How to perform the most accurate possible phase measurements

TL;DR

This paper develops a theoretical framework for achieving near-Heisenberg limit phase measurements with minimal ambiguity, applicable to quantum interferometry and quantum computing, and reports some experimental results.

Contribution

It introduces a new theoretical foundation for optimal phase measurement schemes that minimize variance and ambiguity, with practical measurement strategies.

Findings

Achieves phase measurement uncertainty close to the Heisenberg limit.

Provides schemes to eliminate phase ambiguity efficiently.

Demonstrates experimental implementation of some measurement schemes.

Abstract

We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as those obtained from NOON states, have commensurately high information yield. However this information is also highly ambiguous because it does not distinguish between phases at the same point on different fringes. We provide schemes to eliminate this phase ambiguity in a highly efficient way, providing phase estimates with uncertainty that is within a small constant factor of the Heisenberg limit, the minimum allowed by the laws of quantum mechanics. These techniques apply to NOON state and multi-pass interferometry, as well as phase measurements in quantum computing. We have reported the experimental implementation of some of these schemes with multi-pass interferometry elsewhere. Here we present the theoretical foundation, and also present some new experimental results. There are three key innovations to the theory in this paper. First, we examine the intrinsic phase properties of the sequence of states (in multiple time modes) via the equivalent two-mode state. Second, we identify the key feature of the equivalent state that enables the optimal scaling of the intrinsic phase uncertainty to be obtained. This enables us to identify appropriate combinations of states to use. The remaining difficulty is that the ideal phase measurements to achieve this intrinic phase uncertainty are often not physically realizable. The third innovation is to solve this problem by using realizable measurements that closely approximate the optimal measurements, enabling the optimal scaling to be preserved.