Unitarity, Feedback, Interactions -- Dynamics Emergent from Repeated Measurements

TL;DR

This paper explores how repeated quantum measurements can produce a range of dynamics from pure unitarity to decoherence, enabling effective interactions and feedback control with implications for gravity-inspired models and quantum control protocols.

Contribution

It introduces a collisional model framework that demonstrates how measurement parameters influence emergent dynamics, including low-decoherence interactions and extensions beyond second-order approximations.

Findings

Dynamics range from unitarity to decoherence.

Multipartite measurements enable low-decoherence interactions.

Re-derivation of quantum filtering equations for various regimes.

Abstract

Motivated by the recent efforts to describe the gravitational interaction as a classical channel arising from continuous quantum measurements, we study what types of dynamics can emerge from a collisional model of repeated interactions between a system and a set of ancillae. We show that contingent on the model parameters the resulting dynamics ranges from exact unitarity to arbitrarily fast decoherence (quantum Zeno effect). For a series of measurements the effective dynamics includes feedback-control, which for a composite system yields effective interactions between the subsystems. We quantify the amount of decoherence accompanying such induced interactions, generalizing the lower bound found for the gravitational example. However, by allowing multipartite measurements, we show that interactions can be induced with arbitrarily low decoherence. These results have implications for gravity-inspired decoherence models. Moreover, we show how the framework can include terms beyond the usual second-order approximation, which can spark new quantum control or simulation protocols. Finally, within our simple approach we re-derive the quantum filtering equations for the different regimes of effective dynamics, which can facilitate new connections between different formulations of open systems.