17 research outputs found
Optimal Decompositions of Barely Separable States
Two families of bipartite mixed quantum states are studied for which it is
proved that the number of members in the optimal-decomposition ensemble --- the
ensemble realizing the entanglement of formation --- is greater than the rank
of the mixed state. We find examples for which the number of states in this
optimal ensemble can be larger than the rank by an arbitrarily large factor. In
one case the proof relies on the fact that the partial transpose of the mixed
state has zero eigenvalues; in the other case the result arises from the
properties of product bases that are completable only by embedding in a larger
Hilbert space.Comment: 14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of
the J. Mod. Opt. V2: Change in terminology from "ensemble length" to
"ensemble cardinality
Exact and Asymptotic Measures of Multipartite Pure State Entanglement
In an effort to simplify the classification of pure entangled states of multi
(m) -partite quantum systems, we study exactly and asymptotically (in n)
reversible transformations among n'th tensor powers of such states (ie n copies
of the state shared among the same m parties) under local quantum operations
and classical communication (LOCC). With regard to exact transformations, we
show that two states whose 1-party entropies agree are either locally-unitarily
(LU) equivalent or else LOCC-incomparable. In particular we show that two
tripartite Greenberger-Horne-Zeilinger (GHZ) states are LOCC-incomparable to
three bipartite Einstein-Podolsky-Rosen (EPR) states symmetrically shared among
the three parties. Asymptotic transformations result in a simpler
classification than exact transformations. We show that m-partite pure states
having an m-way Schmidt decomposition are simply parameterizable, with the
partial entropy across any nontrivial partition representing the number of
standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the
state in question. For general m-partite states, partial entropies across
different partitions need not be equal, and since partial entropies are
conserved by asymptotically reversible LOCC operations, a multicomponent
entanglement measure is needed, with each scalar component representing a
different kind of entanglement, not asymptotically interconvertible to the
other kinds. In particular the m=4 Cat state is not isentropic to, and
therefore not asymptotically interconvertible to, any combination of bipartite
and tripartite states shared among the four parties. Thus, although the m=4 cat
state can be prepared from bipartite EPR states, the preparation process is
necessarily irreversible, and remains so even asymptotically.Comment: 13 pages including 3 PostScript figures. v3 has updated references
and discussion, to appear Phys. Rev.
MaXM: Towards Multilingual Visual Question Answering
Visual Question Answering (VQA) has been primarily studied through the lens
of the English language. Yet, tackling VQA in other languages in the same
manner would require a considerable amount of resources. In this paper, we
propose scalable solutions to multilingual visual question answering (mVQA), on
both data and modeling fronts. We first propose a translation-based framework
to mVQA data generation that requires much less human annotation efforts than
the conventional approach of directly collection questions and answers. Then,
we apply our framework to the multilingual captions in the Crossmodal-3600
dataset and develop an efficient annotation protocol to create MaXM, a
test-only VQA benchmark in 7 diverse languages. Finally, we develop a simple,
lightweight, and effective approach as well as benchmark state-of-the-art
English and multilingual VQA models. We hope that our benchmark encourages
further research on mVQA.Comment: EMNLP 2023 (Findings).
https://github.com/google-research-datasets/max
The Power of LOCCq State Transformations
Reversible state transformations under entanglement non-increasing operations
give rise to entanglement measures. It is well known that asymptotic local
operations and classical communication (LOCC) are required to get a simple
operational measure of bipartite pure state entanglement. For bipartite mixed
states and multipartite pure states it is likely that a more powerful class of
operations will be needed. To this end \cite{BPRST01} have defined more
powerful versions of state transformations (or reducibilities), namely LOCCq
(asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC
(asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state
transformations are only as powerful as asymptotic LOCC state transformations}
for multipartite pure states. We first generalize the concept of entanglement
gambling from two parties to multiple parties: any pure multipartite entangled
state can be transformed to an EPR pair shared by some pair of parties and that
any irreducible party pure state can be used to create any other
state (pure or mixed), using only local operations and classical communication
(LOCC). We then use this tool to prove the result. We mention some applications
of multipartite entanglement gambling to multipartite distillability and to
characterizations of multipartite minimal entanglement generating sets. Finally
we discuss generalizations of this result to mixed states by defining the class
of {\em cat distillable states}
Evidence for Bound Entangled States with Negative Partial Transpose
We exhibit a two-parameter family of bipartite mixed states , in a
Hilbert space, which are negative under partial transposition
(NPT), but for which we conjecture that no maximally entangled pure states in
can be distilled by local quantum operations and classical
communication (LQ+CC). Evidence for this undistillability is provided by the
result that, for certain states in this family, we cannot extract entanglement
from any arbitrarily large number of copies of using a projection
on . These states are canonical NPT states in the sense that any
bipartite mixed state in any dimension with NPT can be reduced by LQ+CC
operations to an NPT state of the form. We show that the main
question about the distillability of mixed states can be formulated as an open
mathematical question about the properties of composed positive linear maps.Comment: Revtex, 19 pages, 2 eps figures. v2,3: very minor changes, submitted
to Phys. Rev. A. v4: minor typos correcte