Ultimate Data Hiding in Quantum Mechanics and Beyond

Lami, L; Palazuelos, C; Winter, A

Ultimate Data Hiding in Quantum Mechanics and Beyond

Lami, L Palazuelos, C Winter, A

Permalink

Publication Type:: Journal Article
Citation:: Communications in Mathematical Physics, 2018, 361 (2), pp. 661 - 708
Issue Date:: 2018-07-01

Closed Access

	Filename	Description	Size
	Lami2018_Article_UltimateDataHidingInQuantumMec.pdf	Published Version	921 kB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Lami, L	en_US
dc.contributor.author	Palazuelos, C	en_US
dc.contributor.author	Winter, A https://orcid.org/0000-0001-6344-4870	en_US
dc.date.issued	2018-07-01	en_US
dc.identifier.citation	Communications in Mathematical Physics, 2018, 361 (2), pp. 661 - 708	en_US
dc.identifier.issn	0010-3616	en_US
dc.identifier.uri	http://hdl.handle.net/10453/131621
dc.description.abstract	© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. The phenomenon of data hiding, i.e. the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under LOCC, is a distinctive signature of nonclassicality. The relevant figure of merit is the maximal ratio (called data hiding ratio) between the distinguishability norms associated with the two sets of measurements we are comparing, typically all measurements vs LOCC protocols. For a bipartite n× n quantum system, it is known that the data hiding ratio scales as n, i.e. the square root of the real dimension of the local state space of density matrices. We show that for bipartite nA× nB systems the maximum data hiding ratio against LOCC protocols is Θ (min { nA, nB}). This scaling is better than the previously obtained upper bounds O(nAnB) and min{nA2,nB2}, and moreover our intuitive argument yields constants close to optimal. In this paper, we investigate data hiding in the more general context of general probabilistic theories (GPTs), an axiomatic framework for physical theories encompassing only the most basic requirements about the predictive power of the theory. The main result of the paper is the determination of the maximal data hiding ratio obtainable in an arbitrary GPT, which is shown to scale linearly in the minimum of the local dimensions. We exhibit an explicit model achieving this bound up to additive constants, finding that quantum mechanical data hiding ratio is only of the order of the square root of the maximal one. Our proof rests crucially on an unexpected link between data hiding and the theory of projective and injective tensor products of Banach spaces. Finally, we develop a body of techniques to compute data hiding ratios for a variety of restricted classes of GPTs that support further symmetries.	en_US
dc.relation.ispartof	Communications in Mathematical Physics	en_US
dc.relation.isbasedon	10.1007/s00220-018-3154-4	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Ultimate Data Hiding in Quantum Mechanics and Beyond	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	361	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	0206 Quantum Physics	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	361	en_US

Abstract:

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. The phenomenon of data hiding, i.e. the existence of pairs of states of a bipartite system that are perfectly distinguishable via general entangled measurements yet almost indistinguishable under LOCC, is a distinctive signature of nonclassicality. The relevant figure of merit is the maximal ratio (called data hiding ratio) between the distinguishability norms associated with the two sets of measurements we are comparing, typically all measurements vs LOCC protocols. For a bipartite n× n quantum system, it is known that the data hiding ratio scales as n, i.e. the square root of the real dimension of the local state space of density matrices. We show that for bipartite nA× nB systems the maximum data hiding ratio against LOCC protocols is Θ (min { nA, nB}). This scaling is better than the previously obtained upper bounds O(nAnB) and min{nA2,nB2}, and moreover our intuitive argument yields constants close to optimal. In this paper, we investigate data hiding in the more general context of general probabilistic theories (GPTs), an axiomatic framework for physical theories encompassing only the most basic requirements about the predictive power of the theory. The main result of the paper is the determination of the maximal data hiding ratio obtainable in an arbitrary GPT, which is shown to scale linearly in the minimum of the local dimensions. We exhibit an explicit model achieving this bound up to additive constants, finding that quantum mechanical data hiding ratio is only of the order of the square root of the maximal one. Our proof rests crucially on an unexpected link between data hiding and the theory of projective and injective tensor products of Banach spaces. Finally, we develop a body of techniques to compute data hiding ratios for a variety of restricted classes of GPTs that support further symmetries.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/131621