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Title: Short proofs of the quantum substate theorem
Authors: Jain, R. 
Nayak, A.
Keywords: Observational divergence
quantum information theory
relative entropy
smooth relative min-entropy
substate theorem
Issue Date: 2012
Source: Jain, R., Nayak, A. (2012). Short proofs of the quantum substate theorem. IEEE Transactions on Information Theory 58 (6) : 3664-3669. ScholarBank@NUS Repository.
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.
Source Title: IEEE Transactions on Information Theory
ISSN: 00189448
DOI: 10.1109/TIT.2012.2184522
Appears in Collections:Staff Publications

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