Multiple Quantum Hypothesis Testing

---
name: multiple-quantum-hypothesis-testing
description: Dimension-free one-shot bounds for multiple quantum state discrimination with sharp asymptotics
category: quantum
---

# Multiple Quantum Hypothesis Testing

## Methodology
Bayesian discrimination among multiple quantum states using dimension-free one-shot upper bounds on minimum probability of error.

## Key Insights
1. **Dimension-free bound**: Upper bound on error probability in terms of sum of pairwise errors, resolving Audenaert-Mosonyi conjecture
2. **Chernoff bound improvement**: Improves multiple quantum Chernoff bound by removing dimension-dependent prefactor
3. **Infinite-dimensional case**: Proves achievability of multiple quantum Chernoff distance for arbitrary separable Hilbert spaces
4. **Binary case characterization**: Minimum error probability characterized by trace harmonic-mean quantity, within factor 2 of optimal classical error

## Mathematical Framework
- Pairwise error decomposition for multi-state discrimination
- Trace harmonic-mean for binary quantum hypothesis testing
- Nussbaum-Szkoła distributions for classical-quantum correspondence

## Activation
hypothesis testing, quantum state discrimination, Chernoff bound, Bayesian, error bounds