Classically-embedded split Cayley hexagons rule three-qubit
contextuality with three-element contexts
- URL: http://arxiv.org/abs/2312.07738v1
- Date: Tue, 12 Dec 2023 21:10:42 GMT
- Title: Classically-embedded split Cayley hexagons rule three-qubit
contextuality with three-element contexts
- Authors: Metod Saniga, Fr\'ed\'eric Holweck, Colm Kelleher, Axel Muller, Alain
Giorgetti, Henri de Boutray
- Abstract summary: We show that split Cayley hexagons of order two live in the three-qubit symplectic polar space in two non-isomorphic embeddings, called classical and skew.
Although neither of the two embeddings yields observable-based contextual configurations of their own, it classically-embedded copies are found to fully rule contextuality properties.
- Score: 0.0699049312989311
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: As it is well known, split Cayley hexagons of order two live in the
three-qubit symplectic polar space in two non-isomorphic embeddings, called
classical and skew. Although neither of the two embeddings yields
observable-based contextual configurations of their own, {\it
classically}-embedded copies are found to fully rule contextuality properties
of the most prominent three-qubit contextual configurations in the following
sense: each set of unsatisfiable contexts of such a contextual configuration is
isomorphic to the set of lines that certain classically-embedded hexagon shares
with this particular configuration. In particular, for a doily this shared set
comprises three pairwise disjoint lines belonging to a grid of the doily, for
an elliptic quadric the corresponding set features nine mutually disjoint lines
forming a (Desarguesian) spread on the quadric, for a hyperbolic quadric the
set entails 21 lines that are in bijection with the edges of the Heawood graph
and, finally, for the configuration that consists of all the 315 contexts of
the space its 63 unsatisfiable ones cover an entire hexagon. A particular
illustration of this encoding is provided by the {\it line-complement} of a
skew-embedded hexagon; its 24 unsatisfiable contexts correspond exactly to
those 24 lines in which a particular classical copy of the hexagon differs from
the considered skew-embedded one. In connection with the last-mentioned case we
also conducted some experimental tests on a Noisy Intermediate Scale Quantum
(NISQ) computer to validate our theoretical findings.
Related papers
- On Multiquantum Bits, Segre Embeddings and Coxeter Chambers [0.0]
We develop a systematic study of qubit moduli spaces, illustrating the geometric structure of entanglement through hypercube constructions and Coxeter chamber decompositions.
This reveals a structure underlying the hierarchy of embeddings, with direct implications for quantum error correction schemes.
The symmetry of the Segre variety under the Coxeter group of type $A$ allows us to analyze quantum states and errors through the lens of reflection groups.
arXiv Detail & Related papers (2025-02-01T15:39:28Z) - A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals [0.0699049312989311]
We introduce and describe a new method for finding an upper bound on the degree of contextuality and the corresponding unsatisfied part of a quantum contextual configuration.
While the previously used method based on a SAT solver was limited to three qubits, this new method is much faster and more versatile.
arXiv Detail & Related papers (2024-07-03T08:59:30Z) - Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
We show how to reduce the geometry of degenerate states to the non-abelian connection $A$.
We find independent invariants associated with each triple of subspaces.
Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
arXiv Detail & Related papers (2024-04-04T06:39:28Z) - New and improved bounds on the contextuality degree of multi-qubit configurations [0.0699049312989311]
We present algorithms and a C code to reveal quantum contextuality and evaluate the contextuality degree.
The paper first describes the algorithms and the C code. Then it illustrates its power on a number of subspaces of symplectic polar spaces whose rank ranges from 2 to 7.
The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension 2 and higher, (ii) non-existence of negative subspaces of dimension 3 and higher.
arXiv Detail & Related papers (2023-05-17T14:02:57Z) - Quantum entanglement and contextuality with complexifications of $E_8$
root system [91.3755431537592]
The Witting configuration with 40 complex rays was suggested as a possible reformulation of Penrose model with two spin-3/2 systems based on geometry of dodecahedron.
An analysis of properties of suggested configuration of quantum states is provided using many analogies with properties of Witting configuration.
arXiv Detail & Related papers (2022-10-27T11:23:12Z) - Penrose dodecahedron, Witting configuration and quantum entanglement [55.2480439325792]
A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose.
The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space.
Two entangled systems with quantum states described by Witting configurations are discussed in presented work.
arXiv Detail & Related papers (2022-08-29T14:46:44Z) - Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive [0.0]
It is known that there are two non-equivalent embeddings of the split Cayley hexagon of order two into $mathcalW(5,2)$, the binary symplectic polar space of rank three.
We show that the complement of a classically-embedded hexagon is not contextual, whereas that of a skewly-embedded one is.
arXiv Detail & Related papers (2022-02-01T19:53:27Z) - The Role of Compositionality in Constructing Complementarity Classical
Structures Within Qubit Systems [0.0]
We study the abstraction of observables, which has been dubbed as classical structures, in a sub-theory of quantum mechanics.
We have constructed a procedure that takes the complementary classical structures of a single qubit system and compose them separably.
For two qubits, we found 13 maximal complete sets of mutually complementary classical structures, and for three qubits, we found 32,448 maximal complete sets.
arXiv Detail & Related papers (2021-05-24T06:18:49Z) - Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes.
Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them.
We provide theoretical insights of our approach using tools from the mesh-simplification literature.
arXiv Detail & Related papers (2020-10-23T14:49:02Z) - Quantum anomalous Hall phase in synthetic bilayers via twistless
twistronics [58.720142291102135]
We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions.
We show that our system exhibits topologicalband structures under appropriate conditions.
arXiv Detail & Related papers (2020-08-06T19:58:05Z) - Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy.
We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy.
In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
arXiv Detail & Related papers (2020-07-31T19:23:26Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.