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arXiv:1511.08335 · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

Quantum filtering for multiple measurements driven by fields in single-photon states

Zhiyuan Dong, Guofeng Zhang, Nina H. Amini

Published Jul 1, 2016• 10 citations
arXivHTMLPDF

Abstract

In this paper, we derive the stochastic master equations for quantum systems driven by a single-photon input state which is contaminated by quantum vacuum noise. To improve estimation performance, quantum filters based on multiple-channel measurements are designed. Two cases, namely diffusive plus Poissonian measurements and two diffusive measurements, are considered.

DOI
10.1109/acc.2016.7526105

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In this paper, we derive the stochastic master equations for quantum systems driven by a single-photon input state which is contaminated by quantum vacuum noise. To improve estimation performance, quantum filters based on multiple-channel measurements are designed. Two cases, namely diffusive plus Poissonian measurements and two diffusive measurements, are considered.
Summary The single‐photon quantum filtering problems have been investigated recently with applications in quantum computing. In practice, the detector responds with a quantum efficiency of less than unity since there exists some mode mismatch between the detector and the system and the single‐photon signal may be corrupted by quantum white noise. Consequently, quantum filters based on multiple measurements are designed in this paper to improve estimation performance. More specifically, the filtering equations for a 2‐level quantum system driven by a single‐photon input state and under multiple measurements are presented in this paper. Four scenarios, ie, (1) 2 diffusive measurements with Q‐P quadrature form, (2) 2 diffusive measurements with Q‐Q quadrature form, (3) diffusive plus Poissonian measurements, and (4) 2 Poissonian measurements, are considered. It is natural to compare the filtering results, ie, measuring a single channel or both channels, which one is better? By the simulation where we use a single photon to excite an atom, it seems that multiple measurements enable us to excite the atom with higher probability than only measuring a single channel. In addition, a measurement back‐action phenomenon is revealed by the simulation results.
We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations of diffusive and Poissonian processes. This covers the standard cases from quantum optics, where homodyne detection may be described as a diffusive process and photon counting may be described as a Poissonian process. We obtain a necessary and sufficient condition for any pair of such measurements taken at different output channels to satisfy a commutation relationship. Then, we derive a general, multiple-measurement quantum filter as an extension of a single-measurement quantum filter. As an application we explicitly obtain the quantum filter corresponding to homodyne detection and photon counting at the output ports of a beam splitter.
A major component of establishing quantum technologies in the quantum optic platform is the cavity. This paper concerns state estimation (filtering) of a quantum one-sided cavity driven by a vacuum field while the output field is monitored by either Homodyne or photodetector. The stochastic master equation in the schrödinger picture is presented for Homodyne and photon measurements. Then, the infinite state space of the cavity is truncated by considering some reasonable simplifying assumptions. Finally, the number of photons in the cavity is estimated using the derived equations. Simulation results are validated by demonstrating that the average of several paths of the derived filter matches the corresponding master equation.
We consider the problem of optimal estimation of a state of a quantum system interacting with the Bose field being in a mixture of the vacuum and coherent state.The system and electromagnetic field are described by making use of quantum stochastic unitary evolution.We derive stochastic master equation using Gardiner and Collet's input-output theory and the concept of cascade systems.To find the stochastic evolution of the system conditioned on the result of the quadrature measurement of the output field, we extend the compound system by an ancilla driven by the vacuum and generating the desired non-classical state of light.