Ultimate Data Hiding in Quantum Mechanics and Beyond
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 (...
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| Vydané v: | Communications in mathematical physics Ročník 361; číslo 2; s. 661 - 708 |
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01.07.2018
Springer Nature B.V |
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| Abstract | 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
n
A
×
n
B
systems the maximum data hiding ratio against LOCC protocols is
Θ
min
{
n
A
,
n
B
}
. This scaling is better than the previously obtained upper bounds
O
n
A
n
B
and
min
{
n
A
2
,
n
B
2
}
, 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. |
|---|---|
| AbstractList | 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 Θmin{nA,nB}. This scaling is better than the previously obtained upper bounds OnAnB 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. 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 n A × n B systems the maximum data hiding ratio against LOCC protocols is Θ min { n A , n B } . This scaling is better than the previously obtained upper bounds O n A n B and min { n A 2 , n B 2 } , 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. |
| Author | Palazuelos, Carlos Lami, Ludovico Winter, Andreas |
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| Cites_doi | 10.1007/s00220-006-1535-6 10.1103/PhysRevA.64.062307 10.1017/CBO9780511804441 10.1103/PhysRevLett.70.1895 10.1007/BF02393206 10.1007/s00220-014-1953-9 10.1088/1367-2630/13/6/063024 10.1016/S0375-9601(01)00484-4 10.1007/BF00671964 10.1103/PhysRevLett.99.240501 10.2140/pjm.1969.31.469 10.1007/BF01878476 10.1016/j.entcs.2011.01.002 10.4064/sm-58-2-197-208 10.1007/BF01646732 10.1038/ncomms2821 10.1006/jcta.2000.3155 10.1007/978-3-642-71897-7_1 10.1016/0095-8956(88)90040-8 10.1007/s00220-014-2213-8 10.1007/BF00668911 10.1007/s10701-013-9752-2 10.1112/jlms/s1-39.1.730 10.1090/surv/223 10.1103/PhysRevLett.85.4972 10.1007/978-1-4471-3903-4 10.1090/psapm/071/600 10.1088/1367-2630/17/10/103027 10.1007/BF02058098 10.1007/978-3-642-66557-8 10.1103/PhysRevLett.86.5807 10.1103/PhysRevA.59.4206 10.1007/BF01351796 10.1103/PhysRevA.59.141 10.1103/PhysRevA.79.062306 10.1109/18.985948 10.1007/s00220-008-0582-6 10.1073/pnas.1304884110 10.1007/978-3-0348-8871-4_14 10.1016/j.laa.2015.08.024 10.1007/BF01647093 10.1103/PhysRevA.40.4277 10.1103/PhysRevA.75.032304 10.4064/sm-70-3-231-283 10.1007/s00220-009-0890-5 |
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| References | BarrettJ.Information processing in generalized probabilistic theoriesPhys. Rev. A20077503230410.1103/PhysRevA.75.0323042007PhRvA..75c2304BarXiv:quant-ph/0508211 RudinW.Functional Analysis1991New YorkMcGraw-Hill0867.46001 DiVincenzoD.P.LeungD.W.TerhalB.M.Quantum data hidingIEEE Trans. Inf. Theory2002483580599188997010.1109/18.9859481071.81511arXiv:quant-ph/0103098 Pfister, C.: One simple postulate implies that every polytopic state space is classical, Master thesis (2013). arXiv:1203.5622 RödlP. FranklV.Wilson R.M.The number of submatrices of a given type in a Hadamard matrix and related resultsJ. Combin. Theory Ser. B198844331732894144010.1016/0095-8956(88)90040-80658.05015 Lami, L.: Non-classical correlations in quantum mechanics and beyond. Ph.D thesis (2017). arXiv:1803.02092 WilceA.Tensor products in generalized measure theoryInt. J. Theor. Phys.1992311915118629710.1007/BF006719640795.46055 VinbergE.B.Homogeneous conesDokl. Acad. Nauk. SSSR19601412702730143.05203(English trans. Sov. Math. Dokl. 2, 1416–1619 (1961)) ChitambarE.LeungD.MančinskaL.OzolsM.WinterA.Everything you always wanted to know about LOCC (but were afraid to ask)Commun. Math. Phys.20143281303326319698710.1007/s00220-014-1953-91290.810122014CMaPh.328..303C HaagerupU.The best constants in the Khintchine inequalityStud. Math.198170323128365483810.4064/sm-70-3-231-2830501.46015 ErdösP.SpencerJ.Probabilistic Methods in Combinatorics1974CambridgeAcademic Press0308.05001 MatthewsW.WehnerS.WinterA.Distinguishability of quantum states under restricted families of measurements with an application to quantum data hidingCommun. Math. Phys.20092913813843253479310.1007/s00220-009-0890-51179.810202009CMaPh.291..813M KläyM.RandallC.H.FoulisD.J.Tensor products and probability weightsInt. J. Theor. Phys.19872619989241110.1007/BF006689110641.46049 VidalG.TarrachR.Robustness of entanglementPhys. Rev. A199959141155167056210.1103/PhysRevA.59.1411999PhRvA..59..141VarXiv:quant-ph/9806094 EdwardsC.M.The theory of pure operationsCommun. Math. Phys.197224426028829726010.1007/BF018784760227.460731971CMaPh..24..260E HaydenP.LeungD.W.WinterA.Aspects of generic entanglementCommun. Math. Phys.2006265195117221729810.1007/s00220-006-1535-61107.810112006CMaPh.265...95H BarnumH.WilceA.Information processing in convex operational theoriesElectron. Notes Theor. Comput. Sci.2011270131510.1016/j.entcs.2011.01.0021348.81130arXiv:0908.2352 Ludwig, G.: An Axiomatic Basis of Quantum Mechanics, vols. 1, 2. Springer, Berlin (1985, 1987) BoydS.VandenbergheL.Convex Optimization2004CambridgeCambridge University Press10.1017/CBO97805118044411058.90049 AlonN.SpencerJ.H.The Probabilistic Method20153New YorkWiley1333.05001 ChiribellaG.ScandoloC.M.Entanglement and thermodynamics in general probabilistic theoriesNew J. Phys.20151710302710.1088/1367-2630/17/10/1030272015NJPh...17j3027C Pisier, G.: Finite rank projections on Banach spaces and a conjecture of Grothendieck. In: Proceedings of the International Congress of Mathematicians, vol. 2, Warszawa, pp. 1027–1039 (1983) WernerR.F.Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable modelPhys. Rev. A.19894084277428110.1103/PhysRevA.40.42771371.811451989PhRvA..40.4277W BarnumH.BarrettJ.LeiferM.WilceA.Generalized no-broadcasting theoremPhys. Rev. Lett.20079924050110.1103/PhysRevLett.99.2405012007PhRvL..99x0501BarXiv:quant-ph/0611295 BrandãoF.G.S.L.HorodeckiM.Exponential decay of correlations implies area lawCommun. Math. Phys.20153332761798329616210.1007/s00220-014-2213-81317.810212015CMaPh.333..761B Hardy, L.: Quantum theory from five reasonable axioms (2001). arXiv:quant-ph/0101012 HorodeckiM.HorodeckiP.Reduction criterion of separability and limits for a class of protocols of entanglement distillationPhys. Rev. A199959420610.1103/PhysRevA.59.42061999PhRvA..59.4206H VollbrechtK.G.H.WernerR.F.Entanglement measures under symmetryPhys. Rev. A20016406230710.1103/PhysRevA.64.0623072001PhRvA..64f2307V TerhalB.M.DiVincenzoD.P.LeungD.W.Hiding bits in Bell statesPhys. Rev. Lett.200186580710.1103/PhysRevLett.86.58072001PhRvL..86.5807TarXiv:quant-ph/0011042 LatalaR.OleszkiewiczK.On the best constant in the Khintchine-Kahane inequalityStud. Math.199410911011040812.60010 RyanR.A.Introduction to Tensor Products of Banach Spaces2002BerlinSpringer10.1007/978-1-4471-3903-41090.46001 MatthewsW.WinterA.On the Chernoff distance for asymptotic LOCC discrimination of bipartite quantum statesCommun. Math. Phys.20082851161174245359310.1007/s00220-008-0582-61228.811172009CMaPh.285..161MarXiv:0710.4113 AlonN.Approximating sparse binary matrices in the cut-normLinear Algebra Appl.2015486409418340177010.1016/j.laa.2015.08.0241327.15044 KimuraG.MiyaderaT.ImaiH.Optimal state discrimination in general probabilistic theoriesPhys. Rev. A20097906230610.1103/PhysRevA.79.0623062009PhRvA..79f2306K MackeyG.Mathematical Foundations of Quantum Mechanics1963AmsterdamBenjamin0114.44002 PopescuS.RohrlichD.Quantum nonlocality as an axiomFound. Phys.1994243379385126557710.1007/BF020580981994FoPh...24..379P HelstromC.W.Quantum Detection and Estimation Theory1976CambridgeAcademic Press1332.81011 PfisterC.WehnerS.An information-theoretic principle implies that any discrete physical theory is classicalNat. Commun.20134185110.1038/ncomms28212013NatCo...4E1851P EdwardsC.M.Classes of operations in quantum theoryCommun. Math. Phys.1971201265627579910.1007/BF016467320203.570011971CMaPh..20...26E MasanesL.MüllerM.P.AugusiakR.Pérez-GarcíaD.Existence of an information unit as a postulate of quantum theoryProc. Natl Acad. Sci. USA2013110163731637710.1073/pnas.13048841102013PNAS..11016373M VirmaniS.SacchiM.F.PlenioM.B.MarkhamD.Optimal local discrimination of two multipartite pure statesPhys. Lett. A200128826268186088410.1016/S0375-9601(01)00484-40971.810082001PhLA..288...62V EllisA.J.The duality of partially ordered normed linear spacesJ. Lond. Math. Soc.196439173074416902010.1112/jlms/s1-39.1.7300131.11302 NamiokaI.PhelphsR.R.Tensor product of compact convex setsPac. J. Math.196931246948027168910.2140/pjm.1969.31.469 JanottaP.GogolinC.BarrettJ.BrunnerN.Limits on non-local correlations from the structure of the local state spaceNew J. Phys.20111306302410.1088/1367-2630/13/6/0630242011NJPh...13f3024J PisierG.Counterexamples to a conjecture of GrothendieckActa Math.1983151118120872300910.1007/BF023932060542.46038 Mulansky, B.: Tensor products of convex cones. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds.) Multivariate Approximation and Splines, vol. 125. ISNM, Lübeck (1997) KoecherM.Die geoodätischen von PositivitaätsbereichenMath. Ann.195813519220210398710.1007/BF01351796 KreinM.Sur la decomposition minimale d’une fonctionnelle lineaire en composantes positivesDokl. Akad. Nauk SSSR (NS)19402818220024.12203 de LauneyW.GordonD.M.A comment on the Hadamard conjectureJ. Combin. Theory Ser. A2001951180184184048410.1006/jcta.2000.31550973.05011 AubrunG.SzarekS.Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory2017ProvidenceAmerican Mathematical Society10.1090/surv/22306780344 DaviesE.B.LewisJ.T.An operational approach to quantum probabilityCommun. Math. Phys.197017323926026337910.1007/BF016470930194.583041970CMaPh..17..239D SzarekS.On the best constants in the Khinchin InequalityStud. Math.197658219720843066710.4064/sm-58-2-197-2080424.42014 BennettC.H.BrassardG.CrépeauC.JozsaR.PeresA.Wootters W.K.Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channelsPhys. Rev. Lett.19937018951899120824710.1103/PhysRevLett.70.18951051.815051993PhRvL..70.1895B BarnumH.BarrettJ.LeiferM.WilceA.Teleportation in general probabilistic theoriesProc. Symp. Appl. Math.2012712548296314110.1090/psapm/071/6001258.81011arXiv:0805.3553 BarnumH.GaeblerC.P.WilceA.Ensemble steering, weak self-duality, and the structure of probabilistic theoriesFound. Phys.2013431214111427313294010.1007/s10701-013-9752-21286.810202013FoPh...43.1411B LindenstraussJ.TzafririL.Classical Banach Spaces I and II1977BerlinSpringer10.1007/978-3-642-66557-80362.46013 WalgateJ.ShortA.J.HardyL.VedralV.Local distinguishability of multipartite orthogonal quantum statesPhys. Rev. Lett.200085497210.1103/PhysRevLett.85.49722000PhRvL..85.4972W Wilce, A.: Four and a half axioms for finite dimensional quantum mechanics (2009). arXiv:0912.5530 DefantA.FloretK.Tensor Norms and Operator Ideals1993AmsterdamNorth-Holland0774.46018 R.A. Ryan (3154_CR47) 2002 V. RödlP. Frankl (3154_CR52) 1988; 44 R. Latala (3154_CR58) 1994; 109 3154_CR1 3154_CR28 3154_CR21 W. Rudin (3154_CR25) 1991 G. Chiribella (3154_CR20) 2015; 17 A. Defant (3154_CR46) 1993 W. Launey de (3154_CR55) 2001; 95 S. Boyd (3154_CR24) 2004 C. Pfister (3154_CR19) 2013; 4 H. Barnum (3154_CR18) 2013; 43 E. Chitambar (3154_CR31) 2014; 328 W. Matthews (3154_CR34) 2008; 285 N. Alon (3154_CR53) 2015; 486 C.W. Helstrom (3154_CR30) 1976 S. Szarek (3154_CR56) 1976; 58 3154_CR10 G. Kimura (3154_CR29) 2009; 79 D.P. DiVincenzo (3154_CR3) 2002; 48 H. Barnum (3154_CR15) 2012; 71 U. Haagerup (3154_CR57) 1981; 70 P. Janotta (3154_CR16) 2011; 13 E.B. Vinberg (3154_CR45) 1960; 141 H. Barnum (3154_CR17) 2007; 99 J. Walgate (3154_CR32) 2000; 85 F.G.S.L. Brandão (3154_CR35) 2015; 333 G. Mackey (3154_CR5) 1963 3154_CR49 M. Koecher (3154_CR44) 1958; 135 P. Hayden (3154_CR59) 2006; 265 C.M. Edwards (3154_CR8) 1971; 20 H. Barnum (3154_CR22) 2011; 270 3154_CR41 M. Krein (3154_CR23) 1940; 28 3154_CR42 J. Barrett (3154_CR13) 2007; 75 G. Vidal (3154_CR36) 1999; 59 C.M. Edwards (3154_CR9) 1972; 24 R.F. Werner (3154_CR39) 1989; 40 S. Virmani (3154_CR33) 2001; 288 A. Wilce (3154_CR12) 1992; 31 M. Kläy (3154_CR11) 1987; 26 J. Lindenstrauss (3154_CR50) 1977 M. Horodecki (3154_CR37) 1999; 59 C.H. Bennett (3154_CR38) 1993; 70 E.B. Davies (3154_CR6) 1970; 17 B.M. Terhal (3154_CR2) 2001; 86 P. Erdös (3154_CR51) 1974 G. Pisier (3154_CR48) 1983; 151 A.J. Ellis (3154_CR7) 1964; 39 N. Alon (3154_CR54) 2015 I. Namioka (3154_CR27) 1969; 31 S. Popescu (3154_CR14) 1994; 24 G. Aubrun (3154_CR26) 2017 L. Masanes (3154_CR43) 2013; 110 W. Matthews (3154_CR4) 2009; 291 K.G.H. Vollbrecht (3154_CR40) 2001; 64 |
| References_xml | – reference: AlonN.Approximating sparse binary matrices in the cut-normLinear Algebra Appl.2015486409418340177010.1016/j.laa.2015.08.0241327.15044 – reference: SzarekS.On the best constants in the Khinchin InequalityStud. Math.197658219720843066710.4064/sm-58-2-197-2080424.42014 – reference: Hardy, L.: Quantum theory from five reasonable axioms (2001). arXiv:quant-ph/0101012 – reference: VidalG.TarrachR.Robustness of entanglementPhys. Rev. A199959141155167056210.1103/PhysRevA.59.1411999PhRvA..59..141VarXiv:quant-ph/9806094 – reference: HorodeckiM.HorodeckiP.Reduction criterion of separability and limits for a class of protocols of entanglement distillationPhys. Rev. A199959420610.1103/PhysRevA.59.42061999PhRvA..59.4206H – reference: NamiokaI.PhelphsR.R.Tensor product of compact convex setsPac. J. Math.196931246948027168910.2140/pjm.1969.31.469 – reference: MackeyG.Mathematical Foundations of Quantum Mechanics1963AmsterdamBenjamin0114.44002 – reference: HaydenP.LeungD.W.WinterA.Aspects of generic entanglementCommun. Math. Phys.2006265195117221729810.1007/s00220-006-1535-61107.810112006CMaPh.265...95H – reference: WalgateJ.ShortA.J.HardyL.VedralV.Local distinguishability of multipartite orthogonal quantum statesPhys. Rev. Lett.200085497210.1103/PhysRevLett.85.49722000PhRvL..85.4972W – reference: BrandãoF.G.S.L.HorodeckiM.Exponential decay of correlations implies area lawCommun. Math. Phys.20153332761798329616210.1007/s00220-014-2213-81317.810212015CMaPh.333..761B – reference: KimuraG.MiyaderaT.ImaiH.Optimal state discrimination in general probabilistic theoriesPhys. Rev. A20097906230610.1103/PhysRevA.79.0623062009PhRvA..79f2306K – reference: PisierG.Counterexamples to a conjecture of GrothendieckActa Math.1983151118120872300910.1007/BF023932060542.46038 – reference: MatthewsW.WehnerS.WinterA.Distinguishability of quantum states under restricted families of measurements with an application to quantum data hidingCommun. Math. Phys.20092913813843253479310.1007/s00220-009-0890-51179.810202009CMaPh.291..813M – reference: BarnumH.BarrettJ.LeiferM.WilceA.Generalized no-broadcasting theoremPhys. Rev. Lett.20079924050110.1103/PhysRevLett.99.2405012007PhRvL..99x0501BarXiv:quant-ph/0611295 – reference: LatalaR.OleszkiewiczK.On the best constant in the Khintchine-Kahane inequalityStud. Math.199410911011040812.60010 – reference: KläyM.RandallC.H.FoulisD.J.Tensor products and probability weightsInt. J. Theor. Phys.19872619989241110.1007/BF006689110641.46049 – reference: MasanesL.MüllerM.P.AugusiakR.Pérez-GarcíaD.Existence of an information unit as a postulate of quantum theoryProc. Natl Acad. Sci. USA2013110163731637710.1073/pnas.13048841102013PNAS..11016373M – reference: DefantA.FloretK.Tensor Norms and Operator Ideals1993AmsterdamNorth-Holland0774.46018 – reference: EdwardsC.M.Classes of operations in quantum theoryCommun. Math. Phys.1971201265627579910.1007/BF016467320203.570011971CMaPh..20...26E – reference: WernerR.F.Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable modelPhys. Rev. A.19894084277428110.1103/PhysRevA.40.42771371.811451989PhRvA..40.4277W – reference: HelstromC.W.Quantum Detection and Estimation Theory1976CambridgeAcademic Press1332.81011 – reference: PopescuS.RohrlichD.Quantum nonlocality as an axiomFound. Phys.1994243379385126557710.1007/BF020580981994FoPh...24..379P – reference: JanottaP.GogolinC.BarrettJ.BrunnerN.Limits on non-local correlations from the structure of the local state spaceNew J. Phys.20111306302410.1088/1367-2630/13/6/0630242011NJPh...13f3024J – reference: Ludwig, G.: An Axiomatic Basis of Quantum Mechanics, vols. 1, 2. Springer, Berlin (1985, 1987) – reference: VollbrechtK.G.H.WernerR.F.Entanglement measures under symmetryPhys. Rev. A20016406230710.1103/PhysRevA.64.0623072001PhRvA..64f2307V – reference: Lami, L.: Non-classical correlations in quantum mechanics and beyond. Ph.D thesis (2017). arXiv:1803.02092 – reference: BarrettJ.Information processing in generalized probabilistic theoriesPhys. Rev. A20077503230410.1103/PhysRevA.75.0323042007PhRvA..75c2304BarXiv:quant-ph/0508211 – reference: DiVincenzoD.P.LeungD.W.TerhalB.M.Quantum data hidingIEEE Trans. Inf. Theory2002483580599188997010.1109/18.9859481071.81511arXiv:quant-ph/0103098 – reference: PfisterC.WehnerS.An information-theoretic principle implies that any discrete physical theory is classicalNat. Commun.20134185110.1038/ncomms28212013NatCo...4E1851P – reference: TerhalB.M.DiVincenzoD.P.LeungD.W.Hiding bits in Bell statesPhys. Rev. Lett.200186580710.1103/PhysRevLett.86.58072001PhRvL..86.5807TarXiv:quant-ph/0011042 – reference: AlonN.SpencerJ.H.The Probabilistic Method20153New YorkWiley1333.05001 – reference: WilceA.Tensor products in generalized measure theoryInt. J. Theor. Phys.1992311915118629710.1007/BF006719640795.46055 – reference: BoydS.VandenbergheL.Convex Optimization2004CambridgeCambridge University Press10.1017/CBO97805118044411058.90049 – reference: Mulansky, B.: Tensor products of convex cones. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds.) Multivariate Approximation and Splines, vol. 125. ISNM, Lübeck (1997) – reference: AubrunG.SzarekS.Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory2017ProvidenceAmerican Mathematical Society10.1090/surv/22306780344 – reference: Wilce, A.: Four and a half axioms for finite dimensional quantum mechanics (2009). arXiv:0912.5530 – reference: RyanR.A.Introduction to Tensor Products of Banach Spaces2002BerlinSpringer10.1007/978-1-4471-3903-41090.46001 – reference: MatthewsW.WinterA.On the Chernoff distance for asymptotic LOCC discrimination of bipartite quantum statesCommun. Math. Phys.20082851161174245359310.1007/s00220-008-0582-61228.811172009CMaPh.285..161MarXiv:0710.4113 – reference: ErdösP.SpencerJ.Probabilistic Methods in Combinatorics1974CambridgeAcademic Press0308.05001 – reference: HaagerupU.The best constants in the Khintchine inequalityStud. Math.198170323128365483810.4064/sm-70-3-231-2830501.46015 – reference: VinbergE.B.Homogeneous conesDokl. Acad. Nauk. SSSR19601412702730143.05203(English trans. Sov. Math. Dokl. 2, 1416–1619 (1961)) – reference: Pfister, C.: One simple postulate implies that every polytopic state space is classical, Master thesis (2013). arXiv:1203.5622 – reference: BennettC.H.BrassardG.CrépeauC.JozsaR.PeresA.Wootters W.K.Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channelsPhys. Rev. Lett.19937018951899120824710.1103/PhysRevLett.70.18951051.815051993PhRvL..70.1895B – reference: DaviesE.B.LewisJ.T.An operational approach to quantum probabilityCommun. Math. Phys.197017323926026337910.1007/BF016470930194.583041970CMaPh..17..239D – reference: ChitambarE.LeungD.MančinskaL.OzolsM.WinterA.Everything you always wanted to know about LOCC (but were afraid to ask)Commun. Math. Phys.20143281303326319698710.1007/s00220-014-1953-91290.810122014CMaPh.328..303C – reference: BarnumH.GaeblerC.P.WilceA.Ensemble steering, weak self-duality, and the structure of probabilistic theoriesFound. Phys.2013431214111427313294010.1007/s10701-013-9752-21286.810202013FoPh...43.1411B – reference: RudinW.Functional Analysis1991New YorkMcGraw-Hill0867.46001 – reference: BarnumH.BarrettJ.LeiferM.WilceA.Teleportation in general probabilistic theoriesProc. Symp. Appl. Math.2012712548296314110.1090/psapm/071/6001258.81011arXiv:0805.3553 – reference: KreinM.Sur la decomposition minimale d’une fonctionnelle lineaire en composantes positivesDokl. Akad. Nauk SSSR (NS)19402818220024.12203 – reference: EllisA.J.The duality of partially ordered normed linear spacesJ. Lond. Math. Soc.196439173074416902010.1112/jlms/s1-39.1.7300131.11302 – reference: EdwardsC.M.The theory of pure operationsCommun. Math. Phys.197224426028829726010.1007/BF018784760227.460731971CMaPh..24..260E – reference: VirmaniS.SacchiM.F.PlenioM.B.MarkhamD.Optimal local discrimination of two multipartite pure statesPhys. Lett. A200128826268186088410.1016/S0375-9601(01)00484-40971.810082001PhLA..288...62V – reference: ChiribellaG.ScandoloC.M.Entanglement and thermodynamics in general probabilistic theoriesNew J. Phys.20151710302710.1088/1367-2630/17/10/1030272015NJPh...17j3027C – reference: KoecherM.Die geoodätischen von PositivitaätsbereichenMath. Ann.195813519220210398710.1007/BF01351796 – reference: Pisier, G.: Finite rank projections on Banach spaces and a conjecture of Grothendieck. In: Proceedings of the International Congress of Mathematicians, vol. 2, Warszawa, pp. 1027–1039 (1983) – reference: de LauneyW.GordonD.M.A comment on the Hadamard conjectureJ. Combin. Theory Ser. A2001951180184184048410.1006/jcta.2000.31550973.05011 – reference: BarnumH.WilceA.Information processing in convex operational theoriesElectron. Notes Theor. Comput. Sci.2011270131510.1016/j.entcs.2011.01.0021348.81130arXiv:0908.2352 – reference: LindenstraussJ.TzafririL.Classical Banach Spaces I and II1977BerlinSpringer10.1007/978-3-642-66557-80362.46013 – reference: RödlP. FranklV.Wilson R.M.The number of submatrices of a given type in a Hadamard matrix and related resultsJ. Combin. Theory Ser. B198844331732894144010.1016/0095-8956(88)90040-80658.05015 – ident: 3154_CR49 – volume: 265 start-page: 95 issue: 1 year: 2006 ident: 3154_CR59 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-006-1535-6 – volume: 64 start-page: 062307 year: 2001 ident: 3154_CR40 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.64.062307 – volume: 28 start-page: 18 year: 1940 ident: 3154_CR23 publication-title: Dokl. Akad. Nauk SSSR (NS) – volume-title: Convex Optimization year: 2004 ident: 3154_CR24 doi: 10.1017/CBO9780511804441 – volume-title: Probabilistic Methods in Combinatorics year: 1974 ident: 3154_CR51 – volume: 70 start-page: 1895 year: 1993 ident: 3154_CR38 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.70.1895 – volume-title: Tensor Norms and Operator Ideals year: 1993 ident: 3154_CR46 – volume: 151 start-page: 181 issue: 1 year: 1983 ident: 3154_CR48 publication-title: Acta Math. doi: 10.1007/BF02393206 – volume: 328 start-page: 303 issue: 1 year: 2014 ident: 3154_CR31 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-014-1953-9 – volume: 13 start-page: 063024 year: 2011 ident: 3154_CR16 publication-title: New J. Phys. doi: 10.1088/1367-2630/13/6/063024 – volume: 288 start-page: 62 issue: 2 year: 2001 ident: 3154_CR33 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(01)00484-4 – volume: 31 start-page: 1915 year: 1992 ident: 3154_CR12 publication-title: Int. J. Theor. Phys. doi: 10.1007/BF00671964 – volume: 99 start-page: 240501 year: 2007 ident: 3154_CR17 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.99.240501 – volume: 31 start-page: 469 issue: 2 year: 1969 ident: 3154_CR27 publication-title: Pac. J. Math. doi: 10.2140/pjm.1969.31.469 – volume-title: Quantum Detection and Estimation Theory year: 1976 ident: 3154_CR30 – ident: 3154_CR42 – volume: 24 start-page: 260 issue: 4 year: 1972 ident: 3154_CR9 publication-title: Commun. Math. Phys. doi: 10.1007/BF01878476 – volume-title: Mathematical Foundations of Quantum Mechanics year: 1963 ident: 3154_CR5 – volume: 270 start-page: 3 issue: 1 year: 2011 ident: 3154_CR22 publication-title: Electron. Notes Theor. Comput. Sci. doi: 10.1016/j.entcs.2011.01.002 – volume: 58 start-page: 197 issue: 2 year: 1976 ident: 3154_CR56 publication-title: Stud. Math. doi: 10.4064/sm-58-2-197-208 – volume: 20 start-page: 26 issue: 1 year: 1971 ident: 3154_CR8 publication-title: Commun. Math. Phys. doi: 10.1007/BF01646732 – volume: 4 start-page: 1851 year: 2013 ident: 3154_CR19 publication-title: Nat. Commun. doi: 10.1038/ncomms2821 – volume: 95 start-page: 180 issue: 1 year: 2001 ident: 3154_CR55 publication-title: J. Combin. Theory Ser. A doi: 10.1006/jcta.2000.3155 – volume: 109 start-page: 101 issue: 1 year: 1994 ident: 3154_CR58 publication-title: Stud. Math. – ident: 3154_CR10 doi: 10.1007/978-3-642-71897-7_1 – volume: 44 start-page: 317 issue: 3 year: 1988 ident: 3154_CR52 publication-title: J. Combin. Theory Ser. B doi: 10.1016/0095-8956(88)90040-8 – volume: 333 start-page: 761 issue: 2 year: 2015 ident: 3154_CR35 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-014-2213-8 – volume: 26 start-page: 199 year: 1987 ident: 3154_CR11 publication-title: Int. J. Theor. Phys. doi: 10.1007/BF00668911 – volume: 43 start-page: 1411 issue: 12 year: 2013 ident: 3154_CR18 publication-title: Found. Phys. doi: 10.1007/s10701-013-9752-2 – volume-title: Functional Analysis year: 1991 ident: 3154_CR25 – volume: 39 start-page: 730 issue: 1 year: 1964 ident: 3154_CR7 publication-title: J. Lond. Math. Soc. doi: 10.1112/jlms/s1-39.1.730 – volume-title: Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory year: 2017 ident: 3154_CR26 doi: 10.1090/surv/223 – volume: 85 start-page: 4972 year: 2000 ident: 3154_CR32 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.85.4972 – volume-title: Introduction to Tensor Products of Banach Spaces year: 2002 ident: 3154_CR47 doi: 10.1007/978-1-4471-3903-4 – volume-title: The Probabilistic Method year: 2015 ident: 3154_CR54 – volume: 71 start-page: 25 year: 2012 ident: 3154_CR15 publication-title: Proc. Symp. Appl. Math. doi: 10.1090/psapm/071/600 – volume: 17 start-page: 103027 year: 2015 ident: 3154_CR20 publication-title: New J. Phys. doi: 10.1088/1367-2630/17/10/103027 – volume: 24 start-page: 379 issue: 3 year: 1994 ident: 3154_CR14 publication-title: Found. Phys. doi: 10.1007/BF02058098 – volume-title: Classical Banach Spaces I and II year: 1977 ident: 3154_CR50 doi: 10.1007/978-3-642-66557-8 – volume: 86 start-page: 5807 year: 2001 ident: 3154_CR2 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.86.5807 – volume: 141 start-page: 270 year: 1960 ident: 3154_CR45 publication-title: Dokl. Acad. Nauk. SSSR – volume: 59 start-page: 4206 year: 1999 ident: 3154_CR37 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.59.4206 – volume: 135 start-page: 192 year: 1958 ident: 3154_CR44 publication-title: Math. Ann. doi: 10.1007/BF01351796 – volume: 59 start-page: 141 year: 1999 ident: 3154_CR36 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.59.141 – volume: 79 start-page: 062306 year: 2009 ident: 3154_CR29 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.79.062306 – volume: 48 start-page: 580 issue: 3 year: 2002 ident: 3154_CR3 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/18.985948 – volume: 285 start-page: 161 issue: 1 year: 2008 ident: 3154_CR34 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-008-0582-6 – ident: 3154_CR1 – volume: 110 start-page: 16373 year: 2013 ident: 3154_CR43 publication-title: Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.1304884110 – ident: 3154_CR21 – ident: 3154_CR28 doi: 10.1007/978-3-0348-8871-4_14 – volume: 486 start-page: 409 year: 2015 ident: 3154_CR53 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2015.08.024 – volume: 17 start-page: 239 issue: 3 year: 1970 ident: 3154_CR6 publication-title: Commun. Math. Phys. doi: 10.1007/BF01647093 – volume: 40 start-page: 4277 issue: 8 year: 1989 ident: 3154_CR39 publication-title: Phys. Rev. A. doi: 10.1103/PhysRevA.40.4277 – volume: 75 start-page: 032304 year: 2007 ident: 3154_CR13 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.75.032304 – ident: 3154_CR41 – volume: 70 start-page: 231 issue: 3 year: 1981 ident: 3154_CR57 publication-title: Stud. Math. doi: 10.4064/sm-70-3-231-283 – volume: 291 start-page: 813 issue: 3 year: 2009 ident: 3154_CR4 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-009-0890-5 |
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