2,474 research outputs found
Unique decompositions, faces, and automorphisms of separable states
Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a
representation as a convex combination of k pure product states, or fewer. If
m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that
V_k is dense and open in S_k, and such that each state in V_k has a unique
decomposition as a convex combination of pure product states, and we describe
all possible convex decompositions for a set of separable states that properly
contains V_k. In both cases we describe the associated faces of the space of
separable states, which in the first case are simplexes, and in the second case
are direct convex sums of faces that are isomorphic to state spaces of full
matrix algebras. As an application of these results, we characterize all affine
automorphisms of the convex set of separable states, and all automorphisms of
the state space of B(C^m otimes C^n). that preserve entanglement and
separability.Comment: Since original version:Cor. 6 revised and renamed Thm 6, some
definitions added before Cor. 11, introduction revised and references added,
typos correcte
Local rigidity for actions of Kazhdan groups on non commutative -spaces
Given a discrete group , a finite factor and a real
number with we are concerned with the rigidity
of actions of by linear isometries on the -spaces associated to . More precisely, we show that, when and
have both Property (T) and under some natural ergodicity
condition, such an action is locally rigid in the group of linear
isometries of , that is, every sufficiently small perturbation
of is conjugate to under . As a consequence, when is an
ICC Kazhdan group, the action of on its von Neumann algebra , given by conjugation, is locally rigid in the isometry group of
Comment: 20 page
Unconventional antiferromagnetic correlations of the doped Haldane gap system YBaNiZnO
We make a new proposal to describe the very low temperature susceptibility of
the doped Haldane gap compound YBaNiZnO. We propose a new
mean field model relevant for this compound. The ground state of this mean
field model is unconventional because antiferromagnetism coexists with random
dimers. We present new susceptibility experiments at very low temperature. We
obtain a Curie-Weiss susceptibility as expected
for antiferromagnetic correlations but we do not obtain a direct signature of
antiferromagnetic long range order. We explain how to obtain the ``impurity''
susceptibility by subtracting the Haldane gap contribution to
the total susceptibility. In the temperature range [1 K, 300 K] the
experimental data are well fitted by . In the temperature range [100 mK, 1 K] the experimental data are
well fitted by , where increases with
. This fit suggests the existence of a finite N\'eel temperature which is
however too small to be probed directly in our experiments. We also obtain a
maximum in the temperature dependence of the ac-susceptibility which
suggests the existence of antiferromagnetic correlations at very low
temperature.Comment: 19 pages, 17 figures, revised version (minor modifications
An automated and versatile ultra-low temperature SQUID magnetometer
We present the design and construction of a SQUID-based magnetometer for
operation down to temperatures T = 10 mK, while retaining the compatibility
with the sample holders typically used in commercial SQUID magnetometers. The
system is based on a dc-SQUID coupled to a second-order gradiometer. The sample
is placed inside the plastic mixing chamber of a dilution refrigerator and is
thermalized directly by the 3He flow. The movement though the pickup coils is
obtained by lifting the whole dilution refrigerator insert. A home-developed
software provides full automation and an easy user interface.Comment: RevTex, 10 pages, 10 eps figures. High-resolution figures available
upon reques
The effects of nuclear spins on the quantum relaxation of the magnetization for the molecular nanomagnet Fe_8
The strong influence of nuclear spins on resonant quantum tunneling in the
molecular cluster Fe_8 is demonstrated for the first time by comparing the
relaxation rate of the standard Fe_8 sample with two isotopic modified samples:
(i) 56_Fe is replaced by 57_Fe, and (ii) a fraction of 1_H is replaced by 2_H.
By using a recently developed "hole digging" method, we measured an intrinsic
broadening which is driven by the hyperfine fields. Our measurements are in
good agreement with numerical hyperfine calculations. For T > 1.5 K, the
influence of nuclear spins on the relaxation rate is less important, suggesting
that spin-phonon coupling dominates the relaxation rate at higher temperature.Comment: 4 pages, 5 figure
Classical and nonclassical randomness in quantum measurements
The space of positive operator-valued measures on the Borel sets of a compact
(or even locally compact) Hausdorff space with values in the algebra of linear
operators acting on a d-dimensional Hilbert space is studied from the
perspectives of classical and non-classical convexity through a transform
that associates any positive operator-valued measure with a certain
completely positive linear map of the homogeneous C*-algebra
into . This association is achieved by using an operator-valued integral
in which non-classical random variables (that is, operator-valued functions)
are integrated with respect to positive operator-valued measures and which has
the feature that the integral of a random quantum effect is itself a quantum
effect. A left inverse for yields an integral representation,
along the lines of the classical Riesz Representation Theorem for certain
linear functionals on , of certain (but not all) unital completely
positive linear maps . The extremal and
C*-extremal points of the space of POVMS are determined.Comment: to appear in Journal of Mathematical Physic
Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum
Every completely positive map G that commutes which the Hamiltonian time
evolution is an integral or sum over (densely defined) CP-maps G_\sigma where
\sigma is the energy that is transferred to or taken from the environment. If
the spectrum is non-degenerated each G_\sigma is a dephasing channel followed
by an energy shift. The dephasing is given by the Hadamard product of the
density operator with a (formally defined) positive operator. The Kraus
operator of the energy shift is a partial isometry which defines a translation
on R with respect to a non-translation-invariant measure.
As an example, I calculate this decomposition explicitly for the rotation
invariant gaussian channel on a single mode.
I address the question under what conditions a covariant channel destroys
superpositions between mutually orthogonal states on the same orbit. For
channels which allow mutually orthogonal output states on the same orbit, a
lower bound on the quantum capacity is derived using the Fourier transform of
the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly
specified. Presentation more detailed. Implementing the shift after the
dephasing is sometimes more convenien
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