472 research outputs found
Comparison of subdominant eigenvalues of some linear search schemes
AbstractThe subdominant eigenvalue of the transition probability matrix of a Markov chain is a determining factor in the speed of transition of the chain to a stationary state. However, these eigenvalues can be difficult to estimate in a theoretical sense. In this paper we revisit the problem of dynamically organizing a linear list. Items in the list are selected with certain unknown probabilities and then returned to the list according to one of two schemes: the move-to-front scheme or the transposition scheme. The eigenvalues of the transition probability matrix Q of the former scheme are well-known but those of the latter T are not. Nevertheless the transposition scheme gives rise to a reversible Markov chain. This enables us to employ a generalized Rayleigh-Ritz theorem to show that the subdominant eigenvalue of T is at least as large as the subdominant eigenvalue of Q
Local discrimination of mixed states
We provide rigorous, efficiently computable and tight bounds on the average
error probability of multiple-copy discrimination between qubit mixed states by
Local Operations assisted with Classical Communication (LOCC). In contrast to
the pure-state case, these experimentally feasible protocols perform strictly
worse than the general collective ones. Our numerical results indicate that the
gap between LOCC and collective error rates persists in the asymptotic limit.
In order for LOCC and collective protocols to achieve the same accuracy, the
former requires up to twice the number of copies of the latter. Our techniques
can be used to bound the power of LOCC strategies in other similar settings,
which is still one of the most elusive questions in quantum communication.Comment: 4 pages, 2 figures+ supplementary materia
The power of symmetric extensions for entanglement detection
In this paper, we present new progress on the study of the symmetric
extension criterion for separability. First, we show that a perturbation of
order O(1/N) is sufficient and, in general, necessary to destroy the
entanglement of any state admitting an N Bose symmetric extension. On the other
hand, the minimum amount of local noise necessary to induce separability on
states arising from N Bose symmetric extensions with Positive Partial Transpose
(PPT) decreases at least as fast as O(1/N^2). From these results, we derive
upper bounds on the time and space complexity of the weak membership problem of
separability when attacked via algorithms that search for PPT symmetric
extensions. Finally, we show how to estimate the error we incur when we
approximate the set of separable states by the set of (PPT) N -extendable
quantum states in order to compute the maximum average fidelity in pure state
estimation problems, the maximal output purity of quantum channels, and the
geometric measure of entanglement.Comment: see Video Abstract at
http://www.quantiki.org/video_abstracts/0906273
Data structures
We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case
On utilizing an enhanced object partitioning scheme to optimize self-organizing lists-on-lists
Author's accepted manuscript.This is a post-peer-review, pre-copyedit version of an article published in Evolving Systems. The final authenticated version is available online at: http://dx.doi.org/10.1007/s12530-020-09327-4.acceptedVersio
Cache-oblivious algorithms
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 67-70).by Harald Prokop.S.M
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