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Sci Rep. 2016 Jul 26;6:30306. doi: 10.1038/srep30306.

Quantum phase estimation using path-symmetric entangled states.

Lee SY1,2, Lee CW1, Lee J3, Nha H1,3.

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School of Computational Sciences, Korea Institute for Advanced Study, Hoegi-ro 85, Dongdaemun-gu, Seoul 02455, Korea.
Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore.
Department of Physics, Texas A&M University at Qatar, Education City, PO Box 23874, Doha, Qatar.


We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ〉|0〉 + |0〉|φ〉, where an arbitrary state |φ〉 occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ〉. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ〉. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift ϕ whereas a parity measurement does so in a certain confined range of ϕ. By introducing a component state of the form , we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy Nav > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.

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