9,889 research outputs found
A framework for bounding nonlocality of state discrimination
We consider the class of protocols that can be implemented by local quantum
operations and classical communication (LOCC) between two parties. In
particular, we focus on the task of discriminating a known set of quantum
states by LOCC. Building on the work in the paper "Quantum nonlocality without
entanglement" [BDF+99], we provide a framework for bounding the amount of
nonlocality in a given set of bipartite quantum states in terms of a lower
bound on the probability of error in any LOCC discrimination protocol. We apply
our framework to an orthonormal product basis known as the domino states and
obtain an alternative and simplified proof that quantifies its nonlocality. We
generalize this result for similar bases in larger dimensions, as well as the
"rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl
Tameness and Artinianness of Graded Generalized Local Cohomology Modules
Let , \fa\supseteq \bigoplus_{n> 0}R_n and
and be a standard graded ring, an ideal of and two finitely generated
graded -modules, respectively. This paper studies the homogeneous components
of graded generalized local cohomology modules. First of all, we show that for
all , H^i_{\fa}(M, N)_n, the -th graded component of the -th
generalized local cohomology module of and with respect to \fa,
vanishes for all . Furthermore, some sufficient conditions are proposed
to satisfy the equality \sup\{\en(H^i_{\fa}(M, N))| i\geq 0\}=
\sup\{\en(H^i_{R_+}(M, N))| i\geq 0\}. Some sufficient conditions are also
proposed for tameness of H^i_{\fa}(M, N) such that i= f_{\fa}^{R_+}(M, N)
or i= \cd_{\fa}(M, N), where f_{\fa}^{R_+}(M, N) and \cd_{\fa}(M, N)
denote the -finiteness dimension and the cohomological dimension of
and with respect to \fa, respectively. We finally consider the Artinian
property of some submodules and quotient modules of H^j_{\fa}(M, N), where
is the first or last non-minimax level of H^i_{\fa}(M, N).Comment: 18pages, with some revisions and correction
Asymptotically optimal cooperative wireless networks with reduced signaling complexity
This paper considers an orthogonal amplify-and-forward (OAF) protocol for cooperative relay communication over Rayleigh-fading channels in which the intermediate relays are permitted to linearly transform the received signal and where the source and relays transmit for equal time durations. The diversity-multiplexing gain (D-MG) tradeoff of the equivalent space-time channel associated to this protocol is determined and a cyclic-division-algebra-based D-MG optimal code constructed. The transmission or signaling alphabet of this code is the union of the QAM constellation and a rotated version of QAM. The size of this signaling alphabet is small in comparison with prior D-MG optimal constructions in the literature and is independent of the number of participating nodes in the network
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