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Reversible arithmetic coding for quantum data compression

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2 Author(s)
Chuang, I.L. ; IBM Almaden Res. Center, San Jose, CA, USA ; Modha, D.S.

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 lending 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 (1955) entropy limit. Finally, we propose quantum arithmetic codes to efficiently implement quantum Shannon-Fano (1948) 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

Published in:

Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 3 )