Introduction: Solid-State Quantum Repeaters
Quantum Information Processing [1] (QIP), roughly defined as that branch of physics, engineering and computer science that attempts to incorporate fundamental concepts from quantum mechanics in order to augment and improve on existing information processi
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Introduction: Solid-State Quantum Repeaters
Quantum Information Processing [1] (QIP), roughly defined as that branch of physics, engineering and computer science that attempts to incorporate fundamental concepts from quantum mechanics in order to augment and improve on existing information processing capabilities,1 was initially proposed as an answer to a fundamental question in both theoretical physics and quantum chemistry: how to keep track of the gigantic state space that is present in large-scale quantum mechanical systems [2]? Such quantum simulation has since become the subject of an entire subfield of study [3], building on the intrinsic state space provided by quantum systems to understand fundamental properties of nature, especially in solid-state and many-body physics – properties and studies that would be intractable using classical mathematical tools based on digital computing power. Similarly, and very much in concert with quantum simulation, another branch of QIP known as quantum computation [4] emerged, based on ingenious proposals that build on the full power of the Hilbert space in large-scale quantum systems to dramatically speed up the solution and/or verification of particular, ‘hard’ mathematical problems. The quantum enabled, exponential speedup in primefactoring as demonstrated by Peter Shor in 1994 [5] led to a true explosion of interest in this subfield, as such prime factoring (more specifically: the assumed difficulty thereof) lies at the heart of widely used public-key cryptography systems such as the well-known RSA encryption.2 Similarly, quadratic speedups in searches through unsorted databases were demonstrated by Lov Grover in 1996 [6]. 1 To
quote from [1]: “the study of the information processing tasks that can be accomplished using quantum mechanical systems” 2 An important caveat: not all cryptographic systems rely on the difficulty of prime number factoring. Contrary to popular belief, quantum computing systems are not ‘quantum mechanical equivalents of classical computers’, and in fact, their application scope is, at the time of writing this dissertation, quite limited. It is quite possible, and even likely, that a quantum mechanics based prime factoring machine would make itself instantly obsolete, when publicly announced: the obvious countermeasure in such a cryptographic arms race would be the abandonment of publickey cryptography. . . K. De Greve, Towards Solid-State Quantum Repeaters, Springer Theses: Recognizing Outstanding Ph.D. Research, DOI 10.1007/978-3-319-00074-9 1, © Springer International Publishing Switzerland 2013
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1 Introduction: Solid-State Quantum Repeaters
Fig. 1.1 The outline of the canonical cryptography problem: how can Alice and Bob share a secret message (or a secret key to be used in a one-time pad) without Eve being able to intercept this message?
While fascinating and enormously rich in both physics and fundamental information theory, this dissertation will for the most part steer far away from quantum computation and simulation. Rather, w
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