Quantum Info JC: “An operational continuum limit of quantum processes”

Title: An operational continuum limit of quantum processes

Venue & Time: 11:30 / Gray Room 3

Abstract: Quantum combs are a powerful tool for investigating quantum processes and their multi-time correlations in quantum information theory. However, they do not naturally accommodate a physical connection to time, and their probes are inherently instantaneous, meaning control strength is not encoded in the theory.

In this talk I will present our work which introduces a framework of continuous process tensors (cPTs) for combs in a process context, remedying this situation. Here, process tensors are represented by bosonic field theory vectors on the relevant time interval. Associating controls with particle insertions allows us to relate the distinguishing power of instruments with the energetic resources required to implement them. For example, recovering the discrete case, instantaneous probes correspond to particle number eigenstates with infinite Fock space norm. As I will elaborate, this finite-energy perspective also yields well-behaved measures of non-Markovianity, fixing contradictory properties of standard measures.

Building on this, we also proved via an explicit dilation theorem that our framework connects to the Schrödinger equation. This gives physical context, showing that any cPT can be approximated arbitrarily well in Fock space norm by a coupled system-environment dynamics. I will explain in more detail this theorem and show how it enables a set of structural results, such as Choi duality in the continuum and a rigorous treatment of measurements.

Our framework thus fills a substantial gap in the quantum information literature by enabling the physically-consistent study of open quantum dynamics and multi-time correlations in the continuum.