Wieslaw Laskowski

Fisher information and multiparticle entanglement

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 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 F is able to detect certain bound entangled states.

Do all pure entangled states violate Bell's inequalities for correlation functions?

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisins theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.

Experimentally Friendly Geometrical Criteria for Entanglement

A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.

Tight multipartite Bell's inequalities involving many measurement settings

We derive tight Bells inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are violated by some classes of states, for which all standard Bells inequalities with two measurement settings per observer are satisfied.

Rotational invariance as an additional constraint on local realism.

Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2 correlations. This new constraint rules out such models even in some situations in which standard Bell inequalities allow for explicit construction of such models. The whole analysis is performed without any additional assumptions on the form of local realistic models.

Equivalence between Bell inequalities and quantum minority games

We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality. We conclude the existence of direct correspondences between (i) the payoff rule and Bell inequalities, and (ii) the strategy and the choice of measured observables in evaluating these Bell inequalities. We also show that such a correspondence is unique to minority-like games.

Discriminating Multipartite Entangled States

The variety of multipartite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view, classifications have been introduced. Accordingly, here we derive criteria and demonstrate how to experimentally discriminate an observed state against the ones of certain other classes of multipartite entangled states. Our method, originating in Bell inequalities, adds an important tool for the characterization of multiparty entanglement.

Three-photon W-state

Abstract Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. For entangled three-qubit states it has been shown that there are two inequivalent classes of states, under stochastic local operations and classical communications. The classes are represented by the GHZ- and W-state. The GHZ-state has been used to prove Bells theorem without inequality. Contrary to the GHZ-state, the W-state shows high robustness of entanglement against photon loss. Here we show the first experimental results on the observation of the polarization entangled three-photon W-state from spontaneous parametric down-conversion.

Nonclassicality of pure two-qutrit entangled states

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell-type experiments we allow any pair of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt-rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four- and five-dimensional systems, for which we tested a few interesting examples.

Correlation complementarity yields bell monogamy relations.

We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum nonlocality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on the amount of violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.