283 research outputs found
Separable approximations of density matrices of composite quantum systems
We investigate optimal separable approximations (decompositions) of states
rho of bipartite quantum systems A and B of arbitrary dimensions MxN following
the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261
(1998)]. Such approximations allow to represent in an optimal way any density
operator as a sum of a separable state and an entangled state of a certain
form. For two qubit systems (M=N=2) the best separable approximation has a form
of a mixture of a separable state and a projector onto a pure entangled state.
We formulate a necessary condition that the pure state in the best separable
approximation is not maximally entangled. We demonstrate that the weight of the
entangled state in the best separable approximation in arbitrary dimensions
provides a good entanglement measure. We prove in general for arbitrary M and N
that the best separable approximation corresponds to a mixture of a separable
and an entangled state which are both unique. We develop also a theory of
optimal separable approximations for states with positive partial transpose
(PPT states). Such approximations allow to decompose any density operator with
positive partial transpose as a sum of a separable state and an entangled PPT
state. We discuss procedures of constructing such decompositions.Comment: 12 pages, 2 figure
Classification of mixed three-qubit states
We introduce a classification of mixed three-qubit states, in which we define
the classes of separable, biseparable, W- and GHZ-states. These classes are
successively embedded into each other. We show that contrary to pure W-type
states, the mixed W-class is not of measure zero. We construct witness
operators that detect the class of a mixed state. We discuss the conjecture
that all entangled states with positive partial transpose (PPTES) belong to the
W-class. Finally, we present a new family of PPTES "edge" states with maximal
ranks.Comment: 4 pages, 1 figur
Quantum magnetism and counterflow supersolidity of up-down bosonic dipoles
We study a gas of dipolar Bosons confined in a two-dimensional optical
lattice. Dipoles are considered to point freely in both up and down directions
perpendicular to the lattice plane. This results in a nearest neighbor
repulsive (attractive) interaction for aligned (anti-aligned) dipoles. We find
regions of parameters where the ground state of the system exhibits insulating
phases with ferromagnetic or anti-ferromagnetic ordering, as well as with
rational values of the average magnetization. Evidence for the existence of a
novel counterflow supersolid quantum phase is also presented.Comment: 8 pages, 6 figure
Separability Criterion for all bipartite Gaussian States
We provide a necessary and sufficient condition for separability of Gaussian
states of bipartite systems of arbitrarily many modes. The condition provides
an operational criterion since it can be checked by simple computation.
Moreover, it allows us to find a pure product-state decomposition of any given
separable Gaussian state. Our criterion is independent of the one based on
partial transposition, and is strictly stronger.Comment: 4 pages, 1 figure (.eps
Differential atom interferometry beyond the standard quantum limit
We analyze methods to go beyond the standard quantum limit for a class of
atomic interferometers, where the quantity of interest is the difference of
phase shifts obtained by two independent atomic ensembles. An example is given
by an atomic Sagnac interferometer, where for two ensembles propagating in
opposite directions in the interferometer this phase difference encodes the
angular velocity of the experimental setup. We discuss methods of squeezing
separately or jointly observables of the two atomic ensembles, and compare in
detail advantages and drawbacks of such schemes. In particular we show that the
method of joint squeezing may improve the variance by up to a factor of 2. We
take into account fluctuations of the number of atoms in both the preparation
and the measurement stage, and obtain bounds on the difference of the numbers
of atoms in the two ensembles, as well as on the detection efficiency, which
have to be fulfilled in order to surpass the standard quantum limit. Under
realistic conditions, the performance of both schemes can be improved
significantly by reading out the phase difference via a quantum non-demolition
(QND) measurement. Finally, we discuss a scheme using macroscopically entangled
ensembles.Comment: 10 pages, 5 figures; eq. (3) corrected and other minor change
Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
Topological insulators are fascinating states of matter exhibiting protected
edge states and robust quantized features in their bulk. Here, we propose and
validate experimentally a method to detect topological properties in the bulk
of one-dimensional chiral systems. We first introduce the mean chiral
displacement, and we show that it rapidly approaches a multiple of the Zak
phase in the long time limit. Then we measure the Zak phase in a photonic
quantum walk, by direct observation of the mean chiral displacement in its
bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe,
and combine the two windings to characterize the full phase diagram of this
Floquet system. Finally, we prove the robustness of the measure by introducing
dynamical disorder in the system. This detection method is extremely general,
as it can be applied to all one-dimensional platforms simulating static or
Floquet chiral systems.Comment: 10 pages, 7 color figures (incl. appendices) Close to the published
versio
Quantum Anti-Zeno Effect
We demonstrate that near threshold decay processes may be accelerated by
repeated measurements. Examples include near threshold photodetachment of an
electron from a negative ion, and spontaneous emission in a cavity close to the
cutoff frequency, or in a photon band gap material.Comment: 4 pages, 3 figure
Separable approximation for mixed states of composite quantum systems
We describe a purely algebraic method for finding the best separable
approximation to a mixed state of a composite 2x2 quantum system, consisting of
a decomposition of the state into a linear combination of a mixed separable
part and a pure entangled one. We prove that, in a generic case, the weight of
the pure part in the decomposition equals the concurrence of the state.Comment: 13 pages, no figures; minor changes; accepted for publication in PR
Separability and entanglement in 2x2xN composite quantum systems
We investigate separability and entanglement of mixed states in three party quantum systems. We show
that all states with positive partial transposes that have rank are
separable. For the 3 qubit case (N=2) we prove that all states that have
positive partial transposes and rank 3 are separable. We provide also
constructive separability checks for the states that have the sum of the
rank of and the ranks of partial transposes with respect to all
subsystems smaller than 15N-1.Comment: Finally corrected file submitted. Numerous misprints and small errors
corrected, better versions of constructive separability checks included,
updated and extended reference
Scattering of short laser pulses from trapped fermions
We investigate the scattering of intense short laser pulses off trapped cold
fermionic atoms. We discuss the sensitivity of the scattered light to the
quantum statistics of the atoms. The temperature dependence of the scattered
light spectrum is calculated. Comparisons are made with a system of classical
atoms who obey Maxwell-Boltzmann statistics. We find the total scattering
increases as the fermions become cooler but eventually tails off at very low
temperatures (far below the Fermi temperature). At these low temperatures the
fermionic degeneracy plays an important role in the scattering as it inhibits
spontaneous emission into occupied energy levels below the Fermi surface. We
demonstrate temperature dependent qualitative changes in the differential and
total spectrum can be utilized to probe quantum degeneracy of trapped Fermi gas
when the total number of atoms are sufficiently large . At smaller
number of atoms, incoherent scattering dominates and it displays weak
temperature dependence.Comment: updated figures and revised content, submitted to Phys.Rev.
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