Phase estimation of coherent state with displaced-photon counting

Shuro Izumi, Masahiro Takeoka, Kentaro Wakui +3 more

We consider the phase sensing via a weak optical coherent state at quantum limit precision. A detection scheme for the phase estimation is proposed, which is inspired by the suboptimal quantum measurement in coherent optical communication. We theoretically analyze a performance of our detection scheme, which we call the displaced-photon counting, for phase sensing in terms of the Fisher information and show that the displaced-photon counting outperforms the static homodyne and heterodyne detections in a wide range of the target phase. The proof-of-principle experiment is performed with linear optics and a superconducting nanowire single-photon detector. The result shows that our scheme overcomes the limit of the ideal homodyne measurement, even under practical imperfections.

David Rimmer, William J. Fitzgerald

M. T. DiMario, Elohim Becerra

Marco A. Rodríguez-García, M. T. DiMario, Pablo Barberis-Blostein +1 more

Abstract Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understanding about their fundamental characteristics and demonstrate their superior performance, we develop a comprehensive statistical analysis based on Bayesian optimal design of experiments, which provides a natural description of these non-Gaussian strategies. This mathematical framework, together with numerical analysis and Monte Carlo methods, allows us to determine the asymptotic limits in sensitivity of strategies based on photon counting designed to maximize information gain, which up to now had been a challenging problem. Moreover, we show that these non-Gaussian phase estimation strategies have the same functional form as the canonical phase measurement in the asymptotic limit differing only by a scaling factor, thus providing the highest sensitivity among physically-realizable measurements for single-shot phase estimation of coherent states known to date. This work shines light into the potential of optimized non-Gaussian measurements based on photon counting for optical quantum metrology and phase estimation.

Osama M. Raisuddin, Suvranu De

Francisco Javier Mendieta-Jiménez, Arturo Arvizu‐Mondragón, César A. López-Mercado +1 more

We present the theory and experimental realization of a quantum polarization-displacement receiver for photonic communications with laser coherent states modulated in their polarization degree of freedom, employing an unconditionally polarization-nulling photon counting scheme. We describe the quantum detection analysis for Polarization Shift Keying (PolSK) modulation formats with laser coherent states, deriving their theoretical performance bounds in error probability and mutual information; and we propose a receiver structure based on a polarization-displacement technique, inspired on the conventional quadrature-displacement schemes employed in the reception of Phase Shift Keying (PSK) modulation formats. Experimentally, we implement our coherent states receiver in a polarization-nulling configuration, employing linear optics for the polarization rotations and displacement, with photon counting at the telecommunications wavelength of 1550 nm, and performing post-detection count–to–voltage operations and logical decision with optimized photon number thresholds; additionally, as a reference, we also implement a quadrature-nulling receiver for a binary PSK format. We perform measurements on the symbol error probability of our receiver, as a function of the photon number of the received photonic signal, finding good agreement with the theoretical estimation at low photon numbers. This receiving structure has advantages over the conventional polarization-splitting and separate photon counting schemes, which is of interest in quantum communications, quantum cryptography and other fields in quantum information.