On the reversible extraction of classical information from a quantum source
- 8 July 2001
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 457 (2012) , 2019-2039
- https://doi.org/10.1098/rspa.2001.0816
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.Keywords
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