Quantum Information Theory  

In General > s.a. information; entanglement; quantum correlations; quantum mechanics; Resource Theory.
* Idea: Quantum information theory includes that of quantum measurement; In fact, according to a developing viewpoint, quantum mechanics really is a theory of information; The quantum information in a state includes quantum correlations (entanglement and quantum discord); > s.a. formulations of quantum mechanics.
* History: 2013, The field is now established, no longer emerging.
* Quantum no-hiding theorem: If information is missing from one system (which may happen when the system interacts with the environment), then the information is simply residing somewhere else in the Universe; In other words, the missing information cannot be hidden in the correlations between a system and its environment.
* No-information-without-disturbance theorem: Those observables that do not disturb the measurement of another observable must be trivial.
* No-free-information theorem: Those observables that can be measured jointly with any other observable must be trivial; > s.a. probability in physics.
@ Intros, I: Zeilinger pw(98)mar; news sn(12)apr; Economou et al a2005 [exercises].
@ Intros and reviews: Svozil qp/95-ln [algorithmic]; Nielsen & Chuang 00; Nielsen PhD(98)qp/00, qp/00; Schumann MSc(00)qp; Vedral RMP(02)qp/01; Werner qp/01-ch; Simon PhD(00)qp/01; Gill JKSS(01)m.ST/04, Keyl PRP(02)qp; Galvão PhD(02)qp [and applications]; Jozsa qp/03/IBM [examples]; Lo qp/03 [personal view]; Braunstein & van Loock RMP(05) [continuous variables]; Bub qp/05-ch; Le Bellac 06; Timpson qp/06-ch [philosophical]; Scarani a0910-ln [and correlations]; Caves a1302-in [history]; Girvin a1302-ch; Miszczak a1303-talk [and 0-th quantization]; Navarrete-Benlloch a1504; Grazioso a1507 [applications, black holes and renormalization group]; Strauch AJP(16)jul [RL]; Griffiths Ent(17)-a1710; Landsberg a1801 [for mathematicians]; Sharma a1809 [history, 1970-2018]; Kibler a1811 [and quantum computing]; Lykken a2010-ln [for particle theorists]; Deutsch PRXQ(20) [overview]; Horodecki APPA(21)-a2103.
@ Open problems: Krüger & Werner qp/05; Ruskai a0708-conf.
@ Books: Steeb & Hardy 06 [problems and solutions]; Vedral 07; Bruß & Leuchs ed-07 [lectures]; Diósi 07; Jaeger 07 [r PT(08)mar]; Barnett 09 [r PT(10)jul]; Bokulich & Jaeger ed-10 [philosophy]; Vedral 10; Wilde 13-a1106 [quantum Shannon theory]; Hayashi et al 15; Preskill a1604-ln; Hayashi 17 [group-theoretical approach]; Wilde 17; Watrous 18.
@ General references: Zeh FP(73)qp/03; Schumacher PRA(91); Lyre IJTP(96)qp/97, qp/97-conf; Adami & Cerf qp/98-proc; Green IJTP(98); Winter qp/98; Griffiths PRA(02)qp, Duvenhage FP(02)qp [nature]; Brukner & Zeilinger in(03)qp/02; Khrennikov SPIE(03)qp; Duwell SHPMP(03) [no new concept needed]; Svozil IS(09)-a0711-conf [nature]; Griffiths PRA(07) [types]; Kato PhD(07)-a0803 [geometrical]; Kak a0907-conf [transactional nature]; Dupuis PhD(09)-a1004 [decoupling approach]; Ozawa Sugaku(14)-a1201 [mathematical foundations]; Kent CQG(12)-a1204 [quantum tasks in relativistic quantum mechanics]; Fujii a1306-proc [and statistical mechanics]; Ilgin & Yang IJMPA(14)-a1402 [and energy]; Demarie PhD-a1407 [geometrical and topological aspects]; Modi et al PRL(18)-a1608; Griffiths Ent(17)-a1710.
@ Quantum information measures: Brukner & Zeilinger FP(09)-a0905; Dupuis & Wilde a1506 [swiveled Rényi entropies].
@ Gaussian state quantum information: Ralph et al RMP(12)-a1110; Wang et al PRP(07)-a0801; Adesso et al OSID(14)-a1401 [pedagogical].
@ Quantum version of Shannon theory: Devetak et al IEEE(08)qp/05; Duwell SHPMP(08).
@ Computation, information processing: Bennett PT(95)oct; Lim PhD-qp/05 [with single photons]; Spiller et al CP(05) [rev]; Alicki & Horodecki qp/06 [storage, no-go theorem]; Vedral FP(10) [speedup, interplay between correlations and distinguishability]; Dürr a1303 [physical implementations]; Kastoryano et al PRL(13) + Muschik Phy(13) [engineered dissipative processes]; Flammia et al Quant(17)-a1610 [storage limits]; Benenti et al 18; Carette et al a1902 [graphical languages]; Soljanin a2006 [primer].
@ And network theory: Kauffman & Lomonaco a1404 [diagrammatic methods]; Biamonte et al a1702 [rev]; > s.a. information in physical systems.
@ And quantum dynamics: Nielsen et al PRA(03)qp/02; Garbaczewski CEJP(08)cm/07; Blume-Kohout et al PRL(08)-a0705 [preserved information in quantum processes]; Cao et al a0805 [covariant Margolus-Levitin theorem]; Ciaglia et al OSID(18)-a1608; Lewis-Swan et al nrPhys(19)-a1908 [in quantum many-body systems]; > s.a. quantum state evolution [speed limit]; wigner functions [flux].
@ Quantum theory is not only about information: Hagar & Hemmo FP(06)qp/05; Daumer et al in(06)qp; Felline SHPMP-a1806.
@ And foundations: Svozil qp/00 [information interpretation]; Fuchs qp/01-proc; Ferrero FP(03); Fredkin IJTP(03) [digital philosophy]; Grinbaum IJQI(03)qp [derivation of quantum mechanics]; Hagar PhSc(03)oct; Calude & Stay IJTP(05)qp/04 [algorithmic randomness]; Bub FP(05)qp/04; Shafiee et al FPL(06)qp/04 [re Brukner-Zeilinger]; Timpson PhD(04)qp; Auletta FP(05); Brown & Timpson qp/06-ch [against info-based postulates]; Goyal NJP(10)-a0805 [origin of quantum formalism]; Demopoulos a0809-conf [and quantum logic]; Niestegge a1003; D'Ariano a1012-conf [physics as information processing]; Roederer a1108; Chiribella & Scandolo EPJC(15)-a1411; > s.a. formulations of quantum theory [algebraic]; information ["it from bit"]; origin of quantum mechanics.

Special Topics > s.a. axioms for quantum theory; information in physical theories [including transfer, transmission]; quantum causality [information causality].
* Channel capacity: The capacity of the bosonic channel with thermal noise and linear loss hinges on the bosonic minimum output entropy conjecture, which states that the vacuum input gives the minimum output entropy for a channel with thermal noise, and was proved in 2009; It implies that the bosonic channel attains its capacity for coherent state inputs.
@ And measurement: Rothstein Sci(51)aug; Prugovecki IJTP(77); Cerf & Adami qp/96/PRA; Kak FP(98); Ban IJTP(98), JPA(99), JPA(99), JPA(99) [and entropy]; Childs et al JMO(00); Massar & Popescu PRA(00)qp/99; Deutsch & Hayden PRS(00) [information localization and flow]; Barnum et al PRS(01); Zurek qp/01-ln; Jacobs qp/03, PRA(03)qp; Mayburov qp/04-proc, IJTP-qp/04-conf; Rocchi & Panella AIP(07)-a0710; Paris IJQI(09)-a0804 [parameter estimation and optimization]; Wilde et al JPA(12) [and Winter's measurement compression theorem]; Rastegin PRS(15)-a1506 [Brukner-Zeilinger approach]; Haapasalo et al JMP(18)-a1710 [information flow to the environment].
@ And wave-function collapse: Janssens MSc(04)qp/05; Janssens & Maassen JPA(06)qp; Bondar qp/07 [and many-worlds].
@ And non-locality: Srikanth qp/01, qp/01; Horodecki et al PRA(05)qp/04 [local vs non-local]; Fanchini et al NJP(12)-a1106 [locally inaccessible information].
@ And classical information: Oppenheim et al PRA(03)qp/02; Herrera-Martí MSc(08)-a0810 [classical capacity of quantum channels]; Ostrowski a1011; Landulfo & Torres PRA(13)-a1304 [classical information through relativistic quantum channels]; Heunen et al EPTCS(14)-a1405 [and higher categories].
@ Classical limit: Oppenheim et al PRL(03)qp/02 [phase transition]; Granik qp/05 [transition as information localization]; Blume-Kohout & Zurek PRA(06)qp/05 [information redundancy]; Chiribella & D'Ariano PRL(06) [many users]; Flam et al JHEP(20)-a1906.
@ Mutual information: Hall PRA(97) [correlation bounds]; Casini CQG(07)gq/06 [and entropy bounds]; Bernigau et al JSM(15)-a1301 [thermal free lattice fermions]; Pastorello a1810 [geometric].
@ Compression: Horodecki PRA(98)qp/97; Mitchison & Jozsa PRA(04)qp/03 [geometrical].
@ Fisher information: Hradil & Rehacek qp/03 [and interferometry]; Flego et al a1105 [and the Schrödinger equation]; Liu et al CTP(14)-a1312 [new expression]; Yao et al PRA(14)-a1401 [in non-inertial frames]; Cafaro & Alsing PRE(18)-a1804 [and state evolution]; > s.a. formulations of quantum mechanics.
@ Invariant, relativistic: Brukner & Zeilinger PRL(99)qp/00, PRA(01)qp/00 [Shannon information not appropriate], comment Timpson SHPMP(03), PhSc(03)dec; Rehacek & Hradil PRL(02)qp/01; Peres & Terno RMP(04)qp/02 [and general relativity], IJQI(03)qp [and special relativity]; Bartlett & Terno PRA(05)qp/04; Terno in(06)qp/05; Czachor QIP(10)-a1002 [manifestly covariant]; Bradler a1108 [comment on misconceptions]; Adami in(11)-a1112; issue CQG(12)#22; Palmer PhD-a1312; Metwally et al CTP(14)-a1402 [Lorentz transformations and entanglement loss].
@ Quantum states: Caves & Fuchs qp/96-in; Preskill JMO(00)qp/99; Rudolph qp/99; Vitanyi qp/99-proc; Peacock qp/02 [superposition]; Clifton et al FP(03)qp/02 [and quantum mechanics] + Halvorson SHPMP(04)qp/03; Barnum qp/03; Barndorff-Nielsen et al qp/03, JRSS(03)qp [inference]; Horodecki et al Nat(05)qp [partial and negative info]; Hewitt-Horsman & Vedral NJP(07)qp/06 [Deutsch-Hayden approach to quantum mechanics].
@ Other topics: Pati PRA(02) [impossible operations]; Valentini Pra(02)qp-proc [subquantum information]; Peres qp/03/FP [and EPR]; Benatti et al CMP(06)qp/05 [entropy and complexity]; Cabello FP(06) [communication complexity]; Buscemi NJP(09)-a0901 [information shredding]; Vlasov a0903 [and nanotechnology]; Lloyd et al a0906 [bosonic minimum output entropy conjecture proof]; Goldstein FP(10)-a0907 [and Bohmian mechanics]; Plekhanov a0909, 12 [isotope-based]; Kofler & Zeilinger ER(10)-a1301 [and randomness]; Samal et al PRL(11) + news physorg(11)mar [no-hiding theorem confirmed experimentally]; Berta PhD-a1310 [quantum side information]; Gupta et al a1410-ln [functional analysis]; Modi et al PRL(18) + news PhysOrg(18)jun [no-masking theorem]; Trindade et al IJGMP(20)-a2003 [formulation based on algebraic spinors]; > s.a. clifford algebra.
> Other topics: see categories in physics; complexity; entropy [including Shannon and Rényi]; Erasure; Lieb-Robinson Bounds; uncertainty relations.

Online Resources > see Quantiki.

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