Christopher A. Fuchs (1995), Ph.D. dissertation, University of New Mexico (dated 22 December 1995); posted as arXiv preprint — arXiv:quant-ph/9601020
Key takeaways
- The thesis translates classical distinguishability measures into quantum ones: it derives the mixed-state fidelity as the statistical overlap minimized over all measurements, gives new upper and lower bounds on accessible information (including a simple derivation of the Holevo bound), and proves that noncommuting mixed states cannot be broadcast.
Seeded from the abstract and a skim, before the reading in NOTE-021. What follows is what the work says about itself.
The dissertation turns information-theoretic distinguishability measures for probability distributions (error probability, Kullback-Leibler relative information, mutual information) into measures for quantum states, aiming at applications in quantum cryptography and computation. It derives an exact expression for the fidelity between mixed states and studies the measurement that attains it. It derives and compares several bounds on quantum mutual information, including a short derivation of Holevo’s upper bound and a tighter bound implicit in it, plus bounds on quantum relative information. It then applies these to the inference-disturbance tradeoff and proves a no-broadcasting theorem generalizing no-cloning to mixed states.
Standing in the record
Filed by the reading-time triage of 2026-09-25: 730 seconds of active reading over 1 session in the papers-feed tracker. It was filed Deferred, unread. NOTE-021 is the close reading of 2026-09-25, and it placed the work: Active — still the most self-contained derivation of mixed-state fidelity as an optimal classical overlap, and of the Holevo bound by the curvature (J” vs S”) argument. Read §3.3 and §3.5.1–3.5.2 for those, and Ch. 2 as a tutorial on why error probability, the Chernoff bound, KL and mutual information are the operationally grounded classical measures. The quantum-Kullback bounds (§3.6), the inference–disturbance formalism (§4.2) and the no-broadcasting proof (§4.3) are preliminary or appeared in companion papers. Read those papers for their final forms.
When seeded, before the reading in NOTE-021, the entry gave a priority for a deeper reading: medium — foundational and 174 pages, so a skim captures the map but not the proofs; t=730 s is moderate; read Ch. 2-3 selectively rather than end to end.
What the seeding asked a deeper reading to check (NOTE-021 is that reading):
- Foundational source for the Fuchs-van de Graaf-era toolkit (fidelity, trace-distance relations) and for no-broadcasting. The deeper read should check which results are primary here versus in the companion papers (e.g. Barnum et al. 1996 PRL; Fuchs & van de Graaf 1999 IEEE-IT).
- ML link (real but generic): classical-to-quantum lifts of KL, Bhattacharyya/fidelity and mutual information parallel the divergence choices ML makes. Ch. 2’s operational derivations of KL and mutual information are the most ML-reusable part.
Access when seeded: The hash-titled item resolved via the arXiv abs page for quant-ph/9601020 to this title. Full PDF (174 pp.) retrieved; read title page, table of contents, list of figures, §1.2 Summary of Results (opening), the §3.3.1 fidelity derivation opening and §4.3 opening. No DOI (a dissertation); a Crossref search found no registered version. year is the dissertation date (1995); published is the arXiv posting month, as instructed.