373 research outputs found
Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces
Recently, quantum contextuality has been proved to be the source of quantum computation’s power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their features. The most elaborated contextual sets, which offer blueprints for contextual experiments and computational gates, are the Kochen–Specker (KS) sets. In this paper, we show a method of vector generation that supersedes previous methods. It is implemented by means of algorithms and programs that generate hypergraphs embodying the Kochen–Specker property and that are designed to be carried out on supercomputers. We show that vector component generation of KS hypergraphs exhausts all possible vectors that can be constructed from chosen vector components, in contrast to previous studies that used incomplete lists of vectors and therefore missed a majority of hypergraphs. Consequently, this unified method is far more efficient for generations of KS sets and their implementation in quantum computation and quantum communication. Several new KS classes and their features have been found and are elaborated on in the paper. Greechie diagrams are discussed
Hypergraph Contextuality
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets - the Kochen-Specker ones and the operator-based ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities
Vector Generation of Contextual Sets
As quantum contextuality proves to be a necessary resource for universal
quantum computation, we present a general method for vector generation of
Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method
supersedes all three previous methods: (i) fortuitous discoveries of smallest
KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random
downward generation of sets from fortuitously obtained big master sets. In
contrast to previous works, we can generate master sets which contain all
possible KS sets starting with nothing but a few simple vector components. From
them we can readily generate all KS sets obtained in the last half a century
and any specified new KS sets. Herewith we can generate sufficiently large sets
as well as sets with definite required features and structures to enable
varieties of different implementations in quantum computation and
communication.Comment: 6 pages, 6 figures; Orally presented by M. Pavicic at Quantum
Technology International Conference 2018 (QTech 2018), Paris, France,
September 5-7, 2018; Extended version:
https://www.youtube.com/watch?v=Bw2vItz5tr
The Problem of Contextuality and the Impossibility of Experimental Metaphysics Thereof
Recently a new impulse has been given to the experimental investigation of
contextuality. In this paper we show that for a widely used definition of
contextuality there can be no decisive experiment on the existence of
contextuality. To this end, we give a clear presentation of the hidden variable
models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the
Kochen-Specker Theorem. Although we disagree with this last statement, the
models play a significant role in the discussion on the meaning of
contextuality. In fact, we introduce a specific MKC-model of which we show that
it is non-contextual and completely in agreement with quantum mechanical
predictions. We also investigate the possibility of other definitions of
non-contextuality --with an emphasis on operational definitions-- and argue
that any useful definition relies on the specification of a theoretical
framework. It is therefore concluded that no experimental test can yield any
conclusions about contextuality on a metaphysical level
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