Abstract

We derive a general expression of the expectation value of the parity operator in a Mach–Zehnder interferometer with a Fock state in one input port and an arbitrary state in the other input. We obtain the quantum Crámer–Rao bound via the error propagation method from parity detection for the phase shift around zero. In addition, for an arbitrary state with the same mean photon number, our results show that the same phase resolution and the same phase uncertainty can be obtained for the phase shift around zero. That is to say, when a Mach–Zehnder interferometer is powered by a Fock state into one input port, all quantum states with same mean photon number at the other input may have the same performance in the phase estimation via parity detection. As some specific applications, we consider the arbitrary state being a Fock state, a coherent state, and a squeezed-vacuum state.

© 2018 Optical Society of America

Quantum optical interferometry via the photon-added two-mode squeezed vacuum states

Yi Ouyang, Shuai Wang, and Lijian Zhang
J. Opt. Soc. Am. B 33(7) 1373-1381 (2016)

SU(1,1) interferometry with parity measurement

Shuai Wang and Jian-Dong Zhang
J. Opt. Soc. Am. B 38(9) 2687-2693 (2021)

Quantum-enhanced super-sensitivity of a Mach–Zehnder interferometer with superposition of Schrödinger’s cat-like state and Fock state as inputs using a two-channel detection

Gaurav Shukla, Karunesh Kumar Mishra, Dhiraj Yadav, Ravi Kamal Pandey, and Devendra Kumar Mishra
J. Opt. Soc. Am. B 39(1) 59-68 (2022)

Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of light

Richard Birrittella and Christopher C. Gerry
J. Opt. Soc. Am. B 31(3) 586-593 (2014)

Photon-subtracted two-mode squeezed vacuum states and applications to quantum optical interferometry

Raul Carranza and Christopher C. Gerry
J. Opt. Soc. Am. B 29(9) 2581-2587 (2012)