Universal approximation of multi-copy states and universal quantum lossless data compression

Abstract

We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression.

References in corpus (3)

• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• Universal coding for classical-quantum channel
• Universal entanglement concentration

Cited by in corpus (9)

• Quantum Reverse Shannon Theorem
• Reliable Quantum State Tomography
• Operational Interpretation of Renyi Information Measures via Composite Hypothesis Testing Against Product and Markov Distributions
• Optimal compression for identically prepared qubit states
• Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
• Universal channel coding for general output alphabet
• Reliable Simulation of Quantum Channels: the Error Exponent
• Heisenberg scaling based on population coding
• Universal classical-quantum superposition coding and universal classical-quantum multiple access channel coding