Gaussian Mean Width Identification Capacity

---
name: gaussian-mean-width-identification-capacity
description: Single-letter efficiently computable strong converse bound on classical identification capacity of quantum channels via Gaussian mean width analysis
category: quantum
---

# Gaussian Mean Width Identification Capacity Bound

## Methodology
Single-letter strong converse bound on classical identification capacity of quantum channels using geometric analysis of output space.

## Key Techniques
1. **σ-Euclidean geometry**: Product state-weighted geometry for channel output space
2. **Sudakov's inequality**: Bounds covering numbers via Gaussian mean widths
3. **Semidefinite representation**: Bound admits efficient SDP computation
4. **Channel improvements**: Improves bounds for depolarizing, Pauli, erasure, and amplitude damping channels

## Mathematical Framework
- Trace-distance separation controlled by Euclidean covering estimates
- Exponential growth governed by operator norm of single-letter positive operator
- Optimization over weighting states yields tight bounds

## Activation
identification capacity, Gaussian mean width, strong converse, quantum channels, semidefinite programming