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Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities

Frank, Rupert L. and Lieb, Elliott H. (2013) Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities. Communications in Mathematical Physics, 323 (2). pp. 487-495. ISSN 0010-3616. doi:10.1007/s00220-013-1775-1.

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Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. Our proofs utilize the technique of the original derivation of strong subadditivity of the von Neumann entropy.

Item Type:Article
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URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Lieb, Elliott H.0000-0001-5843-3587
Additional Information:© 2013 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 5 June 2012. Accepted: 3 January 2013. Published online: 11 August 2013. We thank Zhihao Ma for helpful correspondence. U.S. National Science Foundation grants PHY-1068285 (R.F.) and PHY-0965859 (E.L.) and the Simons Foundation grant 230207 (E.L.) are acknowledged.
Funding AgencyGrant Number
Simons Foundation230207
Issue or Number:2
Record Number:CaltechAUTHORS:20170501-112412599
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Official Citation:Frank, R.L. & Lieb, E.H. Commun. Math. Phys. (2013) 323: 487. doi:10.1007/s00220-013-1775-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77106
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 18:34
Last Modified:15 Nov 2021 17:28

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