States of Quantum Systems

In General > s.a. [quantum theory]; fractals; Quantum Carpet; schrödinger equation [solutions]; state of a system.
* Idea: A state can be defined either as a square-integrable, complex-valued function on a suitably defined quantum configuration space , or as a linear functional on an algebra of observables.
@ State recovery / estimation: Moroz & Perelomov TMP(94)mp/01 [from distribution functions]; Leonhardt et al PRA(95) [tomography]; Gill in(01)m.ST/04 [spin-1/2, asymptotics]; Rehácek & Hradil PRL(02) [invariant information]; D'Alessandro JPA(03)qp; Jones & Linden PRA(05)qp/04 [from parts of states]; Adamson et al qp/06 [tomography]; Liu & Sun LMP(06) [from complete set of quantum correlations].
@ Construction: Isidro MPLA(04)qp [from tangent vectors to phase space].
@ Alternative representations: Palmer qp/01 [R, and computability]; Dias & Prata [phase space, admissible states].
@ Meaning: Park AJP(68) [classical vs quantum states]; Mohrhoff qp/01; Marchildon qp/05-in; Spekkens PRA(07) [epistemic view]; Brunet a0804 [partial description]; > s.a. formalism, foundations, interpretations.

Evolution and Transformations > s.a. collapse; geometric phase; quantum effects [including speed of evolution, Margolus-Levitin theorem].
@ Canonical transformations: Anderson PLB(93), PLB(93)ht, AP(94); Schuch & Moshinsky a0807 [and Wigner functions].
@ Other transformations: Doebner & Goldin PRA(96), Czachor PRA(98) [gauge, non-linear]; Luís PRA(04) [in phase space and Hilbert space]; García-Mata et al PRA(05) [and phase space contraction]; Brody & Hook JPA(06) [adapted Hamiltonian]; Weimer et al a0708 [local effective dynamics, work and heat]; > s.a. fock space.
@ Measurement: Embacher & Narnhofer AP(04) [strategies]; > s.a. quantum measurement.
@ Manipulation: Caban et al JPA(02) [destruction]; Lloyd & Viola PRA(02) [engineering]; Herbert a0802 [states cannot be merged]; > s.a. quantum technology [teleportation, no-cloning, etc].
@ Evolution: Macomber AJP(77) [transitions]; Aharonov & Albert PRD(84) [relativistic]; Styer AJP(90), Weigert PRL(00)qp/99 [ito expectation values and uncertainties]; Mohrhoff FP(04)qp/03 [and Pondicherry interpretation]; D'Alessandro & Romano JMP(06)qp [and entanglement]; García Quijas & Arévalo Aguilar PS(07)qp/06 [factorization]; Vaidman qp/06/JPA [backward]; Schuch & Moshinsky PRA(06) [Ermakov invariant]; Mohseni & Lidar PRL(06)qp [direct characterization of quantum dynamics]; Kryukov a0704 [as geodesic motion on space of states]; Andrews a0801 [free wave packets]; > s.a. mixed states [thermalization].
@ From pure to mixed states: Horwitz et al qp/96-in [and Lax-Phillips theory]; Svec a0708 [in pion creation]; > s.a. arrow of time, decoherence, Semigroup.

Other Properties > s.a. classical vs quantum; fluctuations; fock space [number operator]; Phase; uncertainty.
* Inequalities: For any states and ', and any self-adjoint A and B, if cos = ||'|,

(A)_psi (B)_psi   | [A,B]_psi | ,      (A_psi' – A_psi) / (A)_psi' – (A)_psi) tan .

@ Invariants: Albeverio et al PLA(05)qp [mixed states, under unitary transformations]
@ Composition of amplitudes: Vigoureux PRA(94).
@ Related topics: Fleming phy/01 [inequalities]; Zurek Nat(01)qp/02 [sub-Planck structure]; Schirmer et al JPA(02), JPA(02) [controllability-reachability]; Poulin & Blume-Kohout PRA(03) [compatibility]; Arrighi & Patricot AP(04)qp/03 [and quantum operations]; Bartlett et al IJQI(06)qp/05 [coherence, dialogue]; > s.a. quantum effects [state diffusion].

Space of States > s.a. distance types; entanglement; mixed states; non-standard analysis; types of states.
* Metric: Many metrics have been proposed; As a criterion for the choice of an appropriate one, Chentsov has proposed the concept of statistical monotonicity, or contraction under coarse graining, and Petz has classified the metrics with this property.
@ General references: Brody & Hughston JMP(00)qp/99 [density function]; Grasselli mp/00-in [norm, connection]; Walck qp/02-in [decomposition]; Barnett et al PLA(03)qp/02 [comparisons]; Gibilisco & Isola JMP(03) [Wigner-Yanase information]; Brody JPA(04)qp/03 [and sets of points]; Marmo et al IJGMP(05)qp [structure, bi-Hamiltonian systems]; Vicary a0706 [categorical framework, applied to sho]; Shirokov a0804 [and entanglement monotones].
@ Geometry: Field & Hughston JMP(99) [and coherent states]; Zyczkowski & Slomczynski JPA(01)qp/00; Gibilisco & Isola JMP(05) [information geometry curvature]; Andai JPA(06) [volume]; Pandya qp/07 [metric]; > s.a. metric types, poisson structure, topology.
@ Subsets: Narnhofer mp/02-in, IJTP(03) [leaves, from entanglement or conditional entropy]; Shirokov qp/05 [Holevo capacity]; Bengtsson a0707 [maximally entangled].
@ State distinguishability: Barndorff-Nielsen & Gill JPA(00) [and Fisher information]; Jozsa & Schlienz PRA(00) [and vN entropy]; Greentree et al PRL(04) [finite number]; Herzog & Bergou PRA(04)qp, Majtey et al qp/05 [mixed states]; Ericsson JPA(05)qp.
> Related topics: see Born Rule [discrete state space].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 20 jul 2008