Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of causal order structure in distributed quantum information
  processing and its trade-off with entanglement   We prove a trade-off relation between the entanglement cost and classical
communication complexity of causal order structure of a protocol in distributed
quantum information processing. We consider an implementation of a class of
two-qubit unitary gates by local operations and classical communication (LOCC)
assisted with shared entanglement, in an information theoretical scenario of
asymptotically many input pairs and vanishingly small error. We prove the
trade-off relation by showing that (i) one ebit of entanglement per pair is
necessary for implementing the unitary by any two-round protocol, and that (ii)
the entanglement cost by a three-round protocol is strictly smaller than one
ebit per pair. We also provide an example of bipartite unitary gates for which
there is no such trade-off.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat