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- W2154266953 abstract "The Quantum Substate Theorem due to Jain (2002) gives us a powerful operational interpretation of relative entropy, in fact, of the observational divergence of two quantum states, a quantity that is related to their relative entropy. Informally, the theorem states that if the observational divergence between two quantum states ρ, σ is small, then there is a quantum state ρ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>'</sup> close to ρ in trace distance, such that ρ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>'</sup> when scaled down by a small factor becomes a substate of σ. We present new proofs of this theorem. The resulting statement is optimal up to a constant factor in its dependence on observational divergence. In addition, the proofs are both conceptually simpler and significantly shorter than the earlier proof." @default.
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- W2154266953 date "2012-06-01" @default.
- W2154266953 modified "2023-10-02" @default.
- W2154266953 title "Short Proofs of the Quantum Substate Theorem" @default.
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- W2154266953 doi "https://doi.org/10.1109/tit.2012.2184522" @default.
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