Algorithmic Pseudorandomness in Quantum Setups

TL;DR

This paper explores how principles of computer science, like pseudorandomness and computability, influence fundamental quantum physics concepts, revealing new insights into quantum states and non-locality.

Contribution

It introduces the application of algorithmic pseudorandomness to quantum physics, challenging existing notions of quantum states and measurement in Bell experiments.

Findings

Ensembles of quantum states can be distinguishable when prepared by a computer.

Computational limits on eavesdroppers affect Bell test outcomes.

New perspective on unifying computer science and quantum physics.

Abstract

The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of computing devices, its implications in other scientific fields have hardly been explored. Here we start this research programme in the context of quantum physics and show that computer science laws have profound implications for some of the most fundamental results of the theory. We first show how they question our knowledge on what a mixed quantum state is, as we identify situations in which ensembles of quantum states defining the same mixed state, indistinguishable according to the quantum postulates, do become distinguishable when prepared by a computer. We also show a new loophole for Bell-like experiments: if some of the parties in a Bell-like experiment use a computer to decide which measurements to make, then the computational resources of an eavesdropper have to be limited in order to have a proper observation of non-locality. Our work opens a new direction in the search for a framework unifying computer science and quantum physics.