314 research outputs found
Comment on "Probabilistic Quantum Memories"
This is a comment on two wrong Phys. Rev. Letters papers by C.A.
Trugenberger. Trugenberger claimed that quantum registers could be used as
exponentially large "associative" memories. We show that his scheme is no
better than one where the quantum register is replaced with a classical one of
equal size.
We also point out that the Holevo bound and more recent bounds on "quantum
random access codes" pretty much rule out powerful memories (for classical
information) based on quantum states.Comment: REVTeX4, 1 page, published versio
Religion without fear: Plutarch on superstition and early Christian literature
After some introductory remarks on the role of fear in religious discourse
and on the vocabulary, Plutarch's treatise On Superstition
is analysed according to its rhetorical outline. Questions of authenticity are
discussed and answered by locating The essay in Plutarch's early career.
Then we ask for the place of ''fear of God" in biblical teaching and
theology, compare it to Plutarch and show some limits in Plutarch's
youthful thinking, which doesn't yet pay due respect to the life values of
myth. We conclude with two New Testament passages, Romans 8:15,
masterfully interpreted by Martin Luther, and 1 John 4:17f, excellently
explained by 20th century's Swiss theologian and psychologian Oskar
Pfister, and we show that these texts are propagating "belief without fear".Continued 2001 as 'Verbum et Ecclesia'Spine cut of Journal binding and pages scanned on flatbed EPSON Expression 10000 XL; 400dpi; text/lineart - black and white - stored to Tiff Derivation: Abbyy Fine Reader v.9 work with PNG-format (black and white); Photoshop CS3; Adobe Acrobat v.9 Web display format PDFhttp://explore.up.ac.za/record=b102527
New bounds on the classical and quantum communication complexity of some graph properties
We study the communication complexity of a number of graph properties where
the edges of the graph are distributed between Alice and Bob (i.e., each
receives some of the edges as input). Our main results are:
* An Omega(n) lower bound on the quantum communication complexity of deciding
whether an n-vertex graph G is connected, nearly matching the trivial classical
upper bound of O(n log n) bits of communication.
* A deterministic upper bound of O(n^{3/2}log n) bits for deciding if a
bipartite graph contains a perfect matching, and a quantum lower bound of
Omega(n) for this problem.
* A Theta(n^2) bound for the randomized communication complexity of deciding
if a graph has an Eulerian tour, and a Theta(n^{3/2}) bound for the quantum
communication complexity of this problem.
The first two quantum lower bounds are obtained by exhibiting a reduction
from the n-bit Inner Product problem to these graph problems, which solves an
open question of Babai, Frankl and Simon. The third quantum lower bound comes
from recent results about the quantum communication complexity of composed
functions. We also obtain essentially tight bounds for the quantum
communication complexity of a few other problems, such as deciding if G is
triangle-free, or if G is bipartite, as well as computing the determinant of a
distributed matrix.Comment: 12 pages LaTe
Quantum and classical strong direct product theorems and optimal time-space tradeoffs
A strong direct product theorem says that if we want to compute
independent instances of a function, using less than times
the resources needed for one instance, then our overall success
probability will be exponentially small in .
We establish such theorems for the classical as well as quantum
query complexity of the OR-function. This implies slightly
weaker direct product results for all total functions.
We prove a similar result for quantum communication
protocols computing instances of the disjointness function.
Our direct product theorems imply a time-space tradeoff
T^2S=\Om{N^3} for sorting items on a quantum computer, which
is optimal up to polylog factors. They also give several tight
time-space and communication-space tradeoffs for the problems of
Boolean matrix-vector multiplication and matrix multiplication
Unbounded-Error Classical and Quantum Communication Complexity
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86},
the unbounded-error classical communication complexity of a Boolean function
has been studied based on the arrangement of points and hyperplanes. Recently,
\cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum}
communication complexity in the {\em one-way communication} model can also be
investigated using the arrangement, and showed that it is exactly (without a
difference of even one qubit) half of the classical one-way communication
complexity. In this paper, we extend the arrangement argument to the {\em
two-way} and {\em simultaneous message passing} (SMP) models. As a result, we
show similarly tight bounds of the unbounded-error two-way/one-way/SMP
quantum/classical communication complexities for {\em any} partial/total
Boolean function, implying that all of them are equivalent up to a
multiplicative constant of four. Moreover, the arrangement argument is also
used to show that the gap between {\em weakly} unbounded-error quantum and
classical communication complexities is at most a factor of three.Comment: 11 pages. To appear at Proc. ISAAC 200
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