Leveraging small quantum states: applications to linear optics and position verification
40 years after Feynman’s pioneering talk, it is clear that Quantum Information (QI) is here to stay. Research in this field is building a bridge between computer science and quantum mechanics, which is advancing our understanding of both disciplines as well as providing fertile ground for new applications. My research work focuses on two tasks pertaining to separate areas of QI, quantum linear optics and quantum cryptography.
In the first part of the manuscript, we characterize the effectiveness of small auxiliary states in boosting the success probability of linear optical Bell measurement, which is the basis of many of the promising applications of quantum linear optics. Auxiliary states are interesting in this context even if they cannot be deterministically prepared, because their creation can happen offline and they can be stored until the measurement is performed. We give analytical bounds to the success probability, under certain restrictions on the class of unitaries representing the interferometer, which are tight for known strategies. We then explore the space of all possible interferometers through a custom linear optics numerical optimization package. We confirm the optimality of known schemes and find some with intermediate performance.
In part two, we explore a cryptographic primitive known as position verification in the quantum setting. We characterize the space of attacks to a simple, well known protocol parametrized by an angle θ, where the adversaries make use of precise timing and an entangled state to spoof their spacetime location. Through a circuit representation of the attacks, we determine necessary and sufficient conditions for the adversaries to succeed in breaking a specific θ when using a d-dimensional state. Exploiting a graphical representation of the Hilbert space, we discover simpler proofs of already known results for d=2 and d=3, and we find many more “weak” angles for d up to 12, as well as explicit circuits of the attacking strategies. Finally, we relax the assumption of exact attacks by allowing the adversaries a small probability of failure, discovering that two ebits are sufficient to break every angle with >99.5% probability, and we discuss some modifications of the protocol which could enhance its resistance to these attack strategies.