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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′ close to ρ in trace distance, such that ρ′ 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. © 2012 IEEE.
Keywords
Observational divergence, quantum information theory, relative entropy, smooth relative min-entropy, substate theorem
Source Title
IEEE Transactions on Information Theory
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Date
2012
DOI
10.1109/TIT.2012.2184522
Type
Article