Sensitivity in Quantum Measurements

Alistair S. Lane, Samuel L. Braunstein, Carlton M. Caves

Shapiro, Shepard, and Wong [Phys. Rev. Lett. 62, 2377 (1989)] suggested that a scheme of multiple phase measurements, using quantum states with minimum ``reciprocal peak likelihood,'' could achieve a phase sensitivity scaling as 1/${\mathit{N}}_{\mathrm{tot}}^{2}$, where ${\mathit{N}}_{\mathrm{tot}}$ is the mean number of photons available for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3\ensuremath{\le}${\mathit{N}}_{\mathrm{tot}}$\ensuremath{\le}120; a power-law fit to the simulated data yields a phase sensitivity that scales as 1/${\mathit{N}}_{\mathrm{tot}}^{0.82\ifmmode\pm\else\textpm\fi{}0.01}$. By using a combination of numerical and analytical techniques, we extend our results to higher values of ${\mathit{N}}_{\mathrm{tot}}$ than are accessible to our simulations; we find no evidence for phase sensitivities better than the benchmark 1/${\mathit{N}}_{\mathrm{tot}}$ sensitivity of squeezed-state interferometry. We conclude that reciprocal peak likelihood is not a good measure of phase sensitivity. We discuss other factors that are important to phase sensitivity.

Yu Watanabe

Zhihao Ma, Wang Miao-Yin

In this paper, we compare the quantum operation sensitivity for different distance measures. We find that, among all usual distance measures, Bures fidelity is more sensitive to quantum operation than others. This may explain in some sense why fidelity is so useful in quantum information theory.

Samuel L. Braunstein, Alistair S. Lane, Carlton M. Caves

Shapiro, Shepard, and Wong [Phys. Rev. Lett. 62, 2377 (1989)] suggested that a scheme of multiple phase measurements, using quantum states with minimum ``reciprocal peak likelihood,'' could achieve a phase sensitivity scaling as 1/${\mathit{N}}_{\mathrm{tot}}^{2}$, where ${\mathit{N}}_{\mathrm{tot}}$ is the mean number of photons availavle for all measurements. We have simulated their scheme for as many as 240 measurements and have found optimum phase sensitivities for 3\ensuremath{\le}${\mathit{N}}_{\mathrm{tot}}$\ensuremath{\le}120. A power-law fit to the simulated data yields a phase sensitivity that scales as 1/${\mathit{N}}_{\mathrm{tot}}^{0.85\ifmmode\pm\else\textpm\fi{}0.01}$. We conclude that reciprocal peak likelihood is not a good measure of sensitivity.

Henry Margenau