The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\bar F$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\bar F$ is able to detect certain bound entangled states.Comment: Published version. Notice also the following article [Phys. Rev. A 85, 022322 (2012), DOI: 10.1103/PhysRevA.85.022322] by Geza T\'oth on the same subjec

Interferometers with atomic ensembles are an integral part of modern precision metrology. However, these interferometers are fundamentally restricted by the shot noise limit, which can only be overcome by creating quantum entanglement among the atoms. We used spin dynamics in Bose-Einstein condensates to create large ensembles of up to 10(4) pair-correlated atoms with an interferometric sensitivity -1.61(-1.1)(+0.98) decibels beyond the shot noise limit. Our proof-of-principle results point the way toward a new generation of atom interferometers.

We present the experimental detection of genuine multipartite entanglement using entanglement witness operators. To this aim we introduce a canonical way of constructing and decomposing witness operators so that they can be directly implemented with present technology. We apply this method to three-and four-qubit entangled states of polarized photons, giving experimental evidence that the considered states contain true multipartite entanglement. [3,4] as it gives a simple sufficient and necessary condition for entanglement. Yet, the situation is much more complicated for higher dimensional and multipartite systems, where simple necessary and sufficient conditions are not known [5].In the analysis of multipartite systems, it is important to distinguish between genuine multipartite entanglement and biseparable (triseparable, etc.) entanglement. Genuine multipartite entangled pure states cannot be created without participation of all parties. Conversely, for pure biseparable states of n parties a group of m < n parties can be found which are entangled among each other, but not with any member of the other group of n − m parties [6]. Distinction and detection of genuine multipartite entanglement poses an important challenge in quantum information science. Bell inequalities are not suited to this aim in general. Multiseparable and biseparable states violate known Bell inequalities less than npartite Greenberger-Horne-Zeilinger (GHZ) states. However, for n > 3 there exist even pure n-partite entangled states with a lower violation than biseparable states [7]. Only recently, significant progress in classifying multipartite entanglement has been achieved using entanglement witnesses [4,8]. These observables can always be used to detect various forms of multipartite entanglement, when some a priori knowledge about the states under investigation is provided [9]; they are in this sense more powerful than Bell inequalities.A witness of genuine n-partite entanglement is an observable which has a positive expectation value on states with n − 1 partite entanglement and a negative expectation value on some n-partite entangled states. The latter states and their entanglement, respectively, are said to be detected by W. Witnesses provide sufficient criteria for entanglement and for distinguishing the various classes of genuine multipartite entangled states.The goal of this Letter is twofold. First, we introduce a general scheme for the construction of multipartite witness operators and their decomposition into locally measurable observables. In this way, we demonstrate how witness operators can be implemented experimentally in a straightforward way by using local projective measurements, even for multipartite systems [10]. Then, we apply this scheme to certain states and perform the experimental detection of their multipartite entanglement, which could not be revealed by known Bell inequalities. In particular, we use this method for the characterization of the three-qubit W state [11], and the four-qubit state |Ψ (4) [12]. A wit...

We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge of the density matrix. The idea is based on the minimal decomposition of witness operators into a pseudo-mixture of local operators. We discuss an experimentally relevant case of two qubits, and show an example how bound entanglement can be detected with few local measurements. 03.67.Dd, 03.67.Hk, A central aim in the physics of quantum information is to create and detect entanglement -the resource that allows to realize various quantum protocols. Recently, much progress has been achieved experimentally in creating entangled states [1]. In every real experiment noise and imperfections are present so that the generated states, although intended to be entangled, may in fact be separable. Therefore, it is important to find efficient experimental methods to test whether a given imperfect state ρ is indeed entangled.Obviously, the ultimate goal of entanglement detection is to characterize entanglement quantitatively, and identify regions in the parameter space which allow to maximize entanglement for a particular quantum information processing task. The first step towards this ambitious goal is to detect whether a given state is entangled or not.The question of direct detection of quantum entanglement has been recently addressed in Refs. [2][3][4]. In [3,4] the authors study the case of mixed states and find efficient ways to estimate the entanglement of an unknown state. Their method is based on structural approximations of some linear maps followed by a spectrum estimation. Although experimentally viable the method is not very easy to implement and it requires further modifications in order to be performed by local measurements [5]. Here, we approach the same problem from a different perspective. We use special observables, the so-called witness operators [6,7] and their optimal decomposition into a sum of local projectors. Note that in this way we answer an open question posed recently in [8], where non-local measurements of entanglement witnesses were studied.The construction of a witness for a given arbitrary state is, in general, a formidable task. It can, however, be accomplished in typical experimental situations where one has some a priori information about the density matrix. This is always the case when the experiment is aimed at producing a certain state, rather than checking properties of an a priori unknown state. We discuss two experimentally relevant situations in this paper, namely the generation of a definite pure entangled state of two parties, and the generation of a specific bound entangled edge state. In both cases our method can be applied in arbitrary dimensions.Having constructed a witness, its measurement can be performed locally, since every observable can be decomposed in terms of a product basis in the operator space. Here we propose two ways of optimizing such local measurements. The first one consists in looking for the optimal number of l...