random-dimension-reduction-quantum-learning

name	random-dimension-reduction-quantum-learning
description	Random dimension reduction methodology for learning symmetric properties of quantum states. Black-box procedure that replaces dimension with maximum rank in sample complexity. Use when learning symmetric quantum properties, estimating state distances/fidelities, or reducing quantum tomography overhead.

Random Dimension Reduction for Quantum State Learning

Core Methodology

Procedure simultaneously reduces dimensions of many potentially distinct quantum states while preserving properties invariant under tensor power action of an isometry.

Key Results

• Black-box method to replace dimension with maximum rank in sample complexity
• Applicable to symmetric properties depending on multiple input states
• Efficient quantum circuit implementation using Schur transform

Applications

1. Distance estimation: Improved upper bounds after dimension reduction + full tomography
2. Fidelity estimation: More efficient symmetric property learning
3. Relative entropy: Reduced sample complexity for state comparisons

Implementation

• Apply Schur transform circuit for dimension reduction
• Perform full state tomography on reduced states
• Preserve tensor-power-invariant properties