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

Noiseless Filtering of non-Gaussian Noise from Continuous-Variable Quantum Information

Christoffer Wittmann, Dominique Elser, Ulrik L. Andersen, Radim Filip, Petr Marek, Gerd Leuchs

Published Jun 1, 2007• 0 citations
Publisher

Abstract

In this paper, we consider the process of filtering non-Gaussian noise from binary coherent states using two different measurement methods: homodyne detection and on/off detection. Characteristics of homodyne and on/off detection in such a filter are compared and the optimal device is discussed. The performance of the protocol was characterized by measuring the signal state probability before and after filtration. We also measured the success probability (that is, the probability for a positive filter output) as well as the filter sensitivity for extremely weak signal states. All these results will be presented.

DOI
10.1109/cleoe-iqec.2007.4386763

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Non-Gaussian quantum states are critical resources in photonic quantum information processing, rendering their generation and characterization of increasing importance in quantum optics. In this work, we theoretically and numerically analyze the relative efficiency of homodyne versus heterodyne measurements for reconstructing non-Gaussian states, a major outstanding question in continuous-variable tomography. Combining a Fisher information-based formalism with simulated experiments, we find homodyne tomography to outperform heterodyne measurements for all non-Gaussian states tested, although the separation between the two modalities proves significantly narrower than suggested by the asymptotic Cramer-Rao lower bound. Our results should find use for optimizing measurement strategies in practical continuous-variable quantum systems.
Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.
Standard protocols in optical communication systems employ coherent states of light as the information carriers. The quantum nature inherent to these states introduces a fundamental complexity into the decoding process. In particular, when dealing with attenuated signals, the overlap between different states precludes the possibility of perfectly discriminate them. In this study, we investigate the performance of conventional and nonconventional quantum discrimination strategies under different informational metrics. We focus our analysis on binary coherent states within the ideal case of a lossless channel. The usual homodyne receiver was studied in comparison with the Kennedy and the optimized displacement receiver. We find that nonconventional strategies employing non-Gaussian measurements surpass the conventional homodyne discrimination scheme according to measurement error probability and mutual information.
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Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.