We propose a double blinding-attack on entangled-based quantum key distribution protocols. The principle of the attack is the same as in existing blinding attack except that instead of blinding the detectors on one side only, Eve is blinding the detectors of both Alice and Bob. In the BBM92 protocol, the attack allows Eve to get a full knowledge of the key and remain undetected even if Alice and Bob are using 100% efficient detectors. The attack can be easily extended to Ekert protocol, with an efficiency as high as 85.3%.
In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.
Recently, we proposed a new method to compute probabilities which do not satisfy basic law in classical probability theory. In this note, we analyze glucose effect in Escherichia coli's growth with the method, and we show an invariant quantity which Escherichia coli has.
We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)
We discuss a possibility of resolution nonobjectivity-nonlocality dilemma in the light of experimental tests of the Bell inequality for two entangled photons and Bell-like inequality for a single neutron. Our conclusion is that on the basis of these experiments we can conclude that quantum mechanics is nonobjective, i.e., values of physical observables cannot be assigned to a system before measurement. The Bell's assumption of nonlocality has to be rejected as having no direct experimental confirmation We discuss inter-relation nonobjectivity/contextuality. We analyze the impact of the Kochen-Specker theorem to the problem of contextuality of quantum observables. Our conclusion is that as well as von Neumann no-go theorem the the Kochen-Specker theorem is based on assumptions which do not match the real physical situation Finally, we present theory of measurements for a classical purely wave model (prequantum classical statistical field theory) reproducing quantum probabilities. Here continuous fields are transformed into discrete clicks of detectors. The model is classical. However, it is nonobjective. Here, nonobjectivity is the result of contextuality - dependence on the context of measurement (in complete accordance with Bohr's views).
The distance dependence of the probability of observing two photons in a waveguide is investigated and the Glauber correlation functions of the entangled photons are considered. First the case of a hollow waveguide with modal dispersion is treated in detail: the spatial and temporal dependence of the correlation functions is evaluated and the distance dependence of the probability of observing two photons upper bounds and asymptotic expressions valid for large distances are derived. Second the generalization to a real fibre with both material and modal dispersion, allowing dispersion shift, is discussed.
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and entanglement. We also study the relation between conventional entanglement of complex qubits and our generalized entanglement. Our construction can also be used to describe entanglement in the framework of non-Archimedean physics. It is also possible to construct tensor products of non-Archimedean (e.g., p-adic) and complex Hilbert spaces.
We consider the grading structure on the tensor product corresponding to the tensor rank; the relation to the notion of entanglement is discussed. We also study a complex problem of finding the minimal (with respect to the aforementioned grading structure) representation of elements of the tensor product. The general construction is presented over an arbitrary number field. Hence, it can be applied not only to the conventional notion of entanglement over the field of complex numbers, but even for models of non-Archimedean (in particular, p-adic) quantum physics. The problem of tensor reduction is also studied for an arbitrary number field, but only in the two dimensional case.
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes.These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
The problem of inter-relation between classical and quantum probabilistic data wasdiscussed in numerous papers (from various points of view), see, e.g., [1, 2, 3, 4, 6, 5, 7,8, 14, 15]. We are interested in the problem of representation of probabilistic data of anyorigin 1 by complex probability amplitude, so to say a “wave function”. This problemwas discussed in very detail in [17]. A general QL-representation algorithm (QLRA)was presented in [17]. This algorithm is based on the formula of total probability withinterference term – a disturbance of the standard formula of total probability. Startingwith experimental probabilistic data, QLRA produces a complex probability amplitudesuch that probability can be reconstructed by using Born’s rule.Although the formal scheme of QLRA works for multi-valued observables of anarbitrary dimension, the description of the class of probabilistic data which can betransfered into QL-amplitudes (the domain of application of QLRA) depends very muchon the dimension. In [19] the simplest case of data generated by dichotomous observableswas studied. In this paper we study trichotomous observables. The complexity of theproblem increases incredibly comparing with the two dimensional case.Finally, we remark that our study is closely related to the triple slit interferenceexperiment and Sorkin’s equality [16]. This experiment provides an important test offoundations of QM.The scheme of presentation is the following one. We start with observables given byQM and derive constraints on phases which are necessary and sufficient for the QLrepresentation.Then we use these constraints to produce complex amplitudes from data(of any origin); some examples, including numerical, are given.
It took two millennia after Euclid and until in the early 1880s, when we went beyond the ancient axiom of parallels, and inaugurated geometries of curved spaces. In less than one more century, General Relativity followed. At present, physical thinking is still beheld by the yet deeper and equally ancient Archimedean assumption. In view of that, it is argued with some rather easily accessible mathematical support that Theoretical Physics may at last venture into the non-Archimedean realms. In this introductory paper we stress two fundamental consequences of the non-Archimedean approach to Theoretical Physics: one of them for quantum theory and another for relativity theory. From the non-Archimedean viewpoint, the assumption of the existence of minimal quanta of light (of the fixed frequency) is an artifact of the present Archimedean mathematical basis of quantum mechanics. In the same way the assumption of the existence of the maximal velocity, the velocity of light, is a feature of the real space-time structure which is fundamentally Archimedean. Both these assumptions are not justified in corresponding non-Archimedean models.