Types of Quantum States| 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];
Pandya et al PRA(20)-a1811 [bound on distance between a state and the closest separable state];
Hobson a1903 [interpretation of product states].
@ Schrödinger cat states: Jeong & Ralph qp/05-ch [application].
@ Gravitational cat states: Anastopoulos & Hu CQG(15)-a1504;
Derakhshani et al JPCS(16)-a1603 [gravitational, probes];
Derakhshani a1609 [and collapse];
Anastopoulos & Hu a2007 [quantum superpositions].
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 EJP(11)-a1101 [Wronskian method];
König et al AP(12) [in a finite-size box];
Kastner ch(17)-a1601
[emergent nature, and ontologically relevant degrees of freedom of composite systems];
Xiao et al a2004 [in the continuum];
> 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(14)-a1404 [strongly passive states];
Howard PRA(15)-a1501 [magic states];
Fröwis et al RMP(18)-a1706 [macroscopic states];
Walschaers a2104 [non-Gaussian, tutorial].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 27 apr 2021