Symmetry-based estimation of lower bound on secure key rate of noisy private states

TL;DR

This paper introduces a symmetry-based method to estimate the lower bound on secure key rates in noisy private quantum states, improving efficiency when symmetry is preserved.

Contribution

It develops a practical approach leveraging symmetry to estimate optimal measurements for secure key generation in noisy quantum states.

Findings

Method effectively estimates secure key bounds in symmetric noisy states

Approach simplifies key rate estimation under certain noise conditions

Provides a general paradigm for quantum communication rate estimation

Abstract

Quantum private states are the states that represent some amount of perfect secure key. A simple symmetry of any generalised private quantum state (ie. the states that represent perfect key but not fully random) is provided and extended on Devetak-Winter so called ccq (classical-classical-quantum) and cqq (classical-quantum-quantum) lower bound on secure key. This symmetry is used to develop a practical method of estimating the Alice measurement that is optimal form the perspective of single shot Devetak-Witner lower bound on secure key. The method is particularly good when the noise does not break the symmetry of the state with respect to the lower bound formula. It suggest a general paradigm for quick estimation of quantum communication rates under the symmetry of a given resource like state and/or channel.