Pairing in fermionic systems: A quantum information perspective

TL;DR

This paper introduces a systematic, mathematical framework for defining, detecting, and quantifying pairing in fermionic systems, revealing its distinction from entanglement and its utility in quantum metrology.

Contribution

It provides a new formal definition of pairing, methods for its detection, and demonstrates the resource potential of paired states in quantum precision measurements.

Findings

Pairing is a distinct quantum correlation from entanglement.

The proposed methods are applicable to current experimental setups.

BCS states enable phase measurements at the Heisenberg limit.

Abstract

The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical theory of pairing which would allow to unambiguously characterize and systematically detect paired states. We propose a definition of pairing and develop methods for its detection and quantification applicable to current experimental setups. Pairing is shown to be a quantum correlation different from entanglement, giving further understanding in the structure of highly correlated quantum systems. In addition, we will show the resource character of paired states for precision metrology, proving that the BCS states allow phase measurements at the Heisenberg limit.