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.

@ __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 strucure]; Gillis FP(11) [measurement and elementary interactions]; Ried et al nPhys(15)-a1406 [causal inference for quantum variables]; 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 a1611 [vs no-signaling constraints].

@ __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; > s.a. quantum correlations.

@ __ Specific types of systems__: Srikanth PLA(01)
[entangled systems]; Kent PRD(99)gq/97 [time-neutral
cosmologies]; > s.a. causality in quantum field theory.

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

@ __ 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].

> __Related topics__: see bell's
theorem; Causal Models; Contextuality; 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.

* __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 a1605, PRS(17)-a1709 [entropy-based approach]; Kissinger et al a1708 [and process terminality].

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

@ __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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