Private and Robust States for Distributed Quantum Sensing

TL;DR

This paper develops a framework for private and robust quantum states in distributed sensing, identifying optimal entangled states like GHZ for certain functions and creating loss-tolerant variants, thereby enhancing privacy and robustness in quantum estimation.

Contribution

It introduces a privacy measure for distributed quantum sensing, constructs entangled states that ensure privacy, and designs loss-tolerant private states for multi-parameter quantum estimation.

Findings

GHZ state is the unique private state for certain linear functions under specific conditions.

Families of private states are created that remain robust against qubit loss.

The framework generalizes to various resource distributions and Hamiltonian evolutions.

Abstract

Distributed quantum sensing enables the estimation of multiple parameters encoded in spatially separated probes. While traditional quantum sensing is often focused on estimating a single parameter with maximum precision, distributed quantum sensing seeks to estimate some function of multiple parameters that are only locally accessible for each party involved. In such settings it is natural to not want to give away more information than is necessary. To address this, we use the concept of privacy with respect to a function, ensuring that only information about the target function is available to all the parties, and no other information. We define a measure of privacy (essentially how close we are to this condition being satisfied), and show it satisfies a set of naturally desirable properties of such a measure. Using this privacy measure, we identify and construct entangled resources states that ensure privacy for a given function under different resource distributions and encoding dynamics, characterized by Hamiltonian evolution. For separable and parallel Hamiltonians, we prove that the GHZ state is the only private state for certain linear functions, with the minimum amount of required resources, up to SLOCC. Recognizing the vulnerability of this state to particle loss, we create families of private states, that remain robust even against loss of qubits, by incorporating additional resources. We then extend our findings to different resource distribution scenarios and Hamiltonians, resulting in a comprehensive set of private and robust states for distributed quantum estimation. These results advance the understanding of privacy and robustness in multi-parameter quantum sensing.