1,396 research outputs found
The Least Action Principle And The Spin Of Galaxies In The Local Group
Using Peebles' least action principle, we determine trajectories for the
galaxies in the Local Group and the more massive galaxies in the Local
Neighbourhood. We deduce the resulting angular momentum for the whole of the
Local Group and study the tidal force acting on the Local Group and its
galaxies. Although Andromeda and the Milky Way dominate the tidal force acting
on each other during the present epoch, we show that there is a transition time
at before which the tidal force is dominated by galaxies outside
the Local Group in each case. This shows that the Local Group can not be
considered as an isolated system as far as the tidal forces are concerned. We
integrate the tidal torques acting on the Milky Way and Andromeda and derive
their spin angular momenta, obtaining results which are comparable with
observation.Comment: 16 pages (5 figures available on request), plain TeX, IoA-93-01-AM
Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule
The Born rule is at the foundation of quantum mechanics and transforms our
classical way of understanding probabilities by predicting that interference
occurs between pairs of independent paths of a single object. One consequence
of the Born rule is that three way (or three paths) quantum interference does
not exist. In order to test the consistency of the Born rule, we examine
detection probabilities in three path intereference using an ensemble of
spin-1/2 quantum registers in liquid state nuclear magnetic resonance (LSNMR).
As a measure of the consistency, we evaluate the ratio of three way
interference to two way interference. Our experiment bounded the ratio to the
order of , and hence it is consistent with Born's rule.Comment: 11 pages, 4 figures; Improved presentation of figures 1 and 4,
changes made in section 2 to better describe the experiment, minor changes
throughout, and added several reference
Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
We compare pseudopure state ensemble implementations, quantified by their
initial polarization and ensemble size, of Grover's search algorithm to
probabilistic classical sequential search algorithms in terms of their success
and failure probabilities. We propose a criterion for quantifying the resources
used by the ensemble implementation via the aggregate number of oracle
invocations across the entire ensemble and use this as a basis for comparison
with classical search algorithms. We determine bounds for a critical
polarization such that the ensemble algorithm succeeds with a greater
probability than the probabilistic classical sequential search. Our results
indicate that the critical polarization scales as N^(-1/4) where N is the
database size and that for typical room temperature solution state NMR, the
polarization is such that the ensemble implementation of Grover's algorithm
would be advantageous for N > 10^2
Optimizing the discrete time quantum walk using a SU(2) coin
We present a generalized version of the discrete time quantum walk, using the
SU(2) operation as the quantum coin. By varying the coin parameters, the
quantum walk can be optimized for maximum variance subject to the functional
form and the probability distribution in the position
space can be biased. We also discuss the variation in measurement entropy with
the variation of the parameters in the SU(2) coin. Exploiting this we show how
quantum walk can be optimized for improving mixing time in an -cycle and for
quantum walk search.Comment: 6 pages, 6 figure
Experimental approximation of the Jones polynomial with DQC1
We present experimental results approximating the Jones polynomial using 4
qubits in a liquid state nuclear magnetic resonance quantum information
processor. This is the first experimental implementation of a complete problem
for the deterministic quantum computation with one quantum bit model of quantum
computation, which uses a single qubit accompanied by a register of completely
random states. The Jones polynomial is a knot invariant that is important not
only to knot theory, but also to statistical mechanics and quantum field
theory. The implemented algorithm is a modification of the algorithm developed
by Shor and Jordan suitable for implementation in NMR. These experimental
results show that for the restricted case of knots whose braid representations
have four strands and exactly three crossings, identifying distinct knots is
possible 91% of the time.Comment: 5 figures. Version 2 changes: published version, minor errors
corrected, slight changes to improve readabilit
Quantum phase transition using quantum walks in an optical lattice
We present an approach using quantum walks (QWs) to redistribute ultracold
atoms in an optical lattice. Different density profiles of atoms can be
obtained by exploiting the controllable properties of QWs, such as the variance
and the probability distribution in position space using quantum coin
parameters and engineered noise. The QW evolves the density profile of atoms in
a superposition of position space resulting in a quadratic speedup of the
process of quantum phase transition. We also discuss implementation in
presently available setups of ultracold atoms in optical lattices.Comment: 7 pages, 8 figure
Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance
The role of mixed state entanglement in liquid-state nuclear magnetic
resonance (NMR) quantum computation is not yet well-understood. In particular,
despite the success of quantum information processing with NMR, recent work has
shown that quantum states used in most of those experiments were not entangled.
This is because these states, derived by unitary transforms from the thermal
equilibrium state, were too close to the maximally mixed state. We are thus
motivated to determine whether a given NMR state is entanglable - that is, does
there exist a unitary transform that entangles the state? The boundary between
entanglable and nonentanglable thermal states is a function of the spin system
size and its temperature . We provide new bounds on the location of this
boundary using analytical and numerical methods; our tightest bound scales as
, giving a lower bound requiring at least proton
spins to realize an entanglable thermal state at typical laboratory NMR
magnetic fields. These bounds are tighter than known bounds on the
entanglability of effective pure states.Comment: REVTeX4, 15 pages, 4 figures (one large figure: 414 K
Quantifying nonclassicality: global impact of local unitary evolutions
We show that only those composite quantum systems possessing nonvanishing
quantum correlations have the property that any nontrivial local unitary
evolution changes their global state. We derive the exact relation between the
global state change induced by local unitary evolutions and the amount of
quantum correlations. We prove that the minimal change coincides with the
geometric measure of discord (defined via the Hilbert- Schmidt norm), thus
providing the latter with an operational interpretation in terms of the
capability of a local unitary dynamics to modify a global state. We establish
that two-qubit Werner states are maximally quantum correlated, and are thus the
ones that maximize this type of global quantum effect. Finally, we show that
similar results hold when replacing the Hilbert-Schmidt norm with the trace
norm.Comment: 5 pages, 1 figure. To appear in Physical Review
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