Quantum phase estimation using path-symmetric entangled states

Abstract

We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states $|\phi ⟩|0⟩+|0⟩|\phi ⟩$, where an arbitrary state $|\phi ⟩$ occupies one of two modes in quantum superposition. This class of states includes the previously considered states, i.e. $NOON$ states and entangled coherent states, as special cases. With its generalization, we identify the practical limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state $|\phi ⟩$. We first show that quantum Cramer-Rao bound (QCRB) can be lowered with super-Poissonianity of the state $|\phi ⟩$. By introducing a component state of the form $|\phi ⟩=\sqrt{q}|1⟩+\sqrt{1-q}|N⟩$, we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. For practical measurement schemes, we consider a parity measurement and a full photon-counting method to obtain phase-sensitivity. Without photon loss, the latter scheme employing any path-symmetric states $|\phi ⟩|0⟩+|0⟩|\phi ⟩$ achieves the QCRB over the entire range $[0,2\pi ]$ of unknown phase shift $\varphi$ whereas the former does so in a certain confined range of $\varphi$. We find that the case of $|\phi ⟩=\sqrt{q}|1⟩+\sqrt{1-q}|N⟩$ provides the most robust resource against loss among the considered entangled states over the whole range of input energy. Finally we also propose experimental schemes to generate these path-symmetric entangled states.

10 pages, 5 figures, published version

References in corpus (10)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Quantum Optical Metrology -- The Lowdown on High-N00N States
• General optimality of the Heisenberg limit for quantum metrology
• All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry
• High photon number path entanglement in the interference of spontaneously downconverted photon pairs with coherent laser light
• Quantum metrology for non-linear phase shifts with entangled coherent states
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement
• Practical quantum metrology with large precision gains in the low photon number regime
• Entanglement and phase properties of noisy N00N states

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