Types of Quantum States  

In General > s.a. quantum states / complexity [complexity measures]; entanglement; mixed states; pilot-wave theory; schrödinger equation.
$ Pure states: A state s is pure if there are no two distinct states s1 and s2 and positive c1 and c2 such that s = c1s1 + c2s2.
$ Separable states: A pure state ψ of a quantum system is separable if there is a choice of n subsystems such that ψ can be expressed as a tensor product

|ψ\(\rangle\) = |ψ1\(\rangle\)(1) ⊗ |ψ2\(\rangle\)(2) ⊗ ... ⊗ |ψn\(\rangle\)(n) ;

A mixed state ρ of a system is separable if there is a choice of n subsystems auch that ρ is a convex combination of product states (not entangled),

ρ = ∑k ωk ρ(1)k ⊗ ρ(2)k ... ⊗ ρ(n)k ,       where       ∑k ωk = 1 .

* Schrödinger cat states: Superpositions of well-separated coherent states.
* Passive states: States from which no system energy can be extracted by any cyclic (unitary) process; For example, Gibbs states of all temperatures.
@ Separable states: Peres PRL(96)qp [necessary condition]; Sanpera et al qp/97 [characterization]; Życzkowski et al PRA(98) [volume]; Majewski OSID(99)qp/97 [rigorous description]; Lockhart et al QIC(02)qp/00 [product states]; Shi & Du qp/01 [boundary]; Wu & Anandan PLA(02), Rudolph PLA(04) [criteria]; Albeverio et al PRA(03)qp [reduction criterion]; Wu PLA(04) [as convex sum]; Timpson & Brown IJQI(05)qp/04 [proper vs improper]; Raggio JPA(06)qp/05 [spectral conditions]; Khasin et al PRA(07)qp [negativity as measure of non-separability]; Li & Luo PRA(08) [intrinsic characterization]; Jakubczyk & Pietrzkowski RPMP(09) [integral representations]; Harrow & Montanaro FOCS(10)-a1001 [test for product states]; Chen et al a1204 [product states].
@ Schrödinger cat states: Jeong & Ralph qp/05-ch [application].
@ Gravitational cat states: Anastopoulos & Hu CQG(15)-a1504; Derakhshani et al JPCS-a1603 [gravitational, probes]; Derakhshani a1609 [and collapse].

Unstable States > s.a. quantum systems [unstable]; resonance; state evolution [decay].
* Idea: Unstable/decaying states can be associated with resonances (Gamow vectors), and described by a Rigged Hilbert space.
@ General references: Ordóñez et al PRA(01) [dressed]; Chruściński mp/02 [Wigner functions for damped systems]; Castagnino et al PLA(01)qp/02; Kielanowski qp/03-conf; Civitarese & Gadella PhyA(14) [complex-energy states, entropy].
@ Metastable states: Davies JFA(82) [dynamical stability].

Other Types > s.a. composite systems [N-particle states]; entanglement examples [cluster states]; semiclassical states [including Gaussian].
@ Energy eigenstates: Halliwell & Thorwart PRD(02)gq [and dynamics]; Moriconi AJP(07)mar-qp [number of nodes].
@ Ground state: Mouchet JPA(05)qp/04 [energy estimation method]; > s.a. schrödinger equation [bounds].
@ Bound states: Chadan et al JMP(96) [bound on number]; Chadan & Kobayashi JMP(97) [sufficient condition]; Aktosun et al JMP(98) [number, 1D]; Chadan et al JMP(99) [number]; Brau & Calogero JPA(03)mp/04, Brau JPA(03)mp/04, JPA(04)mp [central V, conditions and bounds]; Chadan et al JMP(03) [number, 1D and 2D]; Ritchie PLA(06) [relativistic]; Fernández a1101 [Wronskian method]; König et al AP(12) [in a finite-size box]; Kastner a1601 [emergent nature, and ontologically relevant degrees of freedom of composite systems]; > s.a. atomic physics; quantum oscillators; quantum systems.
@ Bipartite states: Yu et al RPMP(07)-a0711 [differential geometry]; > s.a. entangled states.
@ In atoms: Białynicka-Birula & Białynicki-Birula PRA(97) + pn(97)nov [Trojan states]; Calsamiglia et al PRL(01)cm [macroscopic superpositions].
@ Discrete: news PhysOrg(16)mar [hypergraph states and local realism violation].
@ Related topics: Mould FPL(01)qp, qp/01, Ferrero et al FP(04) [physical vs subjective]; in Sanz JPA(05)qp/04 [nowhere differentiable]; de Oliveira et al PhyA(05), Malbouisson et al PhyA(07) [displaced number states]; Luís PRA(07) [exponential, using Rényi entropy as uncertainty measure]; Frey et el PRE-a1404 [strongly passive states]; Howard a1501 [magic states]; Fröwis et al a1706 [macroscopic states].


main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 7 aug 2017