Title
A tight lower bound on the classical communication cost of entanglement dilution
Abstract
Suppose two distant observers, Alice and Bob, share some form of entanglement - quantum correlations - in some bipartite pure quantum states. They may apply local operations and classical communication to convert one form of entanglement to another. Since entanglement is regarded as a resource in quantum information processing, it is an important question to ask how much classical communication, which is also a resource, is needed in the inter-conversion process of entanglement. In this paper, we address this important question in the many-copy case. The inter-conversion process of entanglement is usually divided into two types: concentrating the entanglement from many partially entangled states into a smaller number of maximally entangled states (i.e., singlets) and the reverse process of diluting singlets into partially entangled states. It is known that entanglement concentration requires no classical communication, but the best prior art result for diluting to N copies of a partially entangled state requires an amount of communication on the order of √N. Our main result is to prove that this prior art result is optimal up to a constant factor; any procedure for approximately creating N partially entangled states from singlets requires Ω(√N) bits of classical communication. Previously not even a constant bound was known for approximate entanglement transformations. We also prove a lower bound on the inefficiency of the process: to dilute singlets to N copies of a partially entangled state, the entropy of entanglement must decrease by Ω(√N). Moreover, we introduce two new tools - δ-significant subspaces and the standard form protocol reduction in entanglement manipulations. We hope that these two new tools will be useful in other work in quantum information theory.
Year
DOI
Venue
2004
10.1109/TIT.2003.822597
IEEE Transactions on Information Theory
Keywords
DocType
Volume
bipartite pure quantum states,classical communication cost,protocols,entanglement dilution,bipartite pure state entanglement,quantum information theory,quantum entanglement,bbps algorithm,tight lower bound,quantum correlations,inter-conversion process,many-copy case,partially entangled states,singlets,δ-significant subspaces,entropy,quantum communication,protocol reduction,quantum information,indexing terms,quantum physics,lower bound
Journal
50
Issue
ISSN
ISBN
2
0018-9448
0-7803-7728-1
Citations 
PageRank 
References 
13
1.25
4
Authors
2
Name
Order
Citations
PageRank
Aram W. Harrow134634.38
Hoi-Kwong Lo2638.42