[Theory-Talk] [Talk] 2017/02/15 Round Complexity in the Local Transformations of Quantum and Classical States

[洪琮眩]

*Topic：*Round Complexity in the Local Transformations of Quantum and
Classical States

*Speaker：*Prof. Min-Hsiu Hsieh (University of Technology Sydney)

*Location：*Auditorium 106 at IIS new Building

*Date：* 2017-02-15 (Wed) 14:00 – 16:00
*Abstract:*

A natural operational paradigm for distributed quantum and classical
information processing involves local operations coordinated by multiple
rounds of public communication. In this paper we consider the minimum
number of communication rounds needed to perform the locality-constrained
task of entanglement transformation and the analogous classical task of
secrecy manipulation. Specifically we address whether bipartite mixed
entanglement can always be converted into pure entanglement or whether
unsecure classical correlations can always be transformed into secret
shared randomness using local operations and a bounded number of
communication exchanges. Our main contribution in this paper is an explicit
construction of quantum and classical state transformations which, for any
given r, can be achieved using r rounds of classical communication
exchanges but no fewer. Our results reveal that highly complex
communication protocols are indeed necessary to fully harness the
information-theoretic resources contained in general quantum and classical
states. The major technical contribution of this manuscript lies in proving
lower bounds for the required number of communication exchanges using the
notion of common information and various lemmas built upon it. We propose a
classical analog to the Schmidt rank of a bipartite quantum state which we
call the secrecy rank, and we show that it is a monotone under stochastic
local classical operations. This is a joint work with Eric Chitambar.
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