Modes of asymmetry: The application of harmonic analysis to symmetric quantum dynamics and quantum reference frames

TLDR

Symmetry in open‑system quantum dynamics influences thermal relaxation, amplifier limits, and noisy quantum metrology, reflecting either fundamental laws or practical constraints such as missing reference frames. The paper applies harmonic analysis and quantum information concepts to study symmetry in open‑system quantum dynamics. The authors decompose quantum operations into modes of asymmetry, showing that symmetric processing preserves each mode and that monotones can quantify asymmetry, thereby constraining the resources needed to simulate asymmetric operations. They derive bounds on success probabilities for nondeterministic state transitions such as quantum amplification and provide a simplified framework for analyzing quantum reference‑frame degradation.

Abstract

Finding the consequences of symmetry for open-system quantum dynamics is a problem with broad applications, including describing thermal relaxation, deriving quantum limits on the performance of amplifiers, and exploring quantum metrology in the presence of noise. The symmetry of the dynamics may reflect a symmetry of the fundamental laws of nature or a symmetry of a low-energy effective theory, or it may describe a practical restriction such as the lack of a reference frame. In this paper, we apply some tools of harmonic analysis together with ideas from quantum information theory to this problem. The central idea is to study the decomposition of quantum operations---in particular, states, measurements, and channels---into different modes, which we call modes of asymmetry. Under symmetric processing, a given mode of the input is mapped to the corresponding mode of the output, implying that one can only generate a given output if the input contains all of the necessary modes. By defining monotones that quantify the asymmetry in a particular mode, we also derive quantitative constraints on the resources of asymmetry that are required to simulate a given asymmetric operation. We present applications of our results for deriving bounds on the probability of success in nondeterministic state transitions, such as quantum amplification, and a simplified formalism for studying the degradation of quantum reference frames.