Talk: Prof. Andreas Winter (July 14, 2022 at 12:00 PM, LNT Seminar room N2409)
Bosonic data hiding - power of linear vs non-linear optics
Prof. Andreas Winter
Universitat Autònoma de Barcelona (UAB)
We show that the positivity of the Wigner function of Gaussian states and measurements provides an elegant way to bound the discriminating power of "linear optics", which we formalise as Gaussian measurement operations augmented by classical (feed-forward) communication (GOCC). This allows us to reproduce and generalise the result of Takeoka and Sasaki [PRA 78:022320, 2008], which tightly characterises the GOCC norm distance of coherent states, separating it from the optimal distinguishability according to Helstrom's theorem. Furthermore, invoking ideas from classical and quantum Shannon theory we show that there are states, each a probabilistic mixture of multi-mode coherent states, which are exponentially reliably discriminated in principle, but appear exponentially close judging from the output of GOCC measurements. This shows strikingly the limitations of the resource theory of GOCC operations, even we restricting only to binary hypothesis testing. It furthermore points to the possible resources required to overcome or alleviate the GOCC restriction, not only in
measurements but general state transformations. We also present general bounds in the opposite direction, which guarantee a minimum of distinguishability under measurements with positive Wigner function, for any bounded-energy states that are Helstrom distinguishable, and conjecture that a similar bound holds for GOCC measurements. [Joint work with Krishna Kumar Sabapathy, arXiv:2102.01622]
Andreas Winter was born in Altötting, a small rural town near Munich, known also as the Heart of Bavaria. After developing an infatuation with science early on, and in particular with mathematics, he decided to study this subject in Konstanz and Berlin. He graduated in 1997 from the Freie Universität Berlin, and went on to obtain a doctorate in mathematics from the Universität Bielefeld in 1999, with the late Rudolf Ahlswede. In 2001 he joined the quantum information group in Bristol as a postdoc, became Lecturer in Applied Mathematics there in 2003, and Professor of the Physics of Information in 2006. In 2012 he left Bristol after 11 years, to move to the Universitat Autònoma de Barcelona as ICREA Research Professor, where he is now part of the quantum information group.