A contextual extension of Spekkens' toy model

Quantum systems show contextuality. More precisely, it is impossible to reproduce the quantum-mechanical predictions using a non-contextual realist model, i.e., a model where the outcome of one measurement is independent of the choice of compatible measurements performed in the measurement context. There has been several attempts to quantify the amount of contextuality for specific quantum systems, for example, in the number of rays needed in a KS proof, or the number of terms in certain inequalities, or in the violation, noise sensitivity, and other measures. This paper is about another approach: to use a simple contextual model that reproduces the quantum-mechanical contextual behaviour, but not necessarily all quantum predictions. The amount of contextuality can then be quantified in terms of additional resources needed as compared with a similar model without contextuality. In this case the contextual model needs to keep track of the context used, so the appropriate measure would be memory. Another way to view this is as a memory requirement to be able to reproduce quantum contextuality in a realist model. The model we will use can be viewed as an extension of Spekkens' toy model [Phys. Rev. A 75, 032110 (2007)], and the relation is studied in some detail. To reproduce the quantum predictions for the Peres-Mermin square, the memory requirement is more than one bit in addition to the memory used for the individual outcomes in the corresponding noncontextual model.Comment: 10 page

Loopholes in Bell Inequality Tests of Local Realism

Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or "loopholes" in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a "loophole-free" or "definitive" Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world.Comment: 42 pages, 2 figure

Tight Bounds for the Pearle-Braunstein-Caves Chained Inequality Without the Fair-Coincidence Assumption

In any Bell test, loopholes can cause issues in the interpretation of the results, since an apparent violation of the inequality may not correspond to a violation of local realism. An important example is the coincidence-time loophole that arises when detector settings might influence the time when detection will occur. This effect can be observed in many experiments where measurement outcomes are to be compared between remote stations because the interpretation of an ostensible Bell violation strongly depends on the method used to decide coincidence. The coincidence-time loophole has previously been studied for the Clauser-Horne-Shimony-Holt (CHSH) and Clauser-Horne (CH) inequalities, but recent experiments have shown the need for a generalization. Here, we study the generalized "chained" inequality by Pearle-Braunstein-Caves (PBC) with two or more settings per observer. This inequality has applications in, for instance, Quantum Key Distribution where it has been used to re-establish security. In this paper we give the minimum coincidence probability for the PBC inequality for all N and show that this bound is tight for a violation free of the fair-coincidence assumption. Thus, if an experiment has a coincidence probability exceeding the critical value derived here, the coincidence-time loophole is eliminated.Comment: 7 pages, 2 figures, minor correction

Quantum Simulation Logic, Oracles, and the Quantum Advantage

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure

Bell Inequalities for Position Measurements

Bell inequalities for position measurements are derived using the bits of the binary expansion of position-measurement results. Violations of these inequalities are obtained from the output state of the Non-degenerate Optical Parametric Amplifier.Comment: revtex4, 2 figure

Quantum contextuality for rational vectors

The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D. A. Meyer, Phys. Rev. Lett. 83, 3751 (1999)] that the inconsistency would disappear when we are restricted to projectors on unit vectors with rational components; that noncontextual hidden variables could reproduce the quantum predictions for rational vectors. Here we show that a qutrit state with rational components violates an inequality valid for noncontextual hidden-variable models [A. A. Klyachko et al., Phys. Rev. Lett. 101, 020403 (2008)] using rational projectors. This shows that the inconsistency remains even when using only rational vectors.Comment: REVTeX4-1, 1 pag

Героїзм і трагедія 5-ї гвардійської армії в битві за Дніпро у вересні – жовтні 1943 р.

(uk) Дослідження торкається маловідомої сторінки в історії Другої світової війни – форсування Дніпра частинами 5-ї гвардійської армії північніше Кременчука, де бійці 32-го й 33-го гвардійських корпусів виконували роль удаваного маневру в жовтні 1943 року, в той час як 7-а гвардійська й 37-а армії розширювали оперативний плацдарм на фронті Домоткань – Дереївка.(ru) Исследование посвящено малоизвестной странице в истории Второй мировой войны – форсированию Днепра соединениями 5-й гвардейской армии севернее Кременчуга, где бойцы 32-го и 33-го гвардейских корпусов, выполняли роль отвлекающего маневра в октябре 1943 года, в то время как 7-я гвардейская и 37-я армии расширяли оперативный плацдарм на фронте Домоткань – Дереевка.(en) The research concerns the little-known page in the history of the Second World War – the forcing of the Dnieper Parts 5-th Guards Army north of Kremenchug, where fighters of the 32-th and 33-th Guards corps, served as red herring in October 1943, while the 7-th and 37 army expanded operational foothold in the front Domotkan – Dereyivka