## Abstract

Consider a source ε of pure quantum states with von Neumann entropy S. By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits per signal (the Schumacher limit) in such a way that entire strings may be recovered with arbitrarily high fidelity. Suppose that classical storage is free while quantum storage is expensive and suppose that the states of ε do not fall into two or more orthogonal subspaces. We show that if ε can be compressed with arbitrarily high fidelity into A qubits per signal plus any amount of auxiliary classical storage, then A must still be at least as large as the Schumacher limit S of ε. Thus no part of the quantum information content of ε can be faithfully replaced by classical information. If the states do fall into orthogonal subspaces, then A may be less than S, but only by an amount not exceeding the amount of classical information specifying the subspace for a signal from the source.

Original language | English |
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Pages (from-to) | 2019-2039 |

Number of pages | 21 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 457 |

Issue number | 2012 |

DOIs | |

State | Published - 8 Aug 2001 |

Externally published | Yes |

## Keywords

- Information compression
- Quantum information
- Quantum source coding
- Reversible information extraction