Supersensitivity of Kerr phase estimation with two-mode squeezed vaccum states

We analytically investigate the sensitivity of Kerr nonlinear phase estimation in a Mach-Zehnder interferometer with two-mode squeezed vacuum states. We find that such a metrological scheme could access a sensitivity scaling over the Boixo et al.'s generalized sensitivity limit [S. Boixo et al., Phys. Rev. Lett. 98, 090401 (2007)], which is saturable with celebrated NOON states. We also show that parity detection is a quasioptimal measurement which can nearly saturate the quantum Cram\'er-Rao bound in the aforementioned situation. Moreover, we further clarify the supersensitive performance observed in the above scheme is due to the restriction of Boixo et al.'s generalized sensitivity limit (BGSL) to probe states with fixed photon numbers. To conquer this problem, we generalize the BGSL into the case with probe states of a fluctuating number of photons, to which our scheme belongs.We analytically investigate the sensitivity of Kerr nonlinear phase estimation in a Mach-Zehnder interferometer with two-mode squeezed vacuum states. We find that such a metrological scheme could access a sensitivity scaling over the Boixo et al.'s generalized sensitivity limit [S. Boixo et al., Phys. Rev. Lett. 98, 090401 (2007)], which is saturable with celebrated NOON states. We also show that parity detection is a quasioptimal measurement which can nearly saturate the quantum Cram\'er-Rao bound in the aforementioned situation. Moreover, we further clarify the supersensitive performance observed in the above scheme is due to the restriction of Boixo et al.'s generalized sensitivity limit (BGSL) to probe states with fixed photon numbers. To conquer this problem, we generalize the BGSL into the case with probe states of a fluctuating number of photons, to which our scheme belongs.

arXiv:2111.01375Physical Review AMar 17, 202218 citations

Phase estimation with two-mode squeezed vacuum and parity detection: Bayesian analysis

Keith R. Motes, Petr M. Anisimov, Jonathan P. Dowling

A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cramer-Rao bound sensitivity can be obtained [P. M. Anisimov, et al., Phys. Rev. Lett. {\bf104}, 103602 (2010)]. This sensitivity, however, is expected in the case of an infinite number of parity measurements made on an infinite number of photons. Here we consider the case of a finite number of parity measurements and a finite number of photons, implemented with photon-number-resolving detectors. We use Bayesian analysis to characterize the sensitivity of the phase estimation in this scheme. We have found that our phase estimation becomes biased near 0 or $\pi/2$ phase values. Yet there is an in-between region where the bias becomes negligible. In this region, our phase estimation scheme saturates the Cramer-Rao bound and beats the shot-noise limit.A recently proposed phase-estimation protocol that is based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that Cramer-Rao bound sensitivity can be obtained [P. M. Anisimov, et al., Phys. Rev. Lett. {\bf104}, 103602 (2010)]. This sensitivity, however, is expected in the case of an infinite number of parity measurements made on an infinite number of photons. Here we consider the case of a finite number of parity measurements and a finite number of photons, implemented with photon-number-resolving detectors. We use Bayesian analysis to characterize the sensitivity of the phase estimation in this scheme. We have found that our phase estimation becomes biased near 0 or $\pi/2$ phase values. Yet there is an in-between region where the bias becomes negligible. In this region, our phase estimation scheme saturates the Cramer-Rao bound and beats the shot-noise limit.

arXiv:1110.1587Civil War Book ReviewOct 7, 20111 citation

Quantum optical interferometry via general photon-subtracted two-mode squeezed states*

Li-Li Hou, Jianzhong Xue, Yongxing Sui +1 more

We investigate the sensitivity of phase estimation in a Mach–Zehnder interferometer with photon-subtracted two-mode squeezed vacuum states. Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér–Rao bound (i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction. On the other hand, the quantum Cramér–Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states. In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse. Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.We investigate the sensitivity of phase estimation in a Mach–Zehnder interferometer with photon-subtracted two-mode squeezed vacuum states. Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér–Rao bound (i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction. On the other hand, the quantum Cramér–Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states. In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse. Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.

Chinese Physics BAug 6, 20197 citations

Adaptive phase estimation with two-mode squeezed vacuum and parity measurement

Zixin Huang, Keith R. Motes, Petr M. Anisimov +2 more

A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram\'er-Rao sensitivity is sub-Heisenberg [P. M. Anisimov et al., Phys. Rev. Lett. 104, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for a phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon number $\overline{n}=1$ is approximately 100. We show that the Cram\'er-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2$).A proposed phase-estimation protocol based on measuring the parity of a two-mode squeezed-vacuum state at the output of a Mach-Zehnder interferometer shows that the Cram\'er-Rao sensitivity is sub-Heisenberg [P. M. Anisimov et al., Phys. Rev. Lett. 104, 103602 (2010)]. However, these measurements are problematic, making it unclear if this sensitivity can be obtained with a finite number of measurements. This sensitivity is only for a phase near zero, and in this region there is a problem with ambiguity because measurements cannot distinguish the sign of the phase. Here, we consider a finite number of parity measurements and show that an adaptive technique gives a highly accurate phase estimate regardless of the phase. We show that the Heisenberg limit is reachable, where the number of trials needed for mean photon number $\overline{n}=1$ is approximately 100. We show that the Cram\'er-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2$).

arXiv:1609.04689Physical Review AMay 12, 201745 citations

Enhancement of the phase sensitivity with two-mode squeezed coherent state based on a Mach-Zehnder interferometer

Jun Liu, Tao Shao, Yuanxiang Wang +4 more

We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.

Optics ExpressJul 26, 202313 citations

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

Yi Ouyang, Shuai Wang, Lijian Zhang

We investigate the sensitivity and resolution of phase estimation in a Mach–Zehnder interferometer with photon-added two-mode squeezed vacuum states (PA-TMSVS) with a photon-number parity measurement scheme. Our results indicate that, when the phase to be estimated is small, the PA-TMSVS offers an improved phase resolution over both the two-mode squeezed vacuum and the photon-subtracted two-mode squeezed vacuum for a given initial squeezing level. In addition, we study the behavior of the quantum Fisher information of the PA-TMSVS, and show that the optimum phase uncertainty predicted by the corresponding Cramer–Rao bound can be achieved with a parity measurement.We investigate the sensitivity and resolution of phase estimation in a Mach–Zehnder interferometer with photon-added two-mode squeezed vacuum states (PA-TMSVS) with a photon-number parity measurement scheme. Our results indicate that, when the phase to be estimated is small, the PA-TMSVS offers an improved phase resolution over both the two-mode squeezed vacuum and the photon-subtracted two-mode squeezed vacuum for a given initial squeezing level. In addition, we study the behavior of the quantum Fisher information of the PA-TMSVS, and show that the optimum phase uncertainty predicted by the corresponding Cramer–Rao bound can be achieved with a parity measurement.

Journal of the Optical Society of America BJun 3, 201670 citations

\pi/2

phase values. Yet there is an in-between region where the bias becomes negligible. In this region, our phase estimation scheme saturates the Cramer-Rao bound and beats the shot-noise limit.

\overline{n}=1

is approximately 100. We show that the Cram\'er-Rao sensitivity can be achieved approximately, and the estimation is unambiguous in the interval ($\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2$).