Causality in Quantum Theory |

**In General**
> s.a. causality [as emergent]; quantum effects,
locality and measurement; indefinite
causality and causality violations.

* __Idea__: In the operator version
it is built in via the unitarity of time evolution; Quantum non-locality is causal
because it cannot be used to transfer classical information across spacelike intervals,
and measurements of entangled systems cannot be used for superluminal signalling (not
true in non-linear quantum mechanics); But see barrier transmission.

* __Rem__: Causal reversibility is related
to the fact that observables form a real C*-algebra; Locality and separability then
impose restrictions; Causally non-separable processes cannot be embedded in a
well-defined global causal structure.

@ __General references__: Kraus FPL(89) [no action at a distance];
Stapp AJP(97)apr;
Westmoreland & Schumacher qp/98;
Mashkevich qp/98,
qp/98;
Cereceda FPL(00)qp [constraints and EPR];
Segev PRA(01) [phase-space formulation];
Simon et al PRL(01)qp [axioms];
Grove FP(02) [changing the past];
Belavkin RPP(02)qp [trajectories and information];
Palmer qp/05 [causal incompleteness and non-locality];
Pegg PLA(06) [arrow of time];
Evans et al BJPS(12)-a1001 [and spacelike action at a distance];
Hofmann a1005-proc [weak measurements, statistics and causality];
Zaopo a1110 [relativity of causal structure];
Gillis FP(11) [measurement and elementary interactions];
Oreshkov & Giarmatzi NJP(16)-a1506 [causality and causal separability, multipartite causal processes];
Diel a1604 [possibility of local causal models];
Eckstein & Miller PRA(17)-a1610 [evolution of wave packets];
Horodecki & Ramanathan nComm-a1611 [vs no-signaling constraints];
Weilenmann & Colbeck a1812 [in generalized probabilistic theories];
Eckstein et al a1902.

@ __Role of causality in quantum theory__:
Popescu & Rohrlich qp/97-proc [as axiom];
Wharton qp/03/PRA;
Delphenich qp/04-conf;
David PRL(11)-a1103 [role of causality and locality];
Kakushadze UJP-a1505 [rules based on causality];
Winter a1705;
D'Ariano PTRS-a1804 [conceptual];
> s.a. quantum correlations.

@ __Causal inference__: Ried et al nPhys(15)-a1406 [for quantum variables];
Fraser a1902 [possible worlds framework].

@ __Quantitative measures of causality__: Jia a1801 [for general probabilistic theories].

@ __Specific types of systems__: Srikanth PLA(01) [entangled systems];
Kent PRD(99)gq/97 [time-neutral cosmologies];
Cotler et al a1811 [many-body systems, emergence of causal structure];
> s.a. causality in quantum field theory.

@ __ Related topics__: Teufel et al PRA(97) [hidden variables];
Kent PRA(05)qp/02,
Pienaar PhD-a1401 [and non-linear quantum mechanics];
Fitzsimons et al a1302
[pseudo-density matrix for spatial and temporal measurements];
Han & Choi a1307 [and probabilities];
Cavalcanti JPCS(16)-a1602 [proposals for a quantum theory of causation];
Allen et al PRX(17)-a1609
+ Pienaar Phy(17)
[quantum common causes, quantum version of Reichenbach's principle];
Thompson et al PRX(18)-a1712 [causal asymmetry in predictive modelling];
Kent PRS(18)-a1807 [causal quantum theory, implications];
Wechs et al NJP(19)-a1807 [causal non-separability];
Chaves et al nPhys(18)-a1808 [violation of an instrumental test];
Wakakuwa et al PRL(19)-a1810 [complexity of causal order structures].

> __Related topics__: see bell's
theorem; Causal Models; Contextuality;
experiments in quantum theory [delayed-choice]; Lieb-Robinson
Bounds; quantum collapse;
Retrocausation.

**Types of Causality**
> s.a. locality; path integrals.

* __Abstract causal structures__:
A causal structure is a relationship between observed variables that restricts
the set of possible correlations between them; Their study has become important
for the development of quantum technologies, in particular quantum computing.

* __Relativistic__: Versions
include Stochastic Einstein Locality, Reichenbach's Principle of Common Cause,
and Bell's Local Causality.

* __Information causality__:
A principle that places restrictions on physical processes, used in proposals
for deriving quantum theory from information-theoretic considerations.

@ __Abstract causal structures__:
Weilenmann & Colbeck Quant(18)-a1605,
PRS(17)-a1709 [entropy-based approach];
Kissinger et al a1708 [and process terminality];
Milburn & Shrapnel Ent(18)-a1809 [causal interventions, physical basis].

@ __Information-theoretic constraints on correlations__: Chaves et al nComm(15)-a1407;
Weilenmann a1807-PhD.

@ __Bell's local causality__: Norsen AJP(11)-a0707;
Seevink & Uffink in(11)-a1007 [sharp and clean mathematical formulation];
Ringbauer et al a1602 [test].

@ __Information causality__: Pawłowski et al Nat(09)oct-a0905;
Barnum et al NJP(10)-a0909 [in general probabilistic theories];
Ahanj et al PRA(10) [and Hardy's non-locality];
Cavalcanti et al nComm(10)-a1008 [and local quantum correlations];
Gazi et al JPA(10) [and Hardy's correlations];
Al-Safi & Short PRA(11) [entropic and probabilistic perspective];
Beigi & Gohari a1111;
Pawłowski & Scarani a1112 [rev];
Hsu PRA(12) [multipartite];
Yu & Lin a1301 [testing];
Pitalúa-García PRL(13);
Zoka & Ahanj a1510 [and quantum correlations];
> s.a. quantum correlations.

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