizu

Published Aug 10, 2011• 1 citation
Publisher

Abstract

We present an experimental 8-port Balanced Homodyne Detector at 1550 nm wavelength, operating in free space, implemented with polarization devices to produce a circularly polarized local oscillator, splitting its In-Phase and Quadrature components to beat separately with the weak coherent incoming signal. This allows the simultaneous measurements of the 2 quadratures at the price of an additional noise due to the vacuum fields that leak via the unused ports, resulting in a modified Husimi function for joint probability distribution for the quadrature components. These schemes require the proper optical phase synchronization between the local oscillator and the incoming field, which constitutes a challenge for weak coherent state reception. To achieve this we designed and implemented an optical Costas loop; the feedback loop (especially the loop filter) which is a result of the optimal design has an impact on the mutual information between transmitter and receiver, being this parameter a condition to generate the cryptographic key. We present experimental and theoretical results on the performance of the mutual information between the transmitter and the receiver due the phase error for different photon numbers.

DOI
10.1117/12.902191

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We present an experimental 8-port Balanced Homodyne Detector at 1550 nm wavelength, operating in free space, implemented with polarization devices to produce a circularly polarized local oscillator, splitting its In-Phase and Quadrature components to beat separately with the weak coherent incoming signal. This allows the simultaneous measurements of the 2 quadratures at the price of an additional noise due to the vacuum fields that leak via the unused ports, resulting in a modified Husimi function for joint probability distribution for the quadrature components. These schemes require the proper optical phase synchronization between the local oscillator and the incoming field, which constitutes a challenge for weak coherent state reception. To achieve this we designed and implemented an optical Costas loop; the feedback loop (especially the loop filter) which is a result of the optimal design has an impact on the mutual information between transmitter and receiver, being this parameter a condition to generate the cryptographic key. We present experimental and theoretical results on the performance of the mutual information between the transmitter and the receiver due the phase error for different photon numbers.
Weak coherent states (WCS) are being extensively employed in quantum communications and cryptography at telecommunications wavelengths. For these low-photon-number applications, simultaneous field quadrature measurements are frequently required, such as in the detection of multilevel modulations in the communications scenario or in cryptographic applications employing continuous variables. For this task multiport balanced homodyne detection (BHD) structures are employed, based on the splitting of the received field into its (non-commutating) in-phase (I) and quadrature (Q) components and their separate beating with a local oscillator (LO) in two BHD. This allows the simultaneous measurements of the 2 quadratures at the price of an additional noise due to the vacuum fields that leak via the unused ports. These schemes require the proper optical phase synchronization between the LO and the incoming field, which constitutes a challenge for WCS reception, especially for suppressed carrier modulations that are required for power economy. For this task, a Costas loop is implemented for low photon number WCS, with the design of an optimum feedback scheme considering the phase diffusion of WCS generated by semiconductor lasers. We implemented an optical Costas loop at 1550 nm based on polarization splitting of the laser field to detect I and Q quadratures simultaneously. We present results on the performance in phase error and bit error rate and compare with corresponding quantum limit.
We describe a homodyne optical Costas loop receiver intended to detect weak coherent states with diffused phase and suppressed carrier phase modulation. In order to get the information contained in the quadrature components of the optical field, we implement an 8-port receiver operating at 1550 nm, based on the manipulation of the state of polarization of both the local oscillator and the data signal. Employing binary phase-shift keying, we make measurements in the time and frequency domain of the quantum noise and bit error rate using an optimum loop filter, and compare the performance of our receiver against the standard quantum limit for the simultaneous quadrature detection, considering both ideal conditions and the overall efficiency of our set up.
We present an application of coherent homodyne detection to the problem of low photon number communications and cryptography. As the coherent demodulation of an optical field requires the measurement of its (non commutating) inphase and quadrature components, we present the structure and operation of an 8-port optical hybrid comprising 2 balanced homodyne detection structures, for the simultaneous measurement of the 2 quadratures. We analyze this receiver operating with a strong local oscillator field, when the received field is in weak coherent states, with digital phase modulation: we obtain the homodyne statistics and the uncertainty product in the presence of vacuum noises from the input signal port and unused ports and discuss the increase in uncertainty due to the simultaneous measurements of the quadratures. We obtain the signal to noise ratio as well of the bit error rate performance for binary phase shift keying and discuss the departure from the standard quantum limit.
ABSTRACT We present an eight‐port homodyne receiver implemented in free space technology for detection of weak coherent states that carry binary information. For transmitted power economy, we use suppressed‐carrier modulation, therefore, we have implemented an optical Costas‐loop‐type carrier synchronizer. We obtain the quasiprobability Q function from the in‐phase and quadrature observables that are simultaneously measured. Statistical results for the quadrature components are presented. We perform measurements for the bit error rate and the mutual information between transmitter–receiver. The results show that the proposed setup is suitable in quantum communications and continuous variable quantum key distribution systems. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2431–2437, 2013
We present a homodyne receiver structure for the detection of weak coherent states that uses sequential in-phase and quadrature measurements on the received optical signal. This receiver performs the optical carrier phase tracking requiring only a single balanced homodyne detector, by including a postdetection Costas-loop-type feedback, which additionally allows the use of suppressed carrier modulations in the received field, for efficient transmission. We report an experimental interferometric self-homodyne setup for the sequential detection of low photon number, binary phase-modulated optical signals that consist of strongly attenuated laser pulses by using a reference field as the local oscillator with an alternatively switched phase. A Costas loop postdetection subsystem is implemented in discrete time to perform fast real-time optical phase tracking. We also present the experimental results of the homodyne postdetection statistics for received BPSK signals with very low photon numbers, and compare them with the theoretical uncertainty limit. Finally, we conduct bit error rate measurements over a wide range of signal level, as well as a comparison with the standard quantum limit.
Quantum communication protocols require efficient detection schemes to maximize the information transfer rate between the sender and the receiver. To this aim, we have demonstrated that weak-field receivers, merging wave-like and particle-like features, can be considered as a valid alternative to already existing receivers, such as optical homodyne detection. To better emphasize the potential of our receiver, in this work we consider a proof of concept for quaternary communication based on coherent states with the same amplitude and different phase values. The encoding in phase requires a fine control of phase noise obtained through a feedback system. The results achieved in terms of mutual information and secret key generation rate encourage further increase of the alphabet towards an approximately continuous phase modulation.