Short proofs of the Quantum Substate Theorem

Rahul Jain; Ashwin Nayak

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arXiv · 1103.6067

Short proofs of the Quantum Substate Theorem

Rahul Jain·Ashwin Nayak

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Abstract

The Quantum Substate Theorem due to Jain, Radhakrishnan, and Sen (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 rho, sigma is small, then there is a quantum state rho' close to rho in trace distance, such that rho' when scaled down by a small factor becomes a substate of sigma. 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.

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BibTeX RIS

Rahul Jain, Ashwin Nayak. 2012-01-12. Short proofs of the Quantum Substate Theorem. https://arxiv.org/abs/1103.6067

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