Quantum information is incompressible without errors

Abstract

A classical random variable can be faithfully compressed into a sequence of bits with its expected length lies within one bit of Shannon entropy. We generalize this variable-length and faithful scenario to the general quantum source producing mixed states ${\rho }_i$ with probability $p_i$. In contrast to the classical case, the optimal compression rate in the limit of large block length differs from the one in the fixed-length and asymptotically faithful scenario. The amount of this gap is interpreted as the genuinely quantum part being incompressible in the former scenario.

5 pages, no figures

References in corpus (2)

• Compressibility of Mixed-State Signals
• Lossless quantum data compression and variable-length coding

Cited by in corpus (4)

• Efficient classical simulation of slightly entangled quantum computations
• Universal approximation of multi-copy states and universal quantum lossless data compression
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• Universal Compression of Ergodic Quantum Sources