# Continuous monitoring measured signals bounded by past and future conditions in enlarged quantum systems

## TL;DR

This paper introduces an enlarged quantum system approach that combines forward and backward quantum states, enabling continuous monitoring of signals in systems bounded by past and future conditions, with broad physical implementation prospects.

## Contribution

The authors propose an enlarged quantum state framework that unifies forward and backward quantum evolutions, allowing continuous signal monitoring in bounded quantum systems.

## Key findings

- Enlarged quantum state propagates forward in time.
- Continuous signal monitoring becomes feasible.
- Applicable to various physical quantum systems.

## Abstract

In a quantum system that is bounded by past and future conditions, weak continuous monitoring forward-evolving and backward-evolving quantum states are usually carried out separately. Therefore, measured signals at a given time t cannot be monitored continuously. Here, we propose an enlarged-quantum-system method to combine these two processes together. Therein, we introduce an enlarged quantum state that contains both the forward- and backward-evolving quantum states. The enlarged state is governed by an enlarged master equation and propagates one-way forward in time. As a result, the measured signals at time t can be monitored continuously and can provide advantages in the signals amplification and signal processing techniques. Our proposal can be implemented on various physical systems, such as superconducting circuits, NMR systems, ion-traps, quantum photonics, and among others.