3,473 research outputs found
Bell's theorem without inequalities and without unspeakable information
A proof of Bell's theorem without inequalities is presented in which distant
local setups do not need to be aligned, since the required perfect correlations
are achieved for any local rotation of the local setups.Comment: REVTeX4, 4 pages, 1 figure; for Asher Peres' Festschrift, to be
published in Found. Phy
Implications of quantum automata for contextuality
We construct zero-error quantum finite automata (QFAs) for promise problems
which cannot be solved by bounded-error probabilistic finite automata (PFAs).
Here is a summary of our results:
- There is a promise problem solvable by an exact two-way QFA in exponential
expected time, but not by any bounded-error sublogarithmic space probabilistic
Turing machine (PTM).
- There is a promise problem solvable by an exact two-way QFA in quadratic
expected time, but not by any bounded-error -space PTMs in
polynomial expected time. The same problem can be solvable by a one-way Las
Vegas (or exact two-way) QFA with quantum head in linear (expected) time.
- There is a promise problem solvable by a Las Vegas realtime QFA, but not by
any bounded-error realtime PFA. The same problem can be solvable by an exact
two-way QFA in linear expected time but not by any exact two-way PFA.
- There is a family of promise problems such that each promise problem can be
solvable by a two-state exact realtime QFAs, but, there is no such bound on the
number of states of realtime bounded-error PFAs solving the members this
family.
Our results imply that there exist zero-error quantum computational devices
with a \emph{single qubit} of memory that cannot be simulated by any finite
memory classical computational model. This provides a computational perspective
on results regarding ontological theories of quantum mechanics \cite{Hardy04},
\cite{Montina08}. As a consequence we find that classical automata based
simulation models \cite{Kleinmann11}, \cite{Blasiak13} are not sufficiently
powerful to simulate quantum contextuality. We conclude by highlighting the
interplay between results from automata models and their application to
developing a general framework for quantum contextuality.Comment: 22 page
Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by Quantum Hyper-entanglement
Mermin's observation [Phys. Rev. Lett. {\bf 65}, 1838 (1990)] that the
magnitude of the violation of local realism, defined as the ratio between the
quantum prediction and the classical bound, can grow exponentially with the
size of the system is demonstrated using two-photon hyper-entangled states
entangled in polarization and path degrees of freedom, and local measurements
of polarization and path simultaneously.Comment: Minor errors corrected. To appear on Physical Review Letter
Stronger two-observer all-versus-nothing violation of local realism
We introduce a two-observer all-versus-nothing proof of Bell's theorem which
reduces the number of required quantum predictions from 9 [A. Cabello, Phys.
Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408
(2003)] to 4, provides a greater amount of evidence against local realism,
reduces the detection efficiency requirements for a conclusive experimental
test of Bell's theorem, and leads to a Bell's inequality which resembles
Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65,
1838 (1990)] but requires only two observers.Comment: REVTeX4, 5 page
Greenberger-Horne-Zeilinger-like proof of Bell's theorem involving observers who do not share a reference frame
Vaidman described how a team of three players, each of them isolated in a
remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to
always win a game which would be impossible to always win without quantum
resources. However, Vaidman's method requires all three players to share a
common reference frame; it does not work if the adversary is allowed to
disorientate one player. Here we show how to always win the game, even if the
players do not share any reference frame. The introduced method uses a 12-qubit
state which is invariant under any transformation
(where , where is a
unitary operation on a single qubit) and requires only single-qubit
measurements. A number of further applications of this 12-qubit state are
described.Comment: REVTeX4, 6 pages, 1 figur
No-hidden-variables proof for two spin-1/2 particles preselected and postselected in unentangled states
It is a well-known fact that all the statistical predictions of quantum
mechanics on the state of any physical system represented by a two-dimensional
Hilbert space can always be duplicated by a noncontextual hidden-variables
model. In this paper, I show that, in some cases, when we consider an
additional independent (unentangled) two-dimensional system, the quantum
description of the resulting composite system cannot be reproduced using
noncontextual hidden variables. In particular, a no-hidden-variables proof is
presented for two individual spin-1/2 particles preselected in an uncorrelated
state AB and postselected in another uncorrelated state aB, B being the same
state for the second particle in both preselection and postselection.Comment: LaTeX, 8 page
Finding Multiple New Optimal Locations in a Road Network
We study the problem of optimal location querying for location based services
in road networks, which aims to find locations for new servers or facilities.
The existing optimal solutions on this problem consider only the cases with one
new server. When two or more new servers are to be set up, the problem with
minmax cost criteria, MinMax, becomes NP-hard. In this work we identify some
useful properties about the potential locations for the new servers, from which
we derive a novel algorithm for MinMax, and show that it is efficient when the
number of new servers is small. When the number of new servers is large, we
propose an efficient 3-approximate algorithm. We verify with experiments on
real road networks that our solutions are effective and attains significantly
better result quality compared to the existing greedy algorithms
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