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Trading quantum for classical resources in quantum data compression

Hayden, Patrick and Jozsa, Richard and Winter, Andreas (2002) Trading quantum for classical resources in quantum data compression. Journal of Mathematical Physics, 43 (9). pp. 4404-4444. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:HAYjmp02

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Abstract

We study the visible compression of a source [script E] = {|phii>,pi} of pure quantum signal states or, more formally, the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity, when the compressor is given the identity of the input state sequence as classical information. According to the quantum source coding theorem, the optimal quantum rate is the von Neumann entropy S([script E]) qubits per signal. We develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified separately. This leads to a trade-off curve Q*(R), where Q*(R) qubits per signal is the optimal quantum rate for a given classical rate of R bits per signal. Our main result is an explicit characterization of this trade-off function by a simple formula in terms of only single-signal, perfect fidelity encodings of the source. We give a thorough discussion of many further mathematical properties of our formula, including an analysis of its behavior for group covariant sources and a generalization to sources with continuously parametrized states. We also show that our result leads to a number of corollaries characterizing the trade-off between information gain and state disturbance for quantum sources. In addition, we indicate how our techniques also provide a solution to the so-called remote state preparation problem. Finally, we develop a probability-free version of our main result which may be interpreted as an answer to the question: "How many classical bits does a qubit cost?" This theorem provides a type of dual to Holevo's theorem, insofar as the latter characterizes the cost of coding classical bits into qubits.


Item Type:Article
Additional Information:©2002 American Institute of Physics. (Received 12 April 2002; accepted 21 May 2002) We thank Charles H. Bennett, David P. DiVincenzo, Daniel Gottesman, Debbie W. Leung, Michael A. Nielsen, Dénes Petz, Peter W. Shor and John. A. Smolin for enlightening discussions and helpful suggestions. P.H. was supported by US National Science Foundation Grant No. EIA-0086038 and a Sherman Fairchild Fellowship. R.J. and A.W. are supported by the U.K. Engineering and Physical Sciences Research Council.
Subject Keywords:entropy; encoding; quantum theory; quantum computing; data compression; bound states
Record Number:CaltechAUTHORS:HAYjmp02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:HAYjmp02
Alternative URL:http://dx.doi.org/10.1063/1.1497184
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4519
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:25 Aug 2006
Last Modified:26 Dec 2012 08:59

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