524 research outputs found
Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal
structure sheds new light on the old debate on whether space and time are to be
seen as fundamental. Refraining from assuming space-time as given a priori has
a number of consequences. First, the usual definitions of randomness depend on
a causal structure and turn meaningless. So motivated, we propose an intrinsic,
physically motivated measure for the randomness of a string of bits: its length
minus its normalized work value, a quantity we closely relate to its Kolmogorov
complexity (the length of the shortest program making a universal Turing
machine output this string). We test this alternative concept of randomness for
the example of non-local correlations, and we end up with a reasoning that
leads to similar conclusions as in, but is conceptually more direct than, the
probabilistic view since only the outcomes of measurements that can actually
all be carried out together are put into relation to each other. In the same
context-free spirit, we connect the logical reversibility of an evolution to
the second law of thermodynamics and the arrow of time. Refining this, we end
up with a speculation on the emergence of a space-time structure on bit strings
in terms of data-compressibility relations. Finally, we show that logical
consistency, by which we replace the abandoned causality, it strictly weaker a
constraint than the latter in the multi-party case.Comment: 17 pages, 16 figures, small correction
The simplest causal inequalities and their violation
In a scenario where two parties share, act on and exchange some physical
resource, the assumption that the parties' actions are ordered according to a
definite causal structure yields constraints on the possible correlations that
can be established. We show that the set of correlations that are compatible
with a definite causal order forms a polytope, whose facets define causal
inequalities. We fully characterize this causal polytope in the simplest case
of bipartite correlations with binary inputs and outputs. We find two families
of nonequivalent causal inequalities; both can be violated in the recently
introduced framework of process matrices, which extends the standard quantum
formalism by relaxing the implicit assumption of a fixed causal structure. Our
work paves the way to a more systematic investigation of causal inequalities in
a theory-independent way, and of their violation within the framework of
process matrices.Comment: 7 + 4 pages, 2 figure
Admissible Causal Structures and Correlations
It is well-known that if one assumes quantum theory to hold locally, then
processes with indefinite causal order and cyclic causal structures become
feasible. Here, we study qualitative limitations on causal structures and
correlations imposed by local quantum theory. For one, we find a necessary
graph theoretic criterion--the "siblings-on-cycles" property--for a causal
structure to be admissible: Only such causal structures admit a realization
consistent with local quantum theory. We conjecture that this property is
moreover sufficient. This conjecture is motivated by an explicit construction
of quantum causal models, and supported by numerical calculations. We show that
these causal models, in a restricted setting, are indeed consistent. For
another, we identify two sets of causal structures that, in the
classical-deterministic case, give rise to causal and non-causal correlations
respectively.Comment: 11 pages, 6 figures, extended preliminaries, details on numerical
calculations, reference to source code, numerical test increased to six
nodes. Comments welcome
Relating Wigner's Friend scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning
Nonclassical causal modeling was developed in order to explain violations of
Bell inequalities while adhering to relativistic causal structure and
faithfulness -- that is, avoiding fine-tuned causal explanations. Recently, a
no-go theorem stronger than Bell's theorem has been derived, based on
extensions of Wigner's friend thought experiment: the Local Friendliness (LF)
no-go theorem. We herein contend that LF no-go theorem poses formidable
challenges for the field of causal modeling, even when nonclassical and/or
cyclic causal explanations are considered. We first recast the LF inequalities,
one of the key elements of the LF no-go theorem, as special cases of monogamy
relations stemming from a statistical marginal problem; we then further recast
LF inequalities as causal compatibility inequalities emerging from a
nonclassical causal marginal problem. We find that the LF inequalities emerge
from the causal modeling perspective even when allowing the latent causes of
observed events to admit post-quantum descriptions, such as Generalised
Probabilistic Theories (GPT) or even more exotic causal compatibility
prescriptions. We prove that no nonclassical causal model can explain
violations of LF inequalities without both rejecting various well-motivated
causal-metaphysical assumptions and violating the No Fine-Tuning principle.
Finally, we note that these obstacles cannot be overcome even if one were to
appeal to cyclic causal models.Comment: 14+6 pages, 9 figures. Comments welcome
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