Waldemar Kłobus

Entanglement witnessing and quantum cryptography with nonideal ferromagnetic detectors

We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of eta < 1/root 3 approximate to 58% required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell`s inequality with eta < 1/(4)root 2 approximate to 84%. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.

Conjectured strong complementary-correlations tradeoff

National Quantum Information Centre in Gdan´sk, 81-824 Sopot, Poland(Dated: September 16, 2013)We conjecture new uncertainty relations which restrict correlations between results of measure-ments performed by two separated parties on a shared quantum state. The first uncertainty relationbounds the sum of two mutual informations when one party measures a single observable and theother party measures one of two observables. The uncertainty relation does not follow from Maassen-Uffink uncertainty relation and is much stronger than Hall uncertainty relation derived from thelatter. The second uncertainty relation bounds the sum of two mutual informations when eachparty measures one of two observables. We provide numerical evidence for validity of conjectureduncertainty relations and prove them for large classes of states and observables.

Some exact results for the zero-bandwidth extended Hubbard model with intersite charge and magnetic interactions

This is an author-created, un-copyedited version of an article accepted for publication in Acta Physica Polonica A.

Axiomatic approach to contextuality and nonlocality

We present a unified axiomatic approach to contextuality and non-locality based on the fact that both are resource theories. In those theories the main objects are consistent boxes, which can be transformed by certain operations to achieve certain tasks. The amount of resource is quantified by appropriate measures of the resource. Following recent paper [J.I. de Vicente, J. Phys. A: Math. Theor. {\bf 47}, 424017 (2014)], and recent development of abstract approach to resource theories, such as entanglement theory, we propose axioms and welcome properties for operations and measures of resources. As one of the axioms of the measure we propose the asymptotic continuity: the measure should not differ on boxes that are close to each other by more than the distance with a factor depending logarithmically on the dimension of the boxes. We prove that relative entropy of contextuality is asymptotically continuous. Considering another concept from entanglement theory---the convex roof of a measure---we prove that for some non-local and contextual polytopes, the relative entropy of a resource is upper bounded up to a constant factor by the cost of the resource. Finally, we prove that providing a measure

The Conditional Uncertainty Principle

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Nonlocality activation in entanglement-swapping chains

of resource does not increase under allowed class of operations, such as e.g. wirings, the maximal distillable resource which can be obtained by these operations is bounded from above by the value of

Measurement uncertainty from no-signaling and nonlocality

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Communication Strength of Correlations Violating Monogamy Relations

up to a constant factor. We show explicitly which axioms are used in the proofs of presented results, so that analogous results may remain true in other resource theories with analogous axioms. We also make use of the known distillation protocol of bipartite nonlocality to show how contextual resources can be distilled.

Charge orderings and phase separations in the atomic limit of the extended Hubbard model with intersite density-density interactions

We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations: (1) a monotone-based conditional uncertainty relation, (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alices pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent.

Magnetic orderings and phase separations in the zero-bandwidth limit of the extended Hubbard model with intersite magnetic interactions

We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate CHSH inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.