6,465 research outputs found
Upper Bound on the region of Separable States near the Maximally Mixed State
A lower bound on the amount of noise that must be added to a GHZ-like
entangled state to make it separable (also called the random robustness) is
found using the transposition condition. The bound is applicable to arbitrary
numbers of subsystems, and dimensions of Hilbert space, and is shown to be
exact for qubits. The new bound is compared to previous such bounds on this
quantity, and found to be stronger in all cases. It implies that increasing the
number of subsystems, rather than increasing their Hilbert space dimension is a
more effective way of increasing entanglement. An explicit decomposition into
an ensemble of separable states, when the state is not entangled,is given for
the case of qubits.Comment: 2 figures. accepted J. Opt. B: Quantum Semiclass. Opt. (2000
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
Quantum error correction via robust probe modes
We propose a new scheme for quantum error correction using robust continuous
variable probe modes, rather than fragile ancilla qubits, to detect errors
without destroying data qubits. The use of such probe modes reduces the
required number of expensive qubits in error correction and allows efficient
encoding, error detection and error correction. Moreover, the elimination of
the need for direct qubit interactions significantly simplifies the
construction of quantum circuits. We will illustrate how the approach
implements three existing quantum error correcting codes: the 3-qubit bit-flip
(phase-flip) code, the Shor code, and an erasure code.Comment: 5 pages, 3 figure
Ontology mapping neural network: An approach to learning and inferring correspondences among ontologies
An ontology mapping neural network (OMNN) is proposed in order to learn and infer correspondences among ontologies. It extends the Identical Elements Neural Network (IENN)'s ability to represent and map complex relationships. The learning dynamics of simultaneous (interlaced) training of similar tasks interact at the shared connections of the networks. The output of one network in response to a stimulus to another network can be interpreted as an analogical mapping. In a similar fashion, the networks can be explicitly trained to map specific items in one domain to specific items in another domain. Representation layer helps the network learn relationship mapping with direct training method. OMNN is applied to several OAEI benchmark test cases to test its performance on ontology mapping. Results show that OMNN approach is competitive to the top performing systems that participated in OAEI 2009
Solving k-center Clustering (with Outliers) in MapReduce and Streaming, almost as Accurately as Sequentially.
Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular k-center variant which, given a set S of points from some metric space and a parameter k0, the algorithms yield solutions whose approximation ratios are a mere additive term \u3f5 away from those achievable by the best known polynomial-time sequential algorithms, a result that substantially improves upon the state of the art. Our algorithms are rather simple and adapt to the intrinsic complexity of the dataset, captured by the doubling dimension D of the metric space. Specifically, our analysis shows that the algorithms become very space-efficient for the important case of small (constant) D. These theoretical results are complemented with a set of experiments on real-world and synthetic datasets of up to over a billion points, which show that our algorithms yield better quality solutions over the state of the art while featuring excellent scalability, and that they also lend themselves to sequential implementations much faster than existing ones
Attaining subclassical metrology in lossy systems with entangled coherent states
Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the potential to perform robust subclassical measurements [J. Joo et al., Phys. Rev. Lett. 107, 083601 (2011)]. Up to now no read-out scheme has been devised that exploits this robust nature of ECSs, but we present here an experimentally accessible method of achieving precision close to the theoretical bound, even with loss.We show substantial improvements over unentangled classical states and highly entangled NOON states for a wide range of loss values, elevating quantum metrology to a realizable technology in the near future
Selection from read-only memory with limited workspace
Given an unordered array of elements drawn from a totally ordered set and
an integer in the range from to , in the classic selection problem
the task is to find the -th smallest element in the array. We study the
complexity of this problem in the space-restricted random-access model: The
input array is stored on read-only memory, and the algorithm has access to a
limited amount of workspace. We prove that the linear-time prune-and-search
algorithm---presented in most textbooks on algorithms---can be modified to use
bits instead of words of extra space. Prior to our
work, the best known algorithm by Frederickson could perform the task with
bits of extra space in time. Our result separates
the space-restricted random-access model and the multi-pass streaming model,
since we can surpass the lower bound known for the latter
model. We also generalize our algorithm for the case when the size of the
workspace is bits, where . The running time
of our generalized algorithm is ,
slightly improving over the
bound of Frederickson's algorithm. To obtain the improvements mentioned above,
we developed a new data structure, called the wavelet stack, that we use for
repeated pruning. We expect the wavelet stack to be a useful tool in other
applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201
Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light
We describe a system for long-distance distribution of quantum entanglement,
in which coherent light with large average photon number interacts dispersively
with single, far-detuned atoms or semiconductor impurities in optical cavities.
Entanglement is heralded by homodyne detection using a second bright light
pulse for phase reference. The use of bright pulses leads to a high success
probability for the generation of entanglement, at the cost of a lower initial
fidelity. This fidelity may be boosted by entanglement purification techniques,
implemented with the same physical resources. The need for more purification
steps is well compensated for by the increased probability of success when
compared to heralded entanglement schemes using single photons or weak coherent
pulses with realistic detectors. The principle cause of the lower initial
fidelity is fiber loss; however, spontaneous decay and cavity losses during the
dispersive atom/cavity interactions can also impair performance. We show that
these effects may be minimized for emitter-cavity systems in the weak-coupling
regime as long as the resonant Purcell factor is larger than one, the cavity is
over-coupled, and the optical pulses are sufficiently long. We support this
claim with numerical, semiclassical calculations using parameters for three
realistic systems: optically bright donor-bound impurities such as 19-F:ZnSe
with a moderate-Q microcavity, the optically dim 31-P:Si system with a high-Q
microcavity, and trapped ions in large but very high-Q cavities.Comment: Please consult the published version, where assorted typos are
corrected. It is freely available at http://stacks.iop.org/1367-2630/8/18
Generalized Toffoli gates using qudit catalysis
We present quantum networks for a n-qubit controlled gate C^{n-1}(U) which
use a higher dimensional (qudit) ancilla as a catalyser. In its simplest form
the network has only n two-particle gates (qubit-qudit) -- this is the minimum
number of two-body interactions needed to couple all n+1 subsystems (n qubits
plus one ancilla). This class of controlled gates includes the generalised
Toffoli gate C^{n-1}(X) on n qubits, which plays an important role in several
quantum algorithms and error correction. A particular example implementing this
model is given by the dispersive limit of a generalised Jaynes-Cummings
Hamiltonian of an effective spin-s interacting with a cavity mode.Comment: 5 pages, 3 fig
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