A short proof of the Quantum Substate Theorem

The Quantum Substate Theorem due to Jain, Radhakrishnan, and Sen [7] gives us a powerful operational interpretation of the observational divergence of two quantum states, a quantity that is closely 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 a new proof of this theorem. The resulting statement is stronger and its proof is both conceptually simpler and significantly shorter than the earlier proof.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Rahul Jain, Ashwin Nayak
• Keywords: CORR 2011, Education, Observational Divergence, Quantum State, Quantum Substate Theorem