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. 44044444. ISSN 00222488. doi:10.1063/1.1497184. https://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 tradeoff 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 tradeoff function by a simple formula in terms of only singlesignal, 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 tradeoff between information gain and state disturbance for quantum sources. In addition, we indicate how our techniques also provide a solution to the socalled remote state preparation problem. Finally, we develop a probabilityfree 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  

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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. EIA0086038 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  
Issue or Number:  9  
DOI:  10.1063/1.1497184  
Record Number:  CaltechAUTHORS:HAYjmp02  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:HAYjmp02  
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:  08 Nov 2021 20:18 
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