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 ${\cal C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For the 3 qubit case (N=2) we prove that all states $\rho$ that have positive partial transposes and rank 3 are separable. We provide also constructive separability checks for the states $\rho$ that have the sum of the rank of $\rho$ 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 $(\geq 10^6)$. At smaller number of atoms, incoherent scattering dominates and it displays weak temperature dependence.Comment: updated figures and revised content, submitted to Phys.Rev.