Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

TL;DR

This paper links the EPR paradox with quantum metrology, demonstrating how steering enables enhanced precision in phase estimation and proposing a new criterion to detect steering beyond traditional uncertainty-based methods.

Contribution

It formulates the EPR paradox within quantum metrology, introducing a Fisher information-based criterion to detect steering in a broader range of states.

Findings

Steering enables precise local phase estimation.

A new Fisher information criterion detects steering more effectively.

Steering of non-Gaussian states can be observed in experiments.

Abstract

The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.