Quantum / CONCEPT
The equiprobable pretty-good-measurement comparison of Cha and Lee fails
Cha and Lee (arXiv:2507.05778, Quantum Information Processing 25, 310) compare two upper bounds on the optimal success probability of minimum-error state discrimination, one built from the pretty good measurement on all states and one built from it on the active set I_+ of labels with nonzero optimal effects. For equal priors they conjecture (|I_+| - 1)(P^PGM_+ - 1/N) <= (N - 1)(P^PGM - 1/N). Three positive definite qubit states with rational entries violate it.
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The comparison fails for three qubit states
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- Binomial and kappa states do not exhaust truncated entropy minimizersstructural-affinity · Closed
- Completely useless channels and concatenationstructural-affinity · Closed
- In-between states do not always minimize Bayesian transmissivity errorstructural-affinity · Closed
- In-between states need not be optimal for a beta priorstructural-affinity · Closed
- Original Single-Terminal Ternary Obstructionstructural-affinity · Closed
- The sharp local-perception CHSH boundstructural-affinity · Closed
- Weighted multicopy designs need not be optimalstructural-affinity · Closed
- Weil: Rank Tracestructural-affinity · Closed
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