aqora

Quantum splitting of multi-qubit gates

Mario Mastriani

Optical and Quantum ElectronicsDec 29, 20233 citations

Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon

Michel R. P. Planat, Метод Санига, Slovak Republic

Abstract. Disregarding the identity, the remaining 63 elements of the generalized three-qubit Pauli group are found to contain 12 096 distinct copies of Mermin’s magic pentagram. Remarkably, 12 096 is also the number of automorphisms of the smallest split Cayley hexagon. We give a few solid arguments showing that this may not be a mere coincidence. These arguments are mainly tied to the structure of certain types of geometric hyperplanes of the hexagon. It is further demonstrated that also an (182, 123)-type of magic configurations, recently proposed by Waegell and Aravind (J. Phys. A: Math. Theor. 45 (2012) 405301), seems to be intricately linked with automorphisms of the hexagon. Finally, the entanglement properties exhibited by edges of both pentagrams and these particular Waegell-Aravind configurations are addressed. PACS numbers: 03.65.Aa, 03.65.Fd, 03.65.Ud, 02.10.Ox 1.Abstract. Disregarding the identity, the remaining 63 elements of the generalized three-qubit Pauli group are found to contain 12 096 distinct copies of Mermin’s magic pentagram. Remarkably, 12 096 is also the number of automorphisms of the smallest split Cayley hexagon. We give a few solid arguments showing that this may not be a mere coincidence. These arguments are mainly tied to the structure of certain types of geometric hyperplanes of the hexagon. It is further demonstrated that also an (182, 123)-type of magic configurations, recently proposed by Waegell and Aravind (J. Phys. A: Math. Theor. 45 (2012) 405301), seems to be intricately linked with automorphisms of the hexagon. Finally, the entanglement properties exhibited by edges of both pentagrams and these particular Waegell-Aravind configurations are addressed. PACS numbers: 03.65.Aa, 03.65.Fd, 03.65.Ud, 02.10.Ox 1.

Aug 14, 201621 citations

'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon

Метод Санига

Recently Waegell and Aravind [J.Phys.A: Math.Theor.45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furnishing a proof of the Kochen-Specker theorem.Here it is demonstrated that two of these sets/configurations, namely the 18 2 -12 3 and 2 4 14 2 -4 3 6 4 ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types V 22 (37; 0, 12, 15, 10) and V 4 (49; 0, 0, 21, 28) in the classification of Frohardt and Johnson [Comm.Algebra 22 (1994), 773-797].Moreover, employing an automorphism of order seven of the hexagon, six more replicas of either of the two configurations are obtained.Recently Waegell and Aravind [J.Phys.A: Math.Theor.45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furnishing a proof of the Kochen-Specker theorem.Here it is demonstrated that two of these sets/configurations, namely the 18 2 -12 3 and 2 4 14 2 -4 3 6 4 ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types V 22 (37; 0, 12, 15, 10) and V 4 (49; 0, 0, 21, 28) in the classification of Frohardt and Johnson [Comm.Algebra 22 (1994), 773-797].Moreover, employing an automorphism of order seven of the hexagon, six more replicas of either of the two configurations are obtained.

arXiv:1206.3436Symmetry Integrability and Geometry Methods and ApplicationsNov 6, 20124 citations

Quasi-lattice of qubits and its mesoscopic features

Hou Ian, Yu-xi Liu

APSMar 1, 20140 citations

Three-qubit-embedded split Cayley hexagon is contextuality sensitive

Frédéric Holweck, Henri de Boutray, Метод Санига

In this article, we show that sets of three-qubit quantum observables obtained by considering both the classical and skew embeddings of the split Cayley hexagon of order two into the binary symplectic polar space of rank three can be used to detect quantum state-independent contextuality. This reveals a fundamental connection between these two appealing structures and some fundamental tools in quantum mechanics and quantum computation. More precisely, we prove that the complement of a classically embedded hexagon does not provide a Mermin-Peres-like proof of the Kochen-Specker theorem whereas that of a skewly-embedded one does.In this article, we show that sets of three-qubit quantum observables obtained by considering both the classical and skew embeddings of the split Cayley hexagon of order two into the binary symplectic polar space of rank three can be used to detect quantum state-independent contextuality. This reveals a fundamental connection between these two appealing structures and some fundamental tools in quantum mechanics and quantum computation. More precisely, we prove that the complement of a classically embedded hexagon does not provide a Mermin-Peres-like proof of the Kochen-Specker theorem whereas that of a skewly-embedded one does.

arXiv:2202.00726Scientific ReportsMay 26, 20229 citations

Four-Qubit Geometry

Zhang Chi Liu

Sep 1, 20260 citations

Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon

Related papers

Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon

Related papers