# Parallel-in-time optical simulation of history states

## TL;DR

This paper demonstrates an optical experiment simulating quantum evolution over time using entanglement between a photon’s degrees of freedom, enabling efficient measurement of system dynamics and observables.

## Contribution

It introduces a novel optical setup for parallel-in-time quantum simulation using a programmable spatial light modulator to entangle photon properties.

## Key findings

- Successfully simulated a qubit history state with entanglement measurement.
- Able to determine system-time entanglement as a quantum evolution indicator.
- Measured time-averaged observables with a single measurement.

## Abstract

We present an experimental optical implementation of a parallel-in-time discrete model of quantum evolution, based on the entanglement between the quantum system and a finite dimensional quantum clock. The setup is based on a programmable spatial light modulator which entangles the polarization and transverse spatial degrees of freedom of a single photon. It enables the simulation of a qubit history state containing the whole evolution of the system, capturing its main features in a simple and configurable scheme. We experimentally determine the associated system-time entanglement, which is a measure of distinguishable quantum evolution, and also the time average of observables, which in the present realization can be obtained through one single measurement.