Institute for Quantum Information Seminar

The Quantum Substate Theorem due to Jain, Radhakrishnan, and Sen [JACM, 2009] 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 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. In this talk, I will motivate the substate property by reviewing an application, and will then present a new proof of the theorem. The resulting statement is stronger and its proof is both conceptually simpler and significantly shorter than the earlier proof. Joint work with Rahul Jain, CQT, NUS, Singapore.