bibkey: fuchs1996thesislogarithmbasis
authors: Christopher A. Fuchs
year: 1996
title: "Distinguishability and Accessible Information in Quantum Theory"
doi: null
url: https://arxiv.org/abs/quant-ph/9601020v1
claim: "After equation (3.244), Fuchs asks whether a basis can make the matrix appearing in the logarithm diagonal."
strata_touched:
  - D5/S3/Quantum/Foundation/FuchsLogarithmBasisRefutation
license: citation-only
triage: anchor

Fuchs’s physical-basis logarithm question

Verified locator

DOI: null

Source: https://arxiv.org/abs/quant-ph/9601020v1

Source statement

C. A. Fuchs, Distinguishability and Accessible Information in Quantum Theory, PhD thesis, University of New Mexico (1995), arXiv:quant-ph/9601020v1 (23 January 1996), §3.5.3, pp. 77–78.

An interesting open question is whether there exists a basis in which to represent the operators ρ̂₀, ρ̂₁, etc., so that the matrix appearing in the logarithm above is diagonal. If so, this would greatly simply the computation of L(t).

The question follows equations (3.242)–(3.244), with ρ̃₀ = ρ₀ ⊕ ρ₀* and Δ̃ = Δ ⊕ Δ*, where Δ = ρ₁ − ρ₀ is invertible. Equation (3.237) defines the Kronecker sum by I ⊗ B + Cᵀ ⊗ I.

The quotation and bibliographic locator are source information. The finite qutrit refutation in the associated D5 module is a repository derivation.