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Quantum information is incompressible without errors

Masato Koashi·Nobuyuki Imoto
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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 $ρ_i$ 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.

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Masato Koashi, Nobuyuki Imoto. 2002-03-11. Quantum information is incompressible without errors. https://doi.org/10.1103/physrevlett.89.097904

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