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Pavičić M. Non-Kochen-Specker Contextuality. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1117. [PMID: 37628147 PMCID: PMC10453090 DOI: 10.3390/e25081117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Revised: 07/21/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods-whose complexity does not scale up with the dimension-for generating such non-Kochen-Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.
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Affiliation(s)
- Mladen Pavičić
- Center of Excellence for Advanced Materials and Sensors, Research Unit Photonics and Quantum Optics, Institute Ruđer Bošković, 10000 Zagreb, Croatia;
- Institute of Physics, 10000 Zagreb, Croatia
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Gao X, Erhard M, Zeilinger A, Krenn M. Computer-Inspired Concept for High-Dimensional Multipartite Quantum Gates. PHYSICAL REVIEW LETTERS 2020. [PMID: 32794870 DOI: 10.1038/s42254-020-0230-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multiphotonic quantum systems. The proposals rely on two new ideas: (i) a novel high-dimensional quantum nondemolition measurement, (ii) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world and thereby we identify important pathways for experimental research in the near future. The concepts have been found using the computer algorithm melvin for designing computer-inspired quantum experiments. As opposed to the field of machine learning, here the human learns new scientific concepts by interpreting and analyzing the results presented by the machine. This demonstrates that computer algorithms can inspire new ideas in science, which has a widely unexplored potential that goes far beyond experimental quantum information science.
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Affiliation(s)
- Xiaoqin Gao
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
- National Mobile Communications Research Laboratory and Quantum Information Research Center, Southeast University, Nanjing, 210096, China
| | - Manuel Erhard
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
| | - Anton Zeilinger
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
| | - Mario Krenn
- Faculty of Physics, University of Vienna, Vienna, 1190, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences, Vienna, 1190, Austria
- Department of Chemistry and Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada
- Vector Institute for Artificial Intelligence, Toronto, Ontario M5G 1M1, Canada
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What Is So Special about Quantum Clicks? ENTROPY 2020; 22:e22060602. [PMID: 33286374 PMCID: PMC7517140 DOI: 10.3390/e22060602] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 05/19/2020] [Accepted: 05/20/2020] [Indexed: 11/17/2022]
Abstract
This is an elaboration of the "extra" advantage of the performance of quantized physical systems over classical ones, both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based on entities related to (dual) vectors in (dual) Hilbert spaces, as compared to the Boolean algebra of subsets of a set and the additive measures they support.
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Abstract
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.
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