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arXiv quant-ph/0602123quant-ph
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量子干涉仪的保真度

Fidelity of Quantum Interferometers

Thomas B. Bahder, Paul A. Lopata

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4 pages, 3 figures
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摘要：

对于一般干涉仪，给定测量结果$m$的相位$ϕ$的条件概率密度分布$p(ϕ|m)$通常将具有多个峰值。因此，干涉仪的相位灵敏度不能用标准偏差来充分表征，例如$Δϕ\sim 1/\sqrt{N}$（标准极限）或$Δϕ\sim 1/N$（海森堡极限）。我们提出了另一种测量相位灵敏度的方法-干涉仪的保真度-定义为相移$ϕ$ \和测量结果$m$之间的香农互信息。作为干涉仪保真度的一个应用实例，我们考虑一个通用的光学马赫-曾德尔干涉仪，用作经典场的传感器。我们发现了一个令人惊讶的结果，纠缠{ \it N 00 N}态输入导致较低的保真度比Fock态输入，对于相同的光子数。

英文摘要：

For a generic interferometer, the conditional probability density distribution, $p(ϕ|m)$, for the phase $ϕ$ given measurement outcome $m$, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as $Δϕ\sim 1/\sqrt{N}$ (the standard limit), or $Δϕ\sim 1/N$ (the Heisenberg limit). We propose an alternative measure of phase sensitivity--the fidelity of an interferometer--defined as the Shannon mutual information between the phase shift $ϕ$\ and the measurement outcomes $m$. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. We find the surprising result that an entangled {\it N00N} state input leads to a lower fidelity than a Fock state input, for the same photon number.

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