We study the problem of compressing a block of symbols (a block quantum state) emitted by a memoryless quantum Bernoulli source. We present a simple-to-implement quantum algorithm for projecting, with high probability...
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We study the problem of compressing a block of symbols (a block quantum state) emitted by a memoryless quantum Bernoulli source. We present a simple-to-implement quantum algorithm for projecting, with high probability the block quantum state onto the typical subspace spanned by the leading eigenstates of its density matrix. We propose a fixed-rate quantum Shannon-Fano code to compress the projected block quantum state using a per-symbol code rate that is slightly higher than the von Neumann entropy limit. Finally, we propose quantum arithmetic codes to efficiently implement quantum Shannon-Fano codes. Our arithmetic encoder and decoder have a cubic circuit and a cubic computational complexity in the block size. Both the encoder and decoder are quantum-mechanical inverses of each other, and constitute an elegant example of reversible quantum computation.
Some physicists seem to believe that quantum information theory requires a new concept of information (Jozsa, 1998, Quantum information and its properties. In: Hoi-Kwong Lo, S. Popescu, T. Spiller (Eds.), Introduction...
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Some physicists seem to believe that quantum information theory requires a new concept of information (Jozsa, 1998, Quantum information and its properties. In: Hoi-Kwong Lo, S. Popescu, T. Spiller (Eds.), Introduction to Quantum Computation and Information, World Scientific, Singapore, 49pp;Information flow in entangled quantum subsystems, preprint quant-ph/9906007;Deutsch & Hayden, 1999). 1 will argue that no new concept is necessary. Shannon's concept of information is sufficient for quantum information theory. Properties that are cited to contrast quantum information and classical information (i.e., Shannon information) actually point to differences in our ability to manipulate, access, and transfer information depending on whether quantum systems, opposed to classical systems, are used in a communication system. I also demonstrate that conceptually puzzling phenomena in quantum information theory, such as dense coding, teleportation, and schumacher coding, all of which are cited as evidence that a new concept of information is required, do not have to be regarded as such. (C) 2003 Elsevier Science Ltd. All rights reserved.
Some physicists seem to believe that quantum information theory requires a new concept of information (Jozsa, 1998, Quantum information and its properties. In: Hoi-Kwong Lo, S. Popescu, T. Spiller (Eds.), Introduction...
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