Kochen-Specker set with seven contexts

The Kochen-Specker (KS) theorem is a central result in quantum theory and has applications in quantum information. Its proof requires several yes-no tests that can be grouped in contexts or subsets of jointly measurable tests. Arguably, the best measure of simplicity of a KS set is the number of contexts. The smaller this number is, the smaller the number of experiments needed to reveal the conflict between quantum theory and noncontextual theories and to get a quantum vs classical outperformance. The original KS set had 132 contexts. Here we introduce a KS set with seven contexts and prove that this is the simplest KS set that admits a symmetric parity proof.Comment: REVTeX4, 7 pages, 1 figur

Quantum social networks

We introduce a physical approach to social networks (SNs) in which each actor is characterized by a yes-no test on a physical system. This allows us to consider SNs beyond those originated by interactions based on pre-existing properties, as in a classical SN (CSN). As an example of SNs beyond CSNs, we introduce quantum SNs (QSNs) in which actor is characterized by a test of whether or not the system is in a quantum state. We show that QSNs outperform CSNs for a certain task and some graphs. We identify the simplest of these graphs and show that graphs in which QSNs outperform CSNs are increasingly frequent as the number of vertices increases. We also discuss more general SNs and identify the simplest graphs in which QSNs cannot be outperformed.Comment: REVTeX4, 6 pages, 3 figure

Basic exclusivity graphs in quantum correlations

A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates those NC inequalities whose exclusivity graphs contain, as induced subgraphs, odd cycles of length five or more, and/or their complements. In addition, we show that odd cycles are the exclusivity graphs of a well-known family of NC inequalities and that there is also a family of NC inequalities whose exclusivity graphs are the complements of odd cycles. We characterize the maximum noncontextual and quantum values of these inequalities, and provide evidence supporting the conjecture that the maximum quantum violation of these inequalities is exactly singled out by the exclusivity principle.Comment: REVTeX4, 7 pages, 2 figure

Memory cost of quantum contextuality

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimal amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information carrying capacity of the system.Comment: 18 pages, no figures, v2: revised for clarit

Approximate performance analysis of production lines with continuous material flows and finite buffers

In this paper, we analyze production lines consisting of a number of machines or servers in series with a finite buffer between each pair of machines. The flow of products through the machines is continuous. Each machine suffers from breakdowns, because of, for example, failures, cleaning and changeover. The up- and downtimes are independent and generally distributed. We develop a new method to efficiently and accurately estimate the throughput and the mean buffer content of the production line. This method relies on decomposition of the production line into two-stage, one-buffer subsystems aggregating the up- and downstream part of the line. For each subsystem, the parameters of the aggregate up- and downtimes are determined iteratively by employing matrix-analytic techniques. The proposed method performs very well on a large test set consisting of over 49,000 cases. Remarkably, the performance of the method does not deteriorate in case of highly unpredictable up- and downtimes, as often seen in practice. We apply the method to a bottling line at brewery Heineken Den Bosch and an assembly line at NXP Semiconductors