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Round complexity in the local transformations of quantum and classical states
- Source :
- Nature Communications, Vol 8, Iss 1, Pp 1-7 (2017), Nature Communications
- Publication Year :
- 2017
- Publisher :
- Nature Portfolio, 2017.
-
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.<br />Submitted to QIP 2017. Proof strategies have been streamlined and differ from the submitted version
- Subjects :
- Theoretical computer science
Computer science
Science
FOS: Physical sciences
General Physics and Astronomy
02 engineering and technology
Quantum entanglement
01 natural sciences
Article
General Biochemistry, Genetics and Molecular Biology
Quantum state
0103 physical sciences
Secrecy
0202 electrical engineering, electronic engineering, information engineering
lcsh:Science
010306 general physics
Quantum
Randomness
Lemma (mathematics)
Quantum Physics
Multidisciplinary
Rank (computer programming)
TheoryofComputation_GENERAL
020206 networking & telecommunications
General Chemistry
Bounded function
Bipartite graph
lcsh:Q
Quantum Physics (quant-ph)
Subjects
Details
- Language :
- English
- ISSN :
- 20411723
- Volume :
- 8
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Nature Communications
- Accession number :
- edsair.doi.dedup.....03cfd3e87243fca1330a089ea2f29a10