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Remote preparation of quantum states

Bennett, Charles H. and Hayden, Patrick and Leung, Debbie W. and Shor, Peter W. and Winter, Andreas (2005) Remote preparation of quantum states. IEEE Transactions on Information Theory, 51 (1). pp. 56-74. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:BENieeetit05

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Abstract

Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.


Item Type:Article
Additional Information:© Copyright 2005 IEEE. Reprinted with permission. Manuscript received August 22, 2003; revised June 7, 2004. [Posted online: 2005-01-10] The work of C. H. Bennett was supported by the U.S. National Security Agency and Advanced Research and Development Activity under Contracts DAAD19-01-1-06 and DAAD19-01-C-0056. The work of P. Hayden was supported by the Sherman Fairchild Foundation and the U.S. National Science Foundation under Grant EIA-0086038. The work of D. W. Leung was supported by the Richard C. Tolman Endowment Fund, the Croucher Foundation, and the U.S. National Science Foundation under Grant EIA-0086038. A. Winter was supported by the U.K. Engineering and Physical Sciences Research Council. Communicated by E. Knill, Associate Editor for Quantum Information Theory. The authors wish to thank Anura Abeyesinghe, Igor Devetak, Chris Fuchs, Aram Harrow, Daniel Gottesman, and John Smolin for interesting and helpful conversations. P. Hayden, D. W. Leung, and A. Winter gratefully acknowledge the hospitality and support of the Mathematical Sciences Research Institute, Berkeley, during part of the autumn term of 2002.
Subject Keywords:Cryptography, entanglement, large deviations, teleportation, tradeoff
Record Number:CaltechAUTHORS:BENieeetit05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BENieeetit05
Alternative URL:http://dx.doi.org/10.1109/TIT.2004.839476
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1887
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:22 Feb 2006
Last Modified:26 Dec 2012 08:46

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