Tata Institute of Fundamental Research
Short Proofs of the Quantum Substate Theorem
Seminar
Speaker:
Ashwin Nayak
Dept. of Combinatorics and Optimization
Faculty of Mathematics
University of Waterloo
200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
Organiser:
John Barretto
Date:
Monday, 9 Jan 2012, 11:30 to 12:30
Venue:
A-212 (STCS Seminar Room)
(Scan to add to calendar)
Abstract:
The Quantum Substate Theorem due to Jain, Radhakrishnan, and (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 (this is joint work with Rahul Jain, National University of Singapore).
| Speaker: | Ashwin Nayak Dept. of Combinatorics and Optimization Faculty of Mathematics University of Waterloo 200 University Avenue West Waterloo, Ontario N2L 3G1 Canada |
| Organiser: | John Barretto |
| Date: | Monday, 9 Jan 2012, 11:30 to 12:30 |
| Venue: | A-212 (STCS Seminar Room) |
(Scan to add to calendar)
Abstract:
The Quantum Substate Theorem due to Jain, Radhakrishnan, and (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 (this is joint work with Rahul Jain, National University of Singapore).