[en] Bell's theorem started with two qubits (spins 1/2). It is a ‘no-go’ statement on classical (local causal) models of quantum correlations. After 25 years, it turned out that for three qubits the situation is even more astonishing. General statements concerning higher dimensional systems, qutrits, etc, started to appear even later, once the picture with spin (higher than 1/2) was replaced by a broader one, allowing all possible observables. This work is a continuation of the Gdansk effort to take advantage of the fact that Bell's theorem can be put in the form of a linear programming problem, which in turn can be translated into a computer code. Our results are numerical and classify the strength of the violation of local causality by various families of three-qutrit states, as measured by the resistance to noise. This is previously uncharted territory. The results may be helpful in suggesting which three-qutrit states will be handy for applications in quantum information protocols. One of the surprises is that the W state turns out to reveal a stronger violation of local causality than the GHZ (Greenberger–Horne–Zeilinger) state. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)

[en] We present a new approach to Stokes parameters, which enables one to see better non-classical properties of bright quantum light, and of undefined overall photon numbers. The crucial difference is as follows. The standard quantum optical Stokes parameters are averages of differences of intensities of light registered at the two exits of polarization analyzers, and one gets their normalized version by dividing them by the average total intensity. The new ones are averages of the registered normalized Stokes parameters, for the duration of the experiment. That is, we redefine each Stokes observable as the difference of photon number operators at the two exits of a polarizing beam splitter multiplied by the inverse of their sum. The vacuum eigenvalue of the operator is defined a zero. We show that with such an approach one can obtain more sensitive entanglement indicators based on polarization measurements. (paper)

[en] We analyze robustness of correlations of the N-qubit GHZ and Dicke states against white noise admixture. For sufficiently large N, the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for N > 8 for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are the GHZ states augmented with fully product states. Based on our numerical analysis conducted up to N = 8, and an analytical formula derived for any N parties, we conjecture that the three-qubit GHZ state augmented with a product of (N − 3) pure qubits is the most robust against white noise admixture among any N-qubit state. As a by-product, we derive a single Bell inequality and show that it is violated by all pure entangled states of a given number of parties. This gives an alternative proof of Gisin’s theorem. (paper)

[en] The ‘Werner gap’ is the range of relevant parameters characterizing a quantum state for which it is both entangled and admits a local hidden variable model. Werner showed that the gap becomes maximal for entanglement mixed with white noise if subsystems have infinitely many levels. Here we study pure entangled states mixed with simple coloured noise modelled as a single pure product state. We provide an explicit local hidden variable model for quantum correlations of some states of this family and provide hints that there is probably a model for all quantum predictions. This demonstrates essentially a maximal Werner gap already for just two qubits. Additionally to its fundamental interest, the study has implications for quantum computation and communication. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’. (paper)

[en] It has been demonstrated both theoretically and experimentally that genuine multipartite entanglement between qubits can exist even in the absence of multipartite correlations. Here, we provide first examples of this effect in higher dimensional systems – qudits. We construct states in which genuine N-partite entanglement between qudits is supported only by correlations involving strictly less than N particles. The construction differs in several aspects from the ones for qubits. The states introduced here are a natural test-bed for candidate quantifiers of genuinely multipartite quantum correlations. Graphical abstract:

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[en] Highlights: • Correlation tensors based on geometry are utilized for entanglement indicator. • Noise resistances for entanglement of higher dimensional systems are analyzed. • Analytical and numerical results on various noises are presented. - Abstract: Noise affects production and transmission of entanglement. We use a handy approach for a noise resistance of entanglement of two-qudit systems. A geometric concept using correlation tensors of separable and entangled states is implemented to formulate entanglement criterion. We apply the criterion to the various types of noise (white, colored, local depolarizing and amplitude damping) admixtures with the initial (pure) state. We also study the noise resistance with respect to the violation of specific family of Bell inequalities (CGLMP). A broad set of numerical and analytical results is presented.

[en] We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations despite sharing many properties with them. It is directly computable for classical as well as quantum systems and reduces to comparing the respective conditional mutual information between any two subsystems. Exemplarily we show the benefits of using the new quantifier for symmetric quantum secret sharing. We also prove an inequality characterizing the lack of monotonicity of conditional mutual information under local operations and provide intuitive understanding for it. This underlines the distinction between the multipartite dependence measure introduced here and multipartite correlations. (paper)