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Open Quantum Systems Decoherence
Quantum Simulation
Entanglement Theory Quantum Correlations
Orthogonal Unitary Bases and a Subfactor Conjecture
arXiv
Authors: Jason Crann, David W. Kribs, Rajesh Pereira
Year
2022
Paper ID
6631
Status
Preprint
Abstract Read
~2 min
Abstract Words
89
Citations
N/A
Abstract
We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of Mn\(mathbb{C}\) admits an orthonormal unitary basis under normalized matrix trace if and only if the normalized matrix trace and standard trace of the von Neumann subalgebra coincide. As an application, we verify a recent conjecture of Bakshi-Gupta, showing that any finite-index regular inclusion Nsubseteq M of II1-factors admits an orthonormal unitary Pimsner-Popa basis.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace.
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