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Abstract: A theorem is proven for quantum information theory that is analogous to the noiseless coding theorem of classical information theory. In the quantum result, the von Neumann entropy S of the density operator describing an ensemble of pure quantum signal states is equal to the number of spin-1/2 systems (quantum bits or "qubits") necessary to represent the signal faithfully. The theorem holds whether or not the signal states are orthogonal. Related results are also presented about the fidelity of ... (Update)
Context of citations to this paper: More
.... is thus stronger than it would be if encodings were restricted to be completely positive maps, as it was in Schumacher s original proof [41]. The encoding used by Jozsa and Schumacher [15] in showing achievability is, however, a completely positive map. Thus, allowing...
...to [17, Sec. 5. 2] the matrices n (u) should prove useful for the universal version of Schumacher data compression [7] 19] 30] [47]. Schumacher s result [47] 30] must be considered as the quantum analogue of Shannon s noiseless coding theorem (see e.g. 60, Sec....
Cited by: More
schums1.tex; submitted to Phys. Rev. A 3/7/96.. - As Quantum Computation (Correct)
quant-ph/9603009 - Mar Schums Tex (Correct)
A Study Of Entanglement In Quantum Information Theory - Verstraete (2002) (Correct)
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0.5: Generic Quantum Block Compression - John Langford October (Correct)
0.1: A New Proof of the Quantum Noiseless Coding Theorem - Richard Jozsa Benjamin (1994) (Correct)
0.1: Sending Entanglement through Noisy Quantum Channels - Schumacher (1996) (Correct)
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15: A new proof of the quantum noiseless coding theorem - Jozsa, Schumacher - 1994
8: A mathematical theory of communication (context) - Shannon - 1948
7: Maintaining coherence in quantum computers (context) - Unruh - 1995
BibTeX entry: (Update)
B. Schumacher, "Quantum Coding", Phys. Rev. A. 51, 2738 (1995). http://citeseer.ist.psu.edu/schumacher95quantum.html More
@misc{ schumacherschumacherquantum,
author = "Benjamin Schumacher",
title = "Quantum Coding",
howpublished = "Preprint at {\url http://vesta.physics.ucla.edu/cgi-bin/uncompress\_ps\_cgi?qubit.ps}.",
url = "citeseer.ist.psu.edu/schumacher95quantum.html" }
Citations (may not include all citations):25 Mathematical Foundations of Quantum Mechanics (context) - von Neumann - 1955
6 Bell System Technical Journal (context) - Shannon - 1948
3 to appear (context) - Jozsa, Schumacher et al.
2 The University of Texas at Austin (context) - Schumacher, Correlation et al. - 1990
1 Introduction to Information Theory (context) - textbook, theory et al. - 1987
1 Mathematishe Annalen (context) - Schmidt - 1906
1 This paper has appeared in English translation in Problems o.. (context) - Kholevo, Informatsii - 1973
1 private communication (context) - Jozsa
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://vesta.physics.ucla.edu/~smolin/index.html): More
Results on Two-Bit Gate Design for Quantum Computers - DiVincenzo, Smolin (1998) (Correct)
Elementary Gates for Quantum Computation - Barenco, Bennett, Cleve, Di.. (1995) (Correct)
Five Two-Bit Quantum Gates are Sufficient to Implement the.. - Smolin, DiVincenzo (1995) (Correct)
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