From Compression to Communication: Performance Limits for Quantum Networks
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Quantum algorithms require quantum computers to perform logical operations on a sufficiently large number of entangled qubits. Unfortunately, state-of-the-art quantum computers can only operate on tens of qubits. A solution to this scalability challenge is to employ the distributed paradigm, where a network of small-scale quantum computers is used in a distributed manner. In this thesis, we study the fundamental limits of distributed quantum problems and enhance their performance using asymptotically-good algebraic codes. We present a novel protocol to faithfully simulate a distributed quantum measurement, and make further improvements by employing structured measurements built using random asymptotically-good algebraic codes. As an application, using these protocols we develop a technique to distill quantum purity from a network. Following that, we consider a lossy quantum compression problem in which the goal is to compress a quantum source below its von Neumann entropy. We introduce a new formulation, and characterize its performance limit in terms of single-letter coherent information. Finally, we revisit the algebraic measurements and study how they can benefit the classical-quantum network problems. In particular, we analyze two problems: a classical-quantum multiple access channel, and a classical-quantum interference channel.
Chair: Professor S. Sandeep Pradhan