Certification of entangled quantum states and quantum measurements in Hilbert spaces of arbitrary dimension

TL;DR

This paper develops methods for device-independent certification of quantum states and measurements in arbitrary-dimensional Hilbert spaces, enabling verification and randomness extraction without trusting the devices.

Contribution

It introduces novel schemes for certifying quantum states and measurements in any dimension, advancing the capabilities of device-independent quantum certification.

Findings

Certification schemes work in arbitrary dimensions

Optimal randomness can be extracted from any quantum system

Methods enhance device-independent quantum verification

Abstract

The emergence of quantum theory at the beginning of 20$-th$ century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a few, that could never have been realised using classical systems. One such application that has attracted considerable attention lately is device-independent (DI) certification of composite quantum systems. The basic idea behind it is to treat a given device as a black box that given some input generates an output, and then to verify whether it works as expected by only studying the statistics generated by this device. The novelty of these certification schemes lies in the fact that one can almost completely characterise the device (up to certain equivalences) under minimal physically well-motivated assumptions such as that the device is described using quantum theory. The resource required in most of these certification schemes is quantum non-locality. In this thesis, we construct schemes to device-independently certify quantum states and quantum measurements in Hilbert spaces of arbitrary dimension along with the optimal amount randomness that one can extract from any quantum system of arbitrary dimension.