175 research outputs found
Catalytic Conversion Probabilities for Bipartite Pure States
For two given bipartite-entangled pure states, an expression is obtained for
the least upper bound of conversion probabilities using catalysis. The
attainability of the upper bound can also be decided if that bound is less than
one.Comment: 4 pages; comments appreciated; the article is a modified version of
this preprint combined with arXiv:0707.044
Low-authority control synthesis for large space structures
The control of vibrations of large space structures by distributed sensors and actuators is studied. A procedure is developed for calculating the feedback loop gains required to achieve specified amounts of damping. For moderate damping (Low Authority Control) the procedure is purely algebraic, but it can be applied iteratively when larger amounts of damping are required and is generalized for arbitrary time invariant systems
Gyrodampers for large space structures
The problem of controlling the vibrations of a large space structures by the use of actively augmented damping devices distributed throughout the structure is addressed. The gyrodamper which consists of a set of single gimbal control moment gyros which are actively controlled to extract the structural vibratory energy through the local rotational deformations of the structure, is described and analyzed. Various linear and nonlinear dynamic simulations of gyrodamped beams are shown, including results on self-induced vibrations due to sensor noise and rotor imbalance. The complete nonlinear dynamic equations are included. The problem of designing and sizing a system of gyrodampers for a given structure, or extrapolating results for one gyrodamped structure to another is solved in terms of scaling laws. Novel scaling laws for gyro systems are derived, based upon fundamental physical principles, and various examples are given
The multiplicative property characterizes and norms
We show that norms are characterized as the unique norms which are
both invariant under coordinate permutation and multiplicative with respect to
tensor products. Similarly, the norms are the unique
rearrangement-invariant norms on a probability space such that for every pair of independent random variables. Our
proof relies on Cram\'er's large deviation theorem.Comment: 8 pages, 1 figur
Phase transitions for random states and a semi-circle law for the partial transpose
For a system of N identical particles in a random pure state, there is a
threshold k_0 = k_0(N) ~ N/5 such that two subsystems of k particles each
typically share entanglement if k > k_0, and typically do not share
entanglement if k < k_0. By "random" we mean here "uniformly distributed on the
sphere of the corresponding Hilbert space." The analogous phase transition for
the positive partial transpose (PPT) property can be described even more
precisely. For example, for N qubits the two subsystems of size k are typically
in a PPT state if k
k_1. Since, for a given state of the entire system, the induced state of a
subsystem is given by the partial trace, the above facts can be rephrased as
properties of random induced states. An important step in the analysis depends
on identifying the asymptotic spectral density of the partial transposes of
such random induced states, a result which is interesting in its own right.Comment: 5 pages, 2 figures. This short note contains a high-level overview of
two long and technical papers, arXiv:1011.0275 and arXiv:1106.2264. Version
2: unchanged results, editorial changes, added reference, close to the
published articl
Non-additivity of Renyi entropy and Dvoretzky's Theorem
The goal of this note is to show that the analysis of the minimum output
p-Renyi entropy of a typical quantum channel essentially amounts to applying
Milman's version of Dvoretzky's Theorem about almost Euclidean sections of
high-dimensional convex bodies. This conceptually simplifies the
(nonconstructive) argument by Hayden-Winter disproving the additivity
conjecture for the minimal output p-Renyi entropy (for p>1).Comment: 8 pages, LaTeX; v2: added and updated references, minor editorial
changes, no content change
Hastings' additivity counterexample via Dvoretzky's theorem
The goal of this note is to show that Hastings' counterexample to the
additivity of minimal output von Neumann entropy can be readily deduced from a
sharp version of Dvoretzky's theorem on almost spherical sections of convex
bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the
paper essentially self-containe
On the structure of the body of states with positive partial transpose
We show that the convex set of separable mixed states of the 2 x 2 system is
a body of constant height. This fact is used to prove that the probability to
find a random state to be separable equals 2 times the probability to find a
random boundary state to be separable, provided the random states are generated
uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An
analogous property holds for the set of positive-partial-transpose states for
an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma
How often is a random quantum state k-entangled?
The set of trace preserving, positive maps acting on density matrices of size
d forms a convex body. We investigate its nested subsets consisting of
k-positive maps, where k=2,...,d. Working with the measure induced by the
Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes
of these sets. Our results strongly suggest that the inner set of
(k+1)-positive maps forms a small fraction of the outer set of k-positive maps.
These results are related to analogous bounds for the relative volume of the
sets of k-entangled states describing a bipartite d X d system.Comment: 19 pages in latex, 1 figure include
Weak multiplicativity for random quantum channels
It is known that random quantum channels exhibit significant violations of
multiplicativity of maximum output p-norms for any p>1. In this work, we show
that a weaker variant of multiplicativity nevertheless holds for these
channels. For any constant p>1, given a random quantum channel N (i.e. a
channel whose Stinespring representation corresponds to a random subspace S),
we show that with high probability the maximum output p-norm of n copies of N
decays exponentially with n. The proof is based on relaxing the maximum output
infinity-norm of N to the operator norm of the partial transpose of the
projector onto S, then calculating upper bounds on this quantity using ideas
from random matrix theory.Comment: 21 pages; v2: corrections and additional remark
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