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We study a damped kicked top dynamics of a large number of qubits ($N \rightarrow \infty$) and focus on an evolution of a reduced single-qubit subsystem. Each subsystem is subjected to the amplitude damping channel controlled by the damping constant $r\in [0,1]$, which plays the role of the single control parameter. In the parameter range for which the classical dynamics is chaotic, while varying $r$ we find the universal period-doubling behavior characteristic to one-dimensional maps: period-two dynamics starts at $r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx 0.5387$. In parallel with period-four oscillations observed for $r \leq r_3 \approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx 0.544$, responsible for a small-scale chaotic dynamics inside the attractor. The doubling of the principal bifurcation tree continues until $r \leq r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos interrupted by the windows of the oscillatory dynamics corresponding to the Sharkovsky order., Comment: 10 pages, 8 figures

We propose a method to witness entanglement between two continuous-variable systems in a Gaussian state. Its key ingredient is a local lossy state transfer from the original spatially separated systems onto two spatially separated qubits. The qubits are initially in a pure product state, therefore by detecting entanglement between the qubits we witness entanglement between the two original systems. This method greatly simplifies entanglement witnessing in complex systems., 5 pages, 2 figures

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., Comment: 9 pages, journal version

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., 6 pages, 1 figure

We investigate the maximum purity that can be achieved by k-uniform mixed states of N parties. Such N-party states have the property that all their k-party reduced states are maximally mixed. A scheme to construct explicitly k-uniform states using a set of specific N-qubit Pauli matrices is proposed. We provide several different examples of such states and demonstrate that in some cases the state corresponds to a particular orthogonal array. The obtained states, despite being mixed, reveal strong non-classical properties such as genuine multipartite entanglement or violation of Bell inequalities., Comment: 10 pages, 2 figures, journal version

In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this aim, we first provide a framework associating them with classical channels whose capacities are then used to quantify the usefulness of these correlations in sending information. Finally, we determine the minimal amount of information that can be sent using signaling correlations violating the monogamy relation associated to the chained Bell inequalities., Comment: 14 pages, 2 figures; improved version; accepted for publication in Foundations of Physics

A simple effective model for a description of magnetically ordered narrow-band insulators is studied. The Hamiltonian considered consists of the effective on-site interaction ( U ) and intersite magnetic exchange interactions ( J z , J x y ) between nearest-neighbours. The phase diagrams and properties of this model for arbitrary chemical potential μ and arbitrary electron density n have been determined within several approaches: (i) the variational method (which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation) for any J z , J x y ≠ 0 (exact in the limit of infinite dimensions), (ii) the Monte Carlo simulations on a square lattice with periodic boundary conditions for J x y = 0 , and (iii) other approximate methods (inter alia: random phase approximation and spin-wave approximation) as well as (iv) rigorous treatment to obtain results concerning the ground state phase diagrams (the two last also for J z , J x y ≠ 0 ). The investigations of the general case show that, depending on the values of interaction parameters and electron concentration n , the system can exhibit not only homogeneous phases: (anti-)ferromagnetic ( F α , α = z , x y ) and nonordered (NO), but also phase separated states ( PS α : F α /NO). For a fixed n one finds the following phase transitions (both continuous and discontinuous ones) and their sequences, which can occur with increasing temperature: F α → NO , PS α → NO , PS α → F α → NO , PS α → F α → PS α → NO . The system analysed exhibits also tricritical behaviour.

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 and (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's 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. Ministry of Education (MOE) National Research Foundation (NRF) Published version This work is supported by ERC Advanced Grant QOLAPS and National Science Centre Grants Mae- stro No. DEC-2011/02/A/ST2/00305 and OPUS 9 No. 2015/17/B/ST2/01945. V.N. acknowledges financial support from the Ministry of Education of Singapore, the National Research Foundation (NRF Fellowship Reference No. NRF- NRFF2016-02), and the John Templeton Foundation (Grant No. 54914).

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (non-locality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit non-local correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of non-locality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by non-locality and no-signaling., Comment: 4 pages main + 8 pages appendix; 3 figures

Entangled states are essential in basics quantum communication protocols and quantum cryptography. Ferromagnetic contacts can work as a spin detector, giving possibility of converting information about electron spin to the electric charge, and therefore, detection of entangled states with the electric current measurements is possible. Method of confirming entanglement with non-ideal detectors is presented, the impact of decoherence and noise on states and quality of entanglement is discussed. Entanglement witness (EW) operator method is compared with the CHSH inequalities approach. Required spin polarization for the EW is lower than for the CHSH inequalities. System with asymmetric spin polarizations of detectors was analyzed, including the CHSH inequalities and the EW method.

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 $X$ 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 $X$ 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., 17 pages, comments are most welcome

We investigate theoretically the use of non-ideal ferromagnetic contacts as a mean to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of $��> 1/\sqrt{3} \approx 58 %$ required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with $��> 1/\sqrt[4]{2}\approx 84%$. 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., 10 pages, 4 figures

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other 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 the latter. The second uncertainty relation bounds the sum of two mutual informations when each party measures one of two observables. We provide numerical evidence for validity of conjectured uncertainty relations and prove them for large classes of states and observables., 7 pages

We study a problem of interconvertibility of two supra-quantum resources: one is so called PR-box, which violates CHSH inequality up to maximal algebraic bound, and second is so called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It has been known, that PR-box supplemented with one bit of communication can be used to simulate RAC. We ask the converse question: to what extent RAC can simulate PR-box? To this end we introduce racbox: a box such that supplemented with one bit of communication offers RAC. As said, PR-box can simulate racbox. The question we raise, is whether any racbox can simulate PR-box. We show that a non-signaling racbox indeed can simulate PR-box, hence those two resources are equivalent. We also provide an example of signalling racbox which cannot simulate PR-box. We give a resource inequality between racbox es and PR-boxes, and show that it is saturated., Comment: 10 pages, 4 figures

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., Comment: 4 pages

A simple effective model of charge ordered and (or) magnetically ordered insulators is studied. The tight binding Hamiltonian analyzed consists of (i) the effective on-site interaction U, (ii) the intersite density-density interaction W and (iii) intersite magnetic exchange interaction Jz (or Jxy) between nearest-neighbors. The intersite interaction are treated within the mean-field approximation. One shows that the systems considered can exhibit very interesting multicritical behaviors, including among others bicritical, tricritical, tetracritical and critical end points. The analysis of the model has been performed for an arbitrary electron concentration as well as an arbitrary chemical potential in the limit of strong on-site repulsion. The phase diagrams obtained in such a case are shown to consist of at least 9 different states, including four homogenous phases: nonordered (NO), ferromagnetic (F), charge ordered (CO), ferrimagnetic (intermediate, I) and five types of phase separation: NO-NO, F-NO, F-F, CO-F, CO-I., 3 pages, 5 figures, pdf-ReVTeX, presented at The European Conference Physics of Magnetism 2011, June 27 - July 1, 2011, Poznan, Poland

We show that recent results on the interaction of causality-respecting particles with particles on closed timelike curves derived in [Phys. Rev. A 82, 062330 (2010)] depend on ambiguous assumptions about the form of the state which is inputted into the proposed equivalent circuit. Choosing a different form of this state leads to an opposite conclusion on the power of closed timelike curves.

A simple effective model of charge ordered insulators is studied. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). In the analysis of the phase diagrams we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. The phase separated states have not been taken into account in previous analyses. Our investigations of two cases of the on-site interaction: attraction (U/(-W_Q)=-10) and repulsion (U/(-W_Q)=1.1) show that, depending on the values of the next-nearest-neighbour attraction, the system can exhibit not only homogeneous phases: charge ordered (CO) and nonordered (NO), but also various phase separated states (CO--NO, CO--CO)., Comment: 3 pages, 2 figures, presented at the 14th National School of Superconductivity - Superconductivity and heterogeneous condensed systems, Ostrow Wielkopolski, Poland, October 13-17, 2009; final version, pdf-ReVTeX, corrected typos

A simple effective model for a description of magnetically ordered insulators is analysed. The tight binding Hamiltonian consists of the effective on-site interaction (U) and intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbours. The phase diagrams of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We show that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F) and nonordered (NO), but also phase separated states (PS: F-NO)., Comment: 3 pages, 3 figures, presented at the 14th National School of Superconductivity - Superconductivity and heterogeneous condensed systems, Ostrow Wielkopolski, Poland, October 13-17, 2009; final version, pdf-ReVTeX, corrected typos

We address the problem of constructing a network of unit resistors such that it enables the retrieval of an arbitrary value of equivalent resistance. In particular, we employ the notion of continued fractions to construct a ladder network by which we can easily obtain any fractional value resistance. In addition, since any irrational number is associated with an infinite continued fraction, we discuss the convergence of the equivalent resistance of an infinite resistive ladder and various aspects concerning the approximations of arbitrary numbers attained by adding additional resistors successively to the network. The presented methods can be easily implemented in an educational laboratory and offer an interesting addition to the topic of Ohm?s law.