Unordered Tuples in Quantum Computation
Robert Furber (Radboud Universiteit Nijmegen), Bas Westerbaan (Radboud, Universiteit Nijmegen)
TL;DR
This paper explores the algebraic structures of unordered tuples of qubits and quantum systems, providing new characterizations of their associated C*-algebras and von Neumann algebras using advanced mathematical tools.
Contribution
It introduces a detailed analysis of unordered tuples in quantum computation, extending known algebraic results to unordered pairs and n-tuples using representation theory and duality.
Findings
M_3 (+) C is the C*-algebra of an unordered pair of qubits
Characterization of C*-algebra of unordered n-tuple of d-level systems
Description of quantum cycles and von Neumann algebra for unordered words
Abstract
It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C*-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra for unordered words.
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