Device-independent quantum tomography and certification

Information science has created key technologies such as the computer---for processing of information---and internet---for dissemination of information---that have greatly benefited the modern society. However, the capacity of information science is still very limited when compared to the amount of information generated nowadays. Quantum information science promises to enhance information processing and and transmission using unique properties of subatomic particles. To do so, we need to construct a relation between these properties and our target application. This is similar to how individual musical notes and their unique properties assemble into a piece that represents a certain idea or story. Here arises the need to understand the behavior of individual quantum system extremely well, especially without any prior and potentially erroneous knowledge. My project will deliver such a tool and contribute to the research activities around device-independent tomography and certification. Physics is about interactions between different systems which means properties of one system cannot exist independent of others. Whenever an experimentalist performs quantum tomography, he/she brings an unknown system X into interaction with a probe and infer the properties of the former using the response of the latter. A simple analogy is that of solving for X in the equation X + 1 = 2 where plus represents the interaction, 1 represents the probe and 2 represents the response. The properties of the probe are assumed known, and this is often a result of quantum measurement tomography: bringing an unknown probe to interact with a known system (in effect swapping the system-probe in quantum tomography). It is then clear that if the assumptions about the probe is wrong then the conclusions about the unknown system is also wrong. Thus, one could try to jointly characterize the unknown system and unknown probe at the same time, similar to solving for X and P in the equation X+P=2. Remarkably, such possibility is possible within quantum theory and is called self-testing. The most famous example is associated with maximal violation of the CHSH inequality: any response that gives CHSH=2.828 must corresponds to a unique system and set of probes. My project will advance our understanding of device-independent tomography and certification by providing a framework to understand the self-testing phenomenon. Given this, we can take any dataset from a quantum experiment and reliably conclude information about the system without having to assume prior knowledge.

This research program has produced a complete and detailed understanding of the set of quantum correlations in the smallest scenario where two parties make two measurements with two outcomes each. This serves as a template for future generalizations into larger scenario (more than two measurements and outcomes) and produces insights into device independent quantum tomography and certification. Concretely, we know exactly what experimental correlations one need to observe in order to characterize an unknown device; therefore trying to achieve these correlations serves as an excellent calibration and initialization technique. Moreover, we also know exactly what kind of correlations is ideal for quantum key distribution and this has unexpectedly suggests a new family of protocols based on the "extreme points on elliptope faces". In addition, the broader understanding gained in this research has also been applied in a completely different problem in quantum foundation. This has led to an unexpected result about real quantum theory and to its disproof. We can experimentally confirm that quantum theory must be formulated with complex numbers. This latter result has received widespread publicity from many popular science journals and youtube channels, and is awarded the Paul Ehrenfest Best Paper Award for Quantum Foundation in 2022.