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We study the non-perfect propagation of information to evolving low-dimensional environment that includes self-evolution as well as noisy initial states and analyze interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast structure formed during the interaction may exhibit non-monotonicity both in the speed of self-dynamics of the environment as well as its mixedness. The former effect is particularly strong, showing that -- considering part of the environment as a measurement apparatus -- an increase of the external magnetic field acting on the environment may turn the very vague measurement into close to ideal. The above effects suggest that quantum objectivity may appear after increasing the dynamics of the environment, although not with respect to the pointer basis, but some other one which we call generalized pointer or indicator basis. Furthermore, it seems also that when the objectivity is poor it may be improved, at least by some amount, by increasing thermal noise. We provide further evidence of that by analyzing the upper bounds on distance to the set of states representing perfect objectivity in the case of a higher number of qubits., Comment: Significantly extended (notion of the indicator basis with further analysis added); version accepted in Special Issue of Entropy "Quantum Darwinism and Friends"

We sketch a relation between two crucial, yet independent, fields in quantum information research, viz. quantum decoherence and quantum cryptography. We investigate here how the standard cryptographic assumption of shielded laboratory, stating that data generated by a secure quantum device remain private unless explicitly published, is disturbed by the einselection mechanism of quantum Darwinism explaining the measurement process by interaction with the external environment. We illustrate the idea with a paradigmatic example of a quantum random number generator compromised by an analog of the Van Eck phreaking. In particular, we derive a trade-off relation between eavesdropper's guessing probability $P_{guess}$ and the collective decoherence factor $\Gamma$ of the simple form $P_{guess} + \Gamma \geq 1$., Comment: A short idea with an illustration. 5 pages

Fundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term $\textbf{HNSQ}$ in the multi-party Bell scenario where some subsystems are locally quantum while the remaining subsystems are only constrained by the no-signaling principle. Specifically, the set $\textbf{HNSQ}$ is a super-quantum set of correlations derived from no-signaling assemblages by performing quantum measurements on the trusted subsystems. As a tool for optimization over the set $\textbf{HNSQ}$, we introduce an outer hierarchy of semi-definite programming approximations to the set following an approach put forward by Doherty-Parillo-Spedalieri. We then show that in contrast to the set $\textbf{NS}$ of no-signaling correlations, there exist extreme points of $\textbf{HNSQ}$ in the tripartite Bell scenario that admit quantum realization. We perform an extensive numerical analysis of the maximal violation of the facet Bell inequalities in the three-party binary input-output scenario and study the corresponding self-testing properties. In contrast to the usual no-signaling correlations, the new set allows for simple security proofs of (one-sided)-device-independent applications against super-quantum adversaries., Comment: 11 pages, 1 figure

We theoretically introduce and experimentally demonstrate the realization of a nonclassicality test that allows for arbitrarily low detection efficiency without invoking any extra assumptions as in ...

In this paper we construct a semi-device-independent protocol able to certify the presence of the generalized measurements. We show robustness of the protocol and conclude that it allows for experimental realisations using current technology.

Symmetric, informationally complete, positive operator-valued measurements (SIC-POVM) are fundamental in quantum information and foundations of quantum theory[1]. For example, SIC-POVMs are crucial for optimal quantum state tomography, quantum key distribution with optimal trade-off between security and key rate, device-independent certification of optimal randomness from one bit of entanglement, and information-based interpretations and operational reconstructions of quantum theory. Experimentally, photonic experiments of qubit and qutrit tomography, and quantum key distribution[2] have aimed for SIC-POVMs. However, these experiments rely on specific models for parts of the experimental setups and do not allow us to test whether the target measurements are truly SIC-POVMs in a "device independent" (DI) way that is, without relying on any modelling of the devices.

We study in detail the decoherence process of a quantum register, coupled to a composite environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available to multiple observers. This process is more subtle and in general qualitatively different than in the case of a single qubit due to the presence of various protected subspaces: decoherence-free subspaces and so-called orthogonalization-free subspaces. We show that this leads to a rich structure of coherence loss or protection in the asymptotic state of the register and a part of its environment. We formulate a series of examples illustrating these structures.

In this paper, a task-scheduling approach to efficiently calculating sparse symmetric matrix-vector products and designed to run on graphics processing units (GPUs) is presented. The main premise is that, for many sparse symmetric matrices occurring in common applications, it is possible to obtain significant reductions in memory usage and improvements in performance when the matrix is prepared in certain ways prior to computation. The preprocessing proposed in this paper employs task scheduling to overcome the difficulties that have suppressed the development of methods taking advantage of the symmetry of sparse matrices. The performance of the proposed task-scheduling method is verified using a Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of cuSPARSE library functions on a GPU and to functions from the Intel MKL on central processing units (CPUs) executed in the parallel mode. The obtained results indicate that the proposed approach for sparse symmetric matrix-vector prod...

One of the fundamental problems of modern physics is how the classical world, the 2nd Law of Thermodynamics and the whole irreversibility emerges from the quantum reality with reversible evolution. This relates to the problem of measurement transforming quantum, non-copyable data, towards intersubjective, copyable classical knowledge. We use the quantum state discrimination to show in a central system model how it's evolution leads to the broadcasting of the classical information. We analyze the process of orthogonalization and decoherence, their time scales and dependence on the environment., Comment: 5 pages + 4 pages of appendix

We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing Semi--Definite Programming techniques., Comment: 5+5 pages; new SDP method added

Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signalling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multi-party non-locality, as evidenced by a generalised Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations., Comment: 15 pages, 5 figures

We provide an analysis of a new family of device independent quantum key distribution (QKD) protocols with several novel features: (a) The bits used for the secret key do not come from the results of the measurements on an entangled state but from the choices of settings; (b) Instead of a single security parameter (a violation of some Bell inequality) a set of them is used to estimate the level of trust in the secrecy of the key. The main advantage of these protocols is a smaller vulnerability to imperfect random number generators made possible by feature (a). We prove the security and the robustness of such protocols. We show that using our method it is possible to construct a QKD protocol which retains its security even if the source of randomness used by communicating parties is strongly biased. As a proof of principle, an explicit example of a protocol based on the Hardy's paradox is presented. Moreover, in the noiseless case, the protocol is secure in a natural way against any type of memory attack, and thus allows to reuse the device in subsequent rounds. We also analyse the robustness of the protocol using semi-definite programming methods. Finally, we present a post-processing method, and observe a paradoxical property that rejecting some random part of the private data can increase the key rate of the protocol., Comment: 10 pages, 5 figure: In this modified version of the manuscript we have added a new section to show fact that our protocol is much better than the standard ones when the random number generators used by the parties are imperfect

We demonstrate that amplification of arbitrarily weak randomness is possible using quantum resources. We present a randomness amplification protocol that involves Bell experiments. We find a Bell inequality which can amplify arbitrarily weak randomness and give a detailed analysis of the protocol involving it. Our analysis includes finding a sufficient violation of Bell inequality as a function of the initial quality of randomness. It has a very important property that for any quality the required violation is strictly lower than possible to obtain using quantum resources. Among other things, it means that the protocol takes a finite amount of time to amplify arbitrarily weak randomness., published version

In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in [Li et al., Phys. Rev. A $\mathbf{87}$, 020302(R) (2013)]. This method allows to lower-bound, with semi-definite programming, the randomness obtained from random number generators based on dimension witnesses. We also investigate the robustness of some randomness expanders using this method. We show the role of an assumption about the trace of the measurement operators and a way to avoid it. The method is also generalized to systems of arbitrary dimension, and for a more general form of dimension witnesses, than it the previous paper. Finally, we introduce a procedure of dimension witness reduction, which can be used to obtain from an existing witness a new one with higher amount of certifiable randomness. The presented methods finds an application for experiments [Ahrens et al., Phys. Rev. Lett. $\mathbf{112}$, 140401 (2014)]., 14 pages, 5 figures

In this paper we investigate properties of several randomness generation protocols in the device independent framework. Using Bell-type inequalities it is possible to certify that the numbers generated by an untrusted device are indeed random. We present a selection of certificates which guarantee two bits of randomness for each run of the experiment in the noiseless case and require the parties to share a maximally entangled state. To compare them we study their efficiency in the presence of white noise. We find that for different amounts of noise different operators are optimal for certifying most randomness. Therefore the vendor of the device should use different protocols depending on the amount of noise expected to occur. Another of our results that we find particularly interesting is that using a single Bell operator as a figure of merit is rarely optimal., Comment: 8 pages, 5 figures

We study the relation between semi and fully device independent protocols. As a tool, we use the correspondence between Bell inequalities and dimension witnesses. We present a method for converting the former into the latter and vice versa. This relation provides us with interesting results for both scenarios. First, we find new random number generation protocols with higher bit rates for both the semi and fully device independent cases. As a byproduct, we obtain whole new classes of Bell inequalities and dimension witnesses. Then, we show how optimization methods used in studies on Bell inequalities can be adopted for dimension witnesses., Comment: published version