On the reversible extraction of classical information from a quantum source

H. Barnum, P. Hayden, R. Jozsa, A. Winter

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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 languageEnglish
Pages (from-to)2019-2039
Number of pages21
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume457
Issue number2012
DOIs
StatePublished - 8 Aug 2001
Externally publishedYes

Keywords

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

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