Ultimate Precision of Adaptive Noise Estimation

TL;DR

This paper establishes the fundamental limits of noise parameter estimation in quantum channels, demonstrating that adaptive strategies cannot surpass the standard quantum limit for teleportation-covariant channels, with implications for quantum cryptography and sensing.

Contribution

It introduces a general framework linking quantum metrology and teleportation, deriving ultimate precision bounds for noise estimation in quantum channels.

Findings

Adaptive noise estimation cannot beat the standard quantum limit for teleportation-covariant channels.

The quantum Fisher information is determined by the channel's Choi matrix.

The methodology simplifies adaptive protocols for quantum channel discrimination.

Abstract

We consider the estimation of noise parameters in a quantum channel, assuming the most general strategy allowed by quantum mechanics. This is based on the exploitation of unlimited entanglement and arbitrary quantum operations, so that the channel inputs may be interactively updated. In this general scenario we draw a novel connection between quantum metrology and teleportation. In fact, for any teleportation-covariant channel (e.g., Pauli, erasure, or Gaussian channel), we find that adaptive noise estimation cannot beat the standard quantum limit, with the quantum Fisher information being determined by the channel's Choi matrix. As an example, we establish the ultimate precision for estimating excess noise in a thermal-loss channel which is crucial for quantum cryptography. Because our general methodology applies to any functional which is monotonic under trace-preserving maps, it can be applied to simplify other adaptive protocols, including those for quantum channel discrimination. Setting the ultimate limits for noise estimation and discrimination paves the way for exploring the boundaries of quantum sensing, imaging and tomography.