Planar algebras, quantum information theory and subfactors

Kodiyalam, Vijay; Sruthymurali,; Sunder, V. S.

doi:10.1142/s0129167x20501244

Cited by 4 publications

(2 citation statements)

References 5 publications

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“…In this context they were called bi-unitary matrices, see for example [15]. Implications for quantum information theory were studied in [16,17].…”

Section: Introductionmentioning

confidence: 99%

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

Mestyán,

Pozsgay,

Wanless

2024

SciPost Phys.

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We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a spatially symmetric pattern and the states have maximal entanglement for all bipartitions that follow from the reflection symmetries of the given geometry. We consider those cases where the state itself is invariant with respect to the geometrical symmetry group. The simplest examples are those dual unitary operators which are also self dual and reflection invariant, but we also consider the generalizations in the hexagonal, cubic, and octahedral geometries. We provide a number of constructions and concrete examples for these objects for various local dimensions. All of our examples can be used to build quantum cellular automata in 1+1 or 2+1 dimensions, with multiple equivalent choices for the “direction of time”.

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“…In this context they were called bi-unitary matrices, see for example [15]. Implications for quantum information theory were studied in [16,17].…”

Section: Introductionmentioning

confidence: 99%

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

Mestyán,

Pozsgay,

Wanless

2024

SciPost Phys.

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“…These notions are closely tied to the classical notions of orthogonal σ-fields, conditional probability and entropy. In the finite-dimensional setting of matrix algebras, commuting squares of subfactors are tied to generalized Hadamard matrices used in quantum computing and Jones' spin models [41,51,52],…”

Section: Introductionmentioning

confidence: 99%

Quantum monadic algebras

Harding¹

2022

J. Phys. A: Math. Theor.

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We introduce quantum monadic and quantum cylindric algebras. These are adaptations to the quantum setting of the monadic algebras of Halmos, and cylindric algebras of Henkin, Monk and Tarski, that are used in algebraic treatments of classical and intuitionistic predicate logic. Primary examples in the quantum setting come from von Neumann algebras and subfactors. Here we develop the basic properties of these quantum monadic and cylindric algebras and relate them to quantum predicate logic.

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Quantum walks on regular graphs with realizations in a system of anyons

Balu

2022

Quantum Inf Process

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Planar algebras, quantum information theory and subfactors

Cited by 4 publications

References 5 publications

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

Quantum monadic algebras

Quantum walks on regular graphs with realizations in a system of anyons

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