Abstract:

We develop an operational framework, combining relativistic quantum measurement theory with quantum reference frames (QRFs), in which local measurements of a quantum field on a background with symmetries are performed relative to a QRF. This yields a joint algebra of quantum-field and reference-frame observables that is invariant under the natural action of the group of spacetime isometries. For the appropriate class of quantum reference frames, this algebra is parameterised in terms of crossed products. Provided that the quantum field has good thermal properties (expressed by the existence of a KMS state at some nonzero temperature), one can use modular theory to show that the invariant algebra admits a semifinite trace. If furthermore the quantum reference frame has good thermal behaviour (expressed in terms of the properties of a KMS weight) at the same temperature, this trace is finite. We give precise conditions for the invariant algebra of physical observables to be a type II_1 factor. Our results build upon recent work of Chandrasekaran, Longo, Penington and Witten [JHEP 2023, 82 (2023)], providing both a significant mathematical generalisation of these findings and a refined operational understanding of their model.

Abstract:

Quantum computers can provide asymptotically faster computation times than their classical counterparts in specific applications. However, to outperform the classical computers we have today, we need large-scale, fault-tolerant devices. Quantum error correction (QEC) is considered one of the most promising ways of achieving this milestone. However, much work is still needed to improve both the QEC methods and the quantum hardware on which they run.

This talk will explore improving the performance of quantum error correction through a more refined approach to evaluating the measurement data we use for error detection. By integrating soft information—analog data that provides probabilistic insights rather than binary results—we can significantly improve the performance of QEC protocols. Initially, I will introduce quantum error correction and a widely used decoding strategy. Then, I will share results from my current master’s thesis on how soft information can more efficiently protect against quantum noise. This talk aims to demonstrate that soft information QEC can contribute meaningfully toward more reliable quantum computing.