QLunch: Sigurd Storgaard

Speaker: Sigurd Storgaard

Title: The geometry of Bloch space in the context of Quantum Random Access Codes


In this talk, I will discuss a certain communication protocol known as a Quantum Random Access Code (QRAC).  A QRAC is a scheme that encodes n classical bits into m qubits (nm) with the possibility of recovering any of the initial n bits with a probability of at least p>1/2. Such a code is denoted by the triple (n,m,p)-QRAC. I will show how the geometry of the set of quantum states in the Bloch vector representation can be used to find upper bounds on the worst case success probabilities of QRACs. In particular, I will resolve the conjecture put forth in a recent paper by Imamichi and Raymond (2018) regarding an upper bound on p in any (n,2,p)-QRAC.
References:   T.   Imamichi   and   R.   Raymond. ‘Constructions of Quantum Random Access Codes’. Asian Quantum Information Symposium (AQIS), (2018). URL: http://www.ngc.is.ritsumei.ac.jp/~ger/static/AQIS18/OnlineBooklet/122.