2000/11/30 by Howard Barnum, Patrick Hayden, Richard Jozsa +1
Computer Science · Engineering · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wireless Communication Security Techniques #quant-ph
paper · pdf · doi:10.1098/rspa.2001.0816
published as Proc. Roy. Soc. (Lond.) A (2001), vol 457, p2019-2039 · 22 pages, Latex2e, journal version
openalex publication_date 2001/07/08 · arxiv created 2003/07/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.