Toronto Quantum Information Seminar
                     Friday March 3, 11-12noon     
                     Fields Institute Room 230



SPEAKER:  Mary Beth Ruskai (Tufts University and Perimeter Institute)

TITLE:    Recent Results Motivated by Investigations of the 
          Additivity  Conjectures in Quantum Information Theory

ABSTRACT: Shor showed that several long-standing conjectures 
          in quantum  information theory, namely,  super-
          additivity of the entanglement of formation 
          and additivity (under tensor  products) of the 
          entanglement of formation, the Holevo capacity of a 
          channel and  the minimal output entropy of a channel 
          are equivalent.   Moreover, the latter (and hence all) 
          would follow from a related conjecture about  
          multiplicativity (for 1 < p < 2) of the maximal 
          p-norm measure of optimal output  purity of a 
          quantum channel.

          Investigations into the last conjecture have stimulated 
          related work.  One is a multiplicativity result for 
          completely bounded (CB) norms which proves additivity 
          of a form of conditional entropy which measures the 
          extent to which a channel breaks entanglement.   Another 
          is the study of the properties of conjugate channels, 
          which describe the  environment's view of a state.    
          Recently, Jencova connected these concepts by showing 
          that p -> p norm of a channel equals the 1 -> p CB norm 
          of its conjugate.

          This talk will provide a overview of these results, with 
          the emphasis on explaining mathematical concepts, such 
          as CB norms, to people in quantum information theory.