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Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time

Author(s)
Tsang, Mankei; Shapiro, Jeffrey H.; Lloyd, Seth
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Abstract
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that postprocessing can further improve the estimation performance if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counterintuitive, we argue that it does not violate any basic principle of quantum mechanics.
Date issued
2009-05
URI
http://hdl.handle.net/1721.1/51033
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Research Laboratory of Electronics
Journal
Physical Review A
Publisher
American Physical Society
Citation
Tsang, Mankei , Jeffrey H. Shapiro, and Seth Lloyd. “Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design.” Physical Review A 79.5 (2009): 053843. (C) 2010 The American Physical Society.
Version: Final published version
ISSN
1094-1622
1050-2947

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