Complex system and untrusted device certification from Bell's inequality

Abstract

In physics, we use fundamental theories to describe and explain phenomena occurring in nature. Two of the most prominent theories are classical mechanics, pioneered in the 17th century by Sir Isaac Newton, and quantum mechanics which arose in the beginning of the 20th century. While classical and quantum mechanics dissent in various aspects, the most pronounced difference is called entanglement. Entanglement provides us with powerful tools that allow us to perform tasks which are not possible by classical means. Quantum computing studies the possible use of quantum principles for computational tasks. For example the factorisation of large numbers is infeasible with classical computers but can be done efficiently with Shor’s algorithm. The power of quantum computers can be intuitively understood by realizing that its basic unit can encode infinitely many states via the superposition principle. Another significant application of quantum mechanics is quantum key distribution (QKD). The goal is to create two identical strings of random bits, called a key, at two spatially-separated locations. This key is then used to encrypt a message allowing for secret communication. Secret communication is essential in our modern society, in which we use the internet to manage our bank account, buy products in online stores and send personal messages to friends. We communicate over great distances and desire that this communication be secure. The current classical cryptographic protocols use complex mathematical problems such as factorization to create secure keys. The downside of this procedure is that the security is based on the complexity of mathematical problems and relies on assumptions about the computational power of the person who wants to break the cryptographic system. Hence there is every chance that a potential eavesdropper hacks the key - especially if he has access to quantum computers. On the other hand, a key can be obtained by performing appropriate measurements on an entangled state. This provides the means to actually create secret keys with provable security. In order to achieve long-distance QKD, we envision quantum networks whose purpose is to transmit entanglement between two arbitrary parties on earth. A network consists of various quantum mechanical devices, including sources for creating quantum information, memories which allow for the storage of it, as well as quantum gates and projective measurements for processing the information. Quantum networks and quantum computers sound very appealing. However, with the benefits of quantum mechanics there also come great challenges. A central challenge we want to tackle in this thesis is how to certify that one indeed works with quantum mechanical devices. The subtlety here lies in the fact that we humans are classical and thus cannot directly observe quantum features such as entanglement. As a consequence, we desire to employ certification schemes which do not overburden our classical competences. The need for such certifications becomes apparent when considering the following scenario: Basic quantum machines are already available commercially, for example true random number generators. If we purchase such a device that promises to prepare entangled states or act as a quantum gate, we aim at verifying that the promise actually holds. We want to do this without breaking or opening the device since we would lose the warranty or anyway be overstrained by the complexity of the physics involved. At best, the certification should be such that even an unqualified user can conduct it. In this thesis we will discuss how this can be achieved.