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Review of the probability representation of qubit states and observables is presented as well as the picture of states of two-level systems in terms of Triada of Malevich's squares. A new relation of introduced probability parameters is obtained. Also, it is offered a method to visualize the quantum channel's maps of qubit states. Evolution of the two-level system is considered in terms of Triada of Malevich's squares in case of Rabi and Demkov models. [ABSTRACT FROM AUTHOR]

We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated ‘non-orthogonality overlap factor’ (also known as the ‘eigenvalue condition number’) of the left and right eigenvectors for non-selfadjoint Gaussian random matrices of size N×N. First we derive the general finite N expression for the JPD of a real eigenvalue λ and the associated non-orthogonality factor in the real Ginibre ensemble, and then analyze its ‘bulk’ and ‘edge’ scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex eigenvalue z and the associated non-orthogonality factor in the complex Ginibre ensemble is presented as well and yields a distribution with the finite first moment. Its ‘bulk’ scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig (Phys Rev Lett 81(16):3367-3370, 1998), and we provide the ‘edge’ scaling distribution for this case as well. Our method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which we perform in the framework of a supersymmetry approach. Our paper complements recent studies by Bourgade and Dubach (The distribution of overlaps between eigenvectors of Ginibre matrices, 2018. arXiv:1801.01219). [ABSTRACT FROM AUTHOR]

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured. [ABSTRACT FROM AUTHOR]

We consider Hermitian random band matrices H in d⩾1 dimensions. The matrix elements Hxy, indexed by x,y∈Λ⊂Zd, are independent, uniformly distributed random variable if |x-y| is less than the band width W,  and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ| of the matrix. [ABSTRACT FROM AUTHOR]

Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it. [ABSTRACT FROM AUTHOR]

The fitting of θ/2θ and ω peaks in X-ray diffraction curves is shown to be most accurate in the case of using an inverse fourth-degree polynomial or probability density function with Student’s distribution (Pearson type VII function). These functions describe well both the highest-intensity central part of the experimental peak and its low-intensity broadened base caused by X-ray diffuse scattering. The mean microdeformation ε and mean vertical domain size D are determined by the Williamson-Hall method for layers of GaN (ε ≈ 0.00006, D ≈ 200 nm) and Al0.32Ga0.68N (ε = 0.0032 ± 0.0005, D = 24 ± 7 nm). The D value obtained for the Al0.32Ga0.68N layer is most likely to result from the nominal thickness of this layer, which is 11 nm. [ABSTRACT FROM AUTHOR]

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts. [ABSTRACT FROM AUTHOR]

Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, location based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point and/or query point is specified as a probability density function and the goal is to return the point that minimizes the expected distance, which we refer to as the expected nearest neighbor ( $$\mathop {\mathrm {ENN}}$$ ). We present methods for computing an exact $$\mathop {\mathrm {ENN}}$$ or an $$\varepsilon $$ -approximate $$\mathop {\mathrm {ENN}}$$ , for a given error parameter $$0<\varepsilon < 1$$ , under different distance functions. These methods build a data structure of near-linear size and answer $$\mathop {\mathrm {ENN}}$$ queries in polylogarithmic or sublinear time, depending on the underlying function. As far as we know, these are the first nontrivial methods for answering exact or $$\varepsilon $$ -approximate $$\mathop {\mathrm {ENN}}$$ queries with provable performance guarantees. Moreover, we extend our results to answer exact or $$\varepsilon $$ -approximate k- $$\mathop {\mathrm {ENN}}$$ queries. [ABSTRACT FROM AUTHOR]

The rise of Performance Based Design methodologies for fire safety engineering has increased the interest of the fire safety community in the concepts of risk and reliability. Practical applications have however been severely hampered by the lack of an efficient unbiased calculation methodology. This is because on the one hand, the distribution types of model output variables in fire safety engineering are not known and traditional distribution types as for example the normal and lognormal distribution may result in unsafe approximations. Therefore unbiased methods must be applied which make no (implicit) assumptions on the PDF type. Traditionally these unbiased methods are based on Monte Carlo simulations. On the other hand, Monte Carlo simulations require a large number of model evaluations and are therefore too computationally expensive when large and nonlinear calculation models are applied, as is common in fire safety engineering. The methodology presented in this paper avoids this deadlock by making an unbiased estimate of the PDF based on only a very limited number of model evaluations. The methodology is known as the Maximum Entropy Multiplicative Dimensional Reduction Method (ME-MDRM) and results in a mathematical formula for the probability density function (PDF) describing the uncertain output variable. The method can be applied with existing models and calculation tools and allows for a parallelization of model evaluations. The example applications given in the paper stem from the field of structural fire safety and illustrate the excellent performance of the method for probabilistic structural fire safety engineering. The ME-MDRM can however be considered applicable to other types of engineering models as well. [ABSTRACT FROM AUTHOR]

Subjects observing many samples from a Bernoulli distribution are able to perceive an estimate of the generating parameter. A question of fundamental importance is how the current percept-what we think the probability now is-depends on the sequence of observed samples. Answers to this question are strongly constrained by the manner in which the current percept changes in response to changes in the hidden parameter. Subjects do not update their percept trial-by-trial when the hidden probability undergoes unpredictable and unsignaled step changes; instead, they update it only intermittently in a step-hold pattern. It could be that the step-hold pattern is not essential to the perception of probability and is only an artifact of step changes in the hidden parameter. However, we now report that the step-hold pattern obtains even when the parameter varies slowly and smoothly. It obtains even when the smooth variation is periodic (sinusoidal) and perceived as such. We elaborate on a previously published theory that accounts for: (i) the quantitative properties of the step-hold update pattern; (ii) subjects' quick and accurate reporting of changes; (iii) subjects' second thoughts about previously reported changes; (iv) subjects' detection of higher-order structure in patterns of change. We also call attention to the challenges these results pose for trial-by-trial updating theories. [ABSTRACT FROM AUTHOR]

We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov's weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality. [ABSTRACT FROM AUTHOR]

In this paper, we carry out statistical fluctuation analysis for the new proposed measurement-device-independent quantum key distribution with heralded single-photon sources and further compare its performance with the mostly often used light sources, i.e., the weak coherent source. Due to a significantly lower probability for events with two photons present on the same side of the beam splitter in former than in latter, it gives drastically reduced quantum bit error rate in the X basis and can thus show splendid behavior in real-life implementations even when taking statistical fluctuations into account. [ABSTRACT FROM AUTHOR]

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using fine-grained uncertainty relations. Fine-grained uncertainty relations can be obtained by consideration of the spectral norms of certain positive matrices. One of possible approaches to separability conditions is connected with upper bounds on the sum of maximal probabilities. Separability conditions are often formulated for measurements that have a special structure. For instance, mutually unbiased bases and mutually unbiased measurements can be utilized for such purposes. Using resolution of the identity for each subsystem of a bipartite system, we construct some resolution of the identity in the product of Hilbert spaces. Separability conditions are then formulated in terms of maximal probabilities for a collection of specific outcomes. The presented conditions are compared with some previous formulations. Our results are exemplified with entangled states of a two-qutrit system. [ABSTRACT FROM AUTHOR]

Functional reliability is one of the important properties of physical systems provided by reliability of system components, in particular, control logical components. The new approach to fully delay testable circuit design oriented to cut overheads and lengths of circuit paths has been developed. Compact representation of all PDF test pairs is reduced to keeping the corresponding generative vector pairs. The number of generative vector pairs does not exceed the doubled number of internal ROBDD nodes originating from the circuit, while the number of the circuit paths can exponentially depend on the number of these internal nodes. The algorithm of involving the PDF test pair from the proper generative vector pair is suggested. This procedure does not require essential calculations. The algorithm of deriving the generative vector pair has a polynomial complexity. [ABSTRACT FROM AUTHOR]

Following a proposal of Vaidman (Int Stud Philos Sci 12:245-261, ) (in: Zalta EN (ed) The Stanford encyclopaedia of philosophy, ) (in: Ben-Menahem Y, Hemmo M (ed) The probable and the improbable: understanding probability in physics, essays in memory of Itamar Pitowsky, ), Sebens and Carroll (Quantum theory: a two-time success story ), (arXiv preprint ) have argued that in Everettian (i.e. purely unitary) quantum theory, observers are uncertain, before they complete their observation, about which Everettian branch they are on. They argue further that this solves the problem of making sense of probabilities within Everettian quantum theory, even though the theory itself is deterministic. We note some problems with these arguments. [ABSTRACT FROM AUTHOR]

A flow of physical events (photons, electrons, etc.) is studied. One of the mathematical models of such flows is the Markovian arrival process (MAP) of flow of events. The flow functions are considered under conditions of unextendable dead time period. Explicit expressions for the probability density and joint probability density of interarrival interval of the observable flow are presented considering the effect of the unextendable dead time period. The recurrence relations for the observable flow of events are formulated. [ABSTRACT FROM AUTHOR]

We study the problem of a quantum particle moving in the Dirac delta potential with instant changes in the well depth using the formalism of the tomographic-probability representation of quantum mechanics. We calculate the Husimi function for a particle moving in the Dirac delta potential and study the relation of the Husimi function to the state tomogram. We check numerically the tomographic entropic uncertainty relation for the bound state of the particle moving in the Dirac delta potential. [ABSTRACT FROM AUTHOR]

We give a scheme for locally implementing an inner product modification onto remote qubit product states using partially entangled states, which is designed for obtaining conclusive result with optimal success probability. We exemplify this remote inner product modification (RIPM) by applying it to two-qubit product states via three partially entangled qubit pairs and, additionally, we construct a quantum network to implement this RIPM. It is interesting that our treatment can save entanglement resources. [ABSTRACT FROM AUTHOR]

The existence of anomalous ionospheric reflections was shown on the basis of vertical soundings at the Moskow station. They are observed at heights of 100-200 km. These anomalous reflections are not related to the main Ne( h) ionospheric profile. Morphological characteristics of such reflections are presented: the daily, seasonal, and cyclic dependences of their appearance. [ABSTRACT FROM AUTHOR]

A new application of the W-class state for quantum state sharing (QSTS) of an arbitrary three-qubit state with a certain probability is presented explicitly. We show that three sets of W-class states can be used to realize the QSTS of an arbitrary three-qubit state involving Bell-state measurement, single-qubit measurement and one high dimensional unitary operation. The performance demonstrates that our scheme can considerably reduce the difficulty of physical implementation. [ABSTRACT FROM AUTHOR]

Using the equality form of the necessary and sufficient conditions introduced in Jafarizadeh (Phys Rev A 84:012102 (9 pp), ), minimum error discrimination between states of the two sets of equiprobable similarity transformed quantum qudit states is investigated. In the case that the unitary operators describing the similarity transformations are generating sets of two irreducible representations and the states fulfill a certain constraint, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form. In the cases that they are generating sets of reducible representations, there exist no closed-form formula in general, but the procedure can be applied properly in each case provided that the states obey some constraints. Finally, we give the maximum success probability of discrimination and optimal measurement operators for some important examples of mixed quantum states, such as generalized Bloch sphere m-qubit states, qubit states and their three special cases. [ABSTRACT FROM AUTHOR]

For mixed input fields quantum information processing, it is very convenient to investigate a specified protocol by employ quasi-probability functions and characteristic functions in phase space. In this work, considering a nonlocal swapping operation labelled by $\hat{E}_{s}$, we derive the entanglement swapping transform rule for entangled Wigner operators. The same rule can be obtained by implementing this nonlocal swapping operation via two entangled pairs channels. And then we apply this rule to examine how does the Wigner function for output states change to demonstrate the entanglement swapping. As a result, this transform rule can be utilized to investigate swapping operation for any two-body entangled system. [ABSTRACT FROM AUTHOR]

We apply our previously developed formalism of contexts of histories, suitable to deal with quantum properties at different times, to the measurement process. We explore the logical implications which are allowed by the quantum theory, about the realization of properties of the microscopic measured system, before and after the measurement process with a given pointer value. [ABSTRACT FROM AUTHOR]

We present a scheme for implementing a remote minimum-error discrimination (MD) among N linearly independent nonorthogonal symmetric qudit states. The probability of correct guesses is in agreement with the optimal probability for local MD among the N nonorthogonal states. The procedure we use is a remote probability operator measure (POM). We show that this remote POM can be performed as a remote von Neumann measurement by remote basis transformation. We construct a quantum network for realizing the remote MD using local operations, classical communications and shared entanglement (LOCCSE), and thus provide a feasible physical means to realize the remote MD. [ABSTRACT FROM AUTHOR]

In the standard approach to quantum games, players’ strategic moves are local unitary transformations on an entangled state that is subsequently measured. Players’ payoffs are then obtained as expected values of the entries in the payoff matrix of the classical game on a set of quantum probabilities obtained from the quantum measurement. In this paper, we approach quantum games from a diametrically opposite perspective. We consider a classical three-player symmetric game along with a known expression for a set of quantum probabilities relevant to a tripartite Einstein-Podolsky-Rosen (EPR) experiment that depends on three players’ directional choices in the experiment. We define the players’ strategic moves as their directional choices in an EPR setting and then express their payoff relations in the resulting quantum game in terms of their directional choices, the entries of the payoff matrix, and the quantum probability distribution relevant to the tripartite EPR experiment. [ABSTRACT FROM AUTHOR]

Overall descriptors of the information (determinicity) and entropy (uncertainty) content of complex molecular states are reexamined. These resultant concepts combine the classical (probability) contributions of Fisher and Shannon, and the relevant nonclassical supplements due to the state phase/current. The information-theoretic principles determining equilibria in molecules and their fragments are explored and the nonadditive part of the global entropy is advocated as a descriptor of the classical index of the quantum entanglement of molecular subsystems. Affinities associated with the probability and phase fluxes are identified and the criterion of vanishing overall information-source is shown to identify the system stationary electronic states. The production of resultant density of the gradient-information is expressed in terms of the conjugate affinities (forces, perturbations) and fluxes (currents, responses). The Schrödinger dynamics of probability and phase components of molecular electronic states is used to determine the temporal evolution of the overall gradient information and complex entropy. The global sources of the resultant information/entropy descriptors are shown to be of purely nonclassical origin, thus identically vanishing in real electronic states, e.g., the nondegenerate ground state of a molecule. [ABSTRACT FROM AUTHOR]

Linearly independent quantum states can be unambiguously discriminated, but linearly dependent ones cannot. For linearly dependent quantum states, however, if C copies of the single states are available, then they may form linearly independent states, and can be unambiguously discriminated. We consider unambiguous discrimination among N = D + 1 linearly dependent states given that C copies are available and that the single copies span a D-dimensional space with equal inner products. The maximum unambiguous discrimination probability is derived for all C with equal a priori probabilities. For this classification of the linearly dependent equidistant states, our result shows that if C is even then adding a further copy fails to increase the maximum discrimination probability. [ABSTRACT FROM AUTHOR]