Computing with Colored Tangles

Carmi, Avishy; Moskovich, Daniel

doi:10.3390/sym7031289

Cited by 5 publications

(9 citation statements)

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“…The inequalities reflecting the cryptographic principle contain a quantity defined in quantum mechanics, and the principle cannot immediately exclude postquantum correlations by itself, but tells us a way to determine the quantum boundaries. Note that a similar principle for a different type of randomness was considered in [20].…”

Section: Introductionmentioning

confidence: 99%

Cryptographic quantum bound on nonlocality

Ishizaka

2017

Phys. Rev. A

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Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and postquantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for the full identification of the quantum boundaries already for bipartite settings. The nonlocality inequalities such as so-called the Tsirelson inequality are extended to show how such randomness affects the strength of nonlocal correlations. As a result, a relation followed by most of quantum correlations in the simplest Bell scenario is revealed. The extended inequalities reflect the cryptographic principle such that a completely scrambled message cannot carry information.

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Section: Introductionmentioning

confidence: 99%

Cryptographic quantum bound on nonlocality

Ishizaka

2017

Phys. Rev. A

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“…The operation together with the set Q = {0, 1, 2} induce a quandle algebra [12], [13]. Consider a set Q together with a set B of binary operations from Q×Q to Q with the following properties:…”

Section: Computational Capabilitiesmentioning

confidence: 99%

“…In particular, it can realize a universal set of Boolean gates, AND and NOT, as well as wire elements for transferring information from a given cell to any other cell. This automaton is also shown to capture trinary logic described by a quandle, a non-associative algebraic structure whose axioms have been interpreted as laws of conservation of information [12], [13].…”

Section: Introductionmentioning

confidence: 99%

Computing by nowhere increasing complexity

Peled

Mishra

Carmi

2017

2017 IEEE Symposium Series on Computational Intelligence (SSCI)

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A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this two-dimensional Kolmogorov complexity the underlying automaton is shown to be capable of simulating logic circuits. It is also shown to capture trianry logic described by a quandle, a non-associative algebraic structure. A similar automaton whose rule permits at times the increase of a cell's neighborhood complexity is shown to produce animated entities which can be used as information carriers akin to gliders in Conway's game of life.

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“…In general, if one message can uniquely be recovered from another by using the quandle axioms and an automorphism of (Q(M), B(M)), the two messages are said to be confused. This same notion was called a tangle machine computation in [7].…”

Section: 4mentioning

confidence: 99%

“…no local knotting) but are still complicated enough to be interesting. The theory of coloured versions of such foams is equivalent to a construction that was used by the authors to topologically model fusion of information and as a model for computation [4,5,7], and it is this that is our main motivation.We describe the contents of this paper. Section 2 defines Inca foams which Section 3 describes in five (5) different diagrammatic ways.…”

mentioning

confidence: 99%