Uncertainty Relations in Quantum Theory| Uncertainty Relations in Quantum Theory |
In General > s.a. equivalence principle;
fluctuations [including classical uncertainty relations];
locality in quantum theory; physics teaching.
* Idea: Some observables can have no
uncertainty, but not all of them, and any change in the expectation value of an
observable quantity must be associated with some degree of uncertainty.
* Heisenberg's version: A lower bound for
the product of the measurement error and the disturbance, stating that in observing the
world we inevitably disturb it by introducing an unavoidable recoil; In the Heisenberg
form the principle is valid only under certain circumstances, but a new universal
error-disturbance relation has been proposed.
* Later version: The uncertainty relation
was later reformulated in terms of standard deviations, where the focus was exclusively
on the indeterminacy of predictions.
* Beating the quantum uncertainties: Some
proposals have been made of types of measurements that have an effect smaller than the
standard uncertainty, for example weak measurements.
@ General references:
DeWitt JMP(62) [and commutation relations];
Hilgevoord & Uffink FP(91) [in prediction and inference];
Franson PRA(96) [and changes of expectation values];
Hilgevoord AJP(02)oct [and standard deviation];
Busch et al PRP(07)qp/06 [rev, conceptual];
Marburger AJP(08)jun [re early derivation];
Dumitru PiP(10)-a1005;
Fujikawa & Umetsu PTP(11)-a1012 [and probability];
Partovi PRA(11) [and majorization theory];
Matía-Hernando & Luis PRA(12) [different measures of quantum uncertainty];
Dumitru a1205;
Li et al JPA(14)-a1302 [as inequality for bipartite correlation functions, and experiment];
de Gosson JPA(13)-a1303 [in the Born-Jordan quantization scheme];
news pw(13)may [tradeoff between measurement uncertainties];
Dumitru a1501;
Narasimhachar et al NJP(16)-a1505 [general framework];
Ozawa a1507-conf;
Busch & Reardon-Smith a1901 [uncertainty region];
Werner & Farrelly FP(19)-a1904 [overview, meanings];
Wigderson & Wigderson a2006 [variations];
Urbanowski Symm(20)-a2010;
Cazacu et al a2012 [mathematical];
Duan a2103 [interpretation].
@ For mixed states: Andersson & Heydari JMP(14)-a1302,
PS(15)-a1412;
Belfield & Brody a2012 [higher-order uncertainty bounds].
@ Approaches:
Ivan et al a1205 [invariant theoretic approach];
Renes et al Quant(17)-a1612 [operational approach];
Mann et al a2005 [successive measurements].
@ Universal form / general theory:
Deutsch PRL(83) [non-canonically-conjugate variables];
Friedland et al PRL(13)-a1304;
Kechrimparis & Weigert JPA(16)-a1509;
Bagchi & Pati PRA(16)-a1511 [arbitrary unitary operators];
Li et al SRep(16)-a1610;
Huang & Huang a1807 [in different quantum theories].
@ Quantum vs classical uncertainties:
Cini & Serva PLA(92);
Luo TMP(05);
Beretta PhD(81)qp/05 [quantum thermodynamics];
Busch PS(10)-a1004-conf;
Huang & Huang PLA(10) [classical statistical and quantum uncertainty relations];
Usha Devi & Karthik AJP(12)aug-a1108 [in the classical limit];
Berta PhD(13)-a1310 [quantum side information];
Gattus & Karamitsos EJP(20)-a2102 [dimensional analysis];
> s.a. diffusion; fluctuations.
@ From lack of information: Rozpędek et al NJP(17)-a1606;
Zhao et al a2105 [tests].
@ Origin of uncertainties: Anderson & Halliwell PRD(93)gq [quantum + thermal fluctuations];
Wesson GRG(04)gq/03 [from higher dimensions];
Arbatsky qp/06 [derivation from "certainty principle"];
Downes et al a1108 [uncertainty relation for the spacetime metric];
Fujikawa PRA(12)-a1205
[incorporating both intrinsic quantum fluctuations and measurement effects];
Girolami et al PRL(13)-a1212 [intrinsic quantum uncertainty on a single observable];
Thuan a1507 [spacetime curvature];
Adami a2005-FQXi
[from the indeterminism inherent in mathematical logic].
@ Beating the quantum uncertainties: Polzik & Hammerer AdP(15)-a1405 [trajectories without quantum uncertainties];
> s.a. types of measurements.
@ Uncertainty conservation relations:
Wang et al a1711 [theory and experiment].
> Related topics: see histories formulations;
mixed states; optics; Reference
Frame; semiclassical states [minimal-uncertainty].
Configuration-Momentum Uncertainty Relations
> s.a. modified and deformed relations
[including entropic]; phenomenology [systems, tests, violations].
* Idea: In any preparation of a
system, uncertainties are constrained to satisfy Δq Δp
≥ \(\hbar\)/2; In the usual approach to quantum theory, the bound can be traced
back to the [q, p] commutation relations.
* In terms of creation-annihilation:
The uncertainty relation is expressed by \(\langle a^\dagger a\rangle \ge \langle
a^\dagger \rangle \langle a\rangle\).
@ General references: Heisenberg ZP(27);
Schrödinger SPAW(30),
translation BulgJP-qp/99;
Gamow SA(58)jan;
Lévy-Leblond AJP(72)jun [non-simultaneous measurements];
Fefferman BAMS(83);
Landsberg FP(88) [and classical and quantum mechanics];
Chisolm AJP(01)mar-qp/00 [restrictions];
D'Ariano FdP(03)qp/02;
Rigolin EJP(15)-phy/05 [derivation];
Schürmann & Hoffmann FP(09)-a0811;
Mandilara & Cerf PRA(12)-a1201;
Hedenmalm JAM(12)-a1203 [in the sense of Beurling];
Rudnicki PRA(12) [sharper bounds
for σrσp];
Busch et al PRA(14)-a1311 [for qubit measurements],
JMP(14)-a1312 [measurement uncertainty relations];
Boughn & Reginatto EJP(18)-a1712 [revisiting Heisenberg's microscope];
> s.a. localization.
@ For angular momentum:
Franke-Arnold et al NJP(04);
Dürr pw(04)oct;
Dammeier et al NJP(15)-a1505;
Lake et al Univ-a1912 [in quantum geometry].
@ And phase space geometry: Curtright & Zachos MPLA(01)ht;
Anastopoulos & Savvidou AP(03)qp;
de Gosson PLA(03) [phase-space quantization],
qp/04 ["quantum blobs"],
mp/06 [and symplectic non-squeezing];
de Gosson & Luef PRP(09) [symplectic capacity];
de Gosson FP(12)-a1106;
Werner a1601-proc [for general phase spaces];
> s.a. phase space.
@ And complementarity:
Uffink & Hilgevoord PhyB(88)qp/99;
Björk et al PRA(99)qp;
Basso & Maziero a2007.
@ In terms of information:
Gibilisco & Isola mp/05,
JMP(07)mp,
Chakrabarty APS(04)qp/05,
Sánchez-Moreno et al JPA(11) [and Fisher information].
@ Error-disturbance relation: Brown & Redhead FP(81); Hofmann PRA(03)qp/02;
Wulleman PE(03)qp/06,
CoP(06)#3;
Rozema et al PRL(12)
+ news UT(12)sep [violation in weak measurements of photons];
Busch et al PRL(13),
a1402
[proof of Heisenberg's relation, as characterizing measuring devices];
Ipsen a1311 [for finite-dimensional systems];
news pw(13)nov [uncertainty vs disturbance debate];
Ozawa a1403-proc [reformulation];
Bastos et al PRD(14)-a1406 [phase-space non-commutative formulation];
Dressel & Nori PRA(14) [definitions of error and disturbance];
Fujikawa et al PRA(15)-a1412 [and Hardy's paradox];
Ozawa a1505 [interpretation];
Nishizawa & Chen a1506 [universal form];
Zhao et al PRA(17)-a1512 [quantum-walk-based experimental test];
Inoue & Ozawa a2009 [violation by Stern-Gerlach measurements].
@ And entanglement: Rigolin FPL(02)qp/00,
qp/01;
Hari Dass et al IJMPB(13)-a1107 [for entangled states];
Berta et al PRA(14)-a1302 [relation between entanglement and uncertainty].
@ Related topics:
Landsberg Mind(47) [philosophy];
Yu PLA(96);
Hewitt-Horsman qp/03 [and many worlds];
Sarris et al PLA(04) [as invariant of motion];
Busch & Pearson JMP(07) [for error-bar widths];
Kryukov PLA(07)-a0710 [geometric];
Zozor et al PRA(11)-a1112 [uncertainty relations based on moments of arbitrary order];
Rudnicki et al PRA(12)-a1204 [for coarse-grained measurements];
Malbouisson PRA(13)-a1307 [in a cavity at finite temperature];
Tomassini & Viaggiu CQG(14)-a1308 [spacetime uncertainty relations];
Bosyk et al PRA(14) [geometric];
Majumdar & Pramanik a1410-proc [applications in quantum information];
Li & Qiao SRep-a1502 [new form];
Kechrimparis & Weigert JPA(18)-a1703 [linear combinations of position and momentum observables];
Pollack & Miret-Artés PRA(19)-a1808 [for time averaged weak values];
Huang et al ChPB(18)-a2003 [new product forms];
> s.a. Gerbe [reformulation].
Time-Energy Uncertainty Relation
> s.a. mixed states; time in quantum mechanics.
@ General references:
Aharonov & Bohm PR(61);
Kijowski RPMP(76);
Sorkin FP(79);
Busch FP(90),
FP(90);
Kobe & Aguilera-Navarro PRA(94);
Pfeifer & Fröhlich RMP(95);
Hilgevoord AJP(96)dec,
AJP(98)may;
Busch in(02)qp/01 [types, history];
Brunetti & Fredenhagen RVMP(02)qp [rigorous derivation];
Miyadera FP(16)-a1505,
comment Yasuda a1809 [in quantum measurements];
Kieu PRS(19)-a1702 [time-dependent Hamiltonians];
Urbanowski MPLA-a1810,
a1908-conf [not universally valid];
Bertoni et al NJP(20)-a2001 [entropic, algebraic approach];
Campaioli a2004-PhD
[improved bounds on the speed limit of quantum evolution];
Roberts & Butterfield JPCS(20)-a2007 [it does not allow particle creation].
@ Time-mass: Kudaka & Matsumoto JMP(99)qp [τ and m as operators];
Ram mp/02;
Dodonov & Dodonov PS-a1504 [exact inequalities].
@ Related topics: Pegg PRA(98) [operator conjugate to H];
Aharonov et al PRA(02)qp/01 [and estimating the Hamiltonian];
Gillies & Allison FPL(05) [time-temperature];
Karkuszewski qp/05 [upper bound on uncertainties];
Denur AJP(10)nov [and quantum phenomena].
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