# Intrinsic and Measured Information in Separable Quantum Processes

## TL;DR

This paper explores how quantum processes can be measured and how classical information emerges from quantum sources.

## Contribution

The paper introduces quantum information properties that bound classical information outcomes and synchronization methods for hidden Markov sources.

## Key findings

- Quantum information properties of separable qudit sequences bound classical information outcomes.
- Adaptive measurements enable synchronization to hidden Markov sources.
- Tomographic reconstruction approximates quantum sources with classical models.

## Abstract

Stationary quantum information sources emit sequences of correlated qudits—that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a classical stochastic process. We introduce quantum-information-theoretic properties for separable qudit sequences that serve as bounds on the classical information properties of subsequent measured processes. For sources driven by hidden Markov dynamics, we describe how an observer can temporarily or permanently synchronize to the source’s internal state using specific positive operator-valued measures or adaptive measurement protocols. We introduce a method for approximating an information source with an independent and identically distributed, Markov, or larger memory model through tomographic reconstruction. We identify broad classes of separable processes based on their quantum information properties and the complexity of measurements required to synchronize to and accurately reconstruct them.