PIRSA:16110042

Video URL

https://pirsa.org/16110042

Uniform Additivity

Smith, G. (2016). Uniform Additivity. Perimeter Institute for Theoretical Physics. https://pirsa.org/16110042

Smith, Graeme. Uniform Additivity. Perimeter Institute for Theoretical Physics, Nov. 16, 2016, https://pirsa.org/16110042 

          @misc{ scivideos_PIRSA:16110042,
            doi = {10.48660/16110042},
            url = {https://pirsa.org/16110042},
            author = {Smith, Graeme},
            keywords = {Other Physics},
            language = {en},
            title = {Uniform Additivity},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2016},
            month = {nov},
            note = {PIRSA:16110042 see, \url{https://scivideos.org/index.php/pirsa/16110042}}
          }

Graeme Smith University of Colorado Boulder

Talk numberPIRSA:16110042
DOI10.48660/16110042
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more accurate and complete theory with new and more powerful possibilities for information processing. The goal of both classical and quantum information theory is to quantify the optimal rates of interconversion of different resources. These rates are usually characterized in terms of entropies. However, nonadditivity of many entropic formulas often makes finding answers to information theoretic questions intractable. In a few auspicious cases, such as the classical capacity of a classical channel, the capacity region of a multiple access channel and the entanglement assisted capacity of a quantum channel, additivity allows a full characterization of optimal rates. Here we present a new mathematical property of entropic formulas, uniform additivity, that is both easily evaluated and rich enough to capture all known quantum additive formulas. We give a complete characterization of uniformly additive functions using the linear programming approach to entropy inequalities. In addition to all known quantum formulas, we find a new and intriguing additive quantity: the completely coherent information. We also uncover a remarkable coincidence---the classical and quantum uniformly additive functions are identical; the tractable answers in classical and quantum information theory are formally equivalent.