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Position-momentum uncertainty relations in the presence of quantum memory

Furrer, Fabian and Berta, Mario and Tomamichel, Marco and Scholz, Volkher B. and Christandl, Matthias (2014) Position-momentum uncertainty relations in the presence of quantum memory. Journal of Mathematical Physics, 55 (12). Art. No. 122205. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20150130-091355290

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Abstract

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.4903989DOIArticle
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903989PublisherArticle
https://arxiv.org/abs/1308.4527arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Tomamichel, Marco0000-0001-5410-3329
Additional Information:© 2014 AIP Publishing LLC. Received 12 October 2014; accepted 29 November 2014; published online 23 December 2014. We gratefully acknowledge discussions with Renato Renner, Reinhard F. Werner, and Jukka Kiukkas and express special thanks to Michael Walter. MB, VBS, and MC acknowledge financial support by the Swiss National Science Foundation (Grant Nos. PP00P2-128455, 20CH21-138799 (CHIST-ERA project CQC)), the Swiss National Center of Competence in Research “Quantum Science and Technology (QSIT),” the Swiss State Secretariat for Education and Research supporting COST action MP1006, and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 337603. MC also acknowledges a Sapere Aude Grant from the Danish Council for Independent Research. VBS is in addition supported by an ETH Postdoctoral Fellowship. FF acknowledges support from Japan Society for the Promotion of Science (JSPS) by KAKENHI Grant No. 24-02793. MT is funded by the Ministry of Education (MOE) and National Research Foundation Singapore, as well as MOE Tier 3 Grant “Random numbers from quantum processes” (MOE2012-T3-1-009).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)PP00P2-128455
Swiss National Science Foundation (SNSF)20CH21-138799
Swiss National Center of Competence in ResearchUNSPECIFIED
Swiss State Secretariat for Education and ResearchUNSPECIFIED
European Research Council (ERC)337603
ETH Postdoctoral FellowshipUNSPECIFIED
Japan Society for the Promotion of Science (JSPS)24-02793
National Research Foundation (Singapore)UNSPECIFIED
Ministry of Education (Singapore)MOE2012-T3-1-009
Record Number:CaltechAUTHORS:20150130-091355290
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150130-091355290
Official Citation:Furrer, F., Berta, M., Tomamichel, M., Scholz, V. B., & Christandl, M. (2014). Position-momentum uncertainty relations in the presence of quantum memory. Journal of Mathematical Physics, 55(12), -. doi: doi:http://dx.doi.org/10.1063/1.4903989
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54241
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:30 Jan 2015 21:53
Last Modified:04 Jun 2018 18:34

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