Quantum Information

L'hypnose ericksonienne est une pratique thérapeutique induisant ce que l'on appelle classiquement une transe (i.e. forme de veille paradoxale ou « rêve éveillé », par opposition au sommeil paradoxal) à partir de laquelle, le patient guidé du thérapeute, peut orienter son attention vers un but spécifique ; l'objectif étant défini selon les besoins du patient, les visées de cette thérapeutique sont potentiellement infinies -- en tant qu'elles respectent, bien-entendu, sa nature profonde (i.e. ses convictions et sa sensibilité).
Élaborée dans les années vingt et développée sur plus d'un demi-siècle par le psychiatre américain Milton H. Erickson, elle porte la filiation d'un usage remontant à l'Égypte ancienne et qui, pourtant, millénaires après millénaires, siècles après siècles, ne bénéficie toujours pas de l'éclairage scientifique nécessaire à sa normalisation ; c'est un fait, l'hypnose résiste au principe de sa naturalisation (i.e. de son appropriation par les sciences de la Nature).
Face à ce constat, on peut continuer d'alimenter les oppositions, s'enfermant dans les digressions infinies du débat : hypnose, état psychique quelconque (i.e. minimise le rôle de la relation et donc du thérapeute, voire de la démarche) vs dramatisation spectaculaire de la suggestion (i.e. la relation est centrale mais elle fait du patient, un faible d'esprit, et du thérapeute, un manipulateur) ; ou, sur un mode plus palo-altien, lui opposer une troisième perspective consistant à « sortir du cadre » trop étroit auquel on aura tenté de la soumettre jusque-là, tout en la fondant sur des principes moins déterministes mais non-moins rigoureux. L'objet de cet article est de soumettre une articulation possible de la pratique de l'hypnose thérapeutique avec une appréhension complexe des critères de scientificité.

The charged quantum geometry of mass-ENERGY-Matter - developed from the foundational postulate that quantised angular momenta of Planck's constant is in fact reflective of an equilateral mass-energy geometry from which all 2d immaterial EM fields and 3D material particles are created.

Общество и политика Соціальна роль NFT -0535

Discourse analysis and semiotic analysis of culture. Moving from contemporary to nft. Definition of the phenomenalist, his mistakes and perspectives.

PS/ Это моя  последняя довоенная статья о культуре Украины. Предчувствие войны дискурсов горожанина и университета..

PS/ This is my last pre-war article about the culture of Ukraine. Premonition of the war between the discourses of the city dweller and the university..

https://syg.ma/@andrei-khanov/sotsialna-rol-nft

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioral sciences teach us that random variables measuring the same content (the answer to the same Yes or No question) may vary, if measured jointly with other random variables. Alice and Bob raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant outcomes and to estimate correlations. Marginal expectations, estimated using these final samples, depend on distant settings. Therefore, a system of random variables measured in Bell tests is inconsistently connected and it should be analyzed using a Contextuality-by-Default approach, what is done for the first time in this paper. The violation of Bell inequalities and inconsistent connectedness may be explained...

"The realization of a quantum internet will enable quantum cryptography, distributed quantum computation and quantum sensing over long distances of more than 1,000 kilometers," Kosaka said. [58]
"While there's a progressive shift with some researchers moving to companies, they keep contributing to the common effort making quantum computing reliable and useful." [57]
We all learn quantum physics as physics students, but in recent years this field has taken on a whole new life. It’s not an esoteric theory anymore, something that only describes tiny effects in extreme forms of matter. It’s going to form the basis for a whole new type of technology. So I think that, because physicists have a bit of a leg up in this area, they should go all-in. [56]

The emerging field of quantum machine learning has the potential to substantially aid in the problems and scope of artificial intelligence. This is only enhanced by recent successes in the field of classical machine learning. In this work we propose an approach for the systematic treatment of machine learning, from the perspective of quantum information. Our approach is general and covers all three main branches of machine learning: supervised, unsupervised, and reinforcement learning. While quantum improvements in supervised and unsupervised learning have been reported, reinforcement learning has received much less attention. Within our approach, we tackle the problem of quantum enhancements in reinforcement learning as well, and propose a systematic scheme for providing improvements. As an example, we show that quadratic improvements in learning efficiency, and exponential improvements in performance over limited time periods, can be obtained for a broad class of learning problems.

In this paper, I will derive the equation X=O+ΣH+(n(log)/Pdx for the representation of our universe under the origin point and dilation of time, t. This theorem will be one of the biggest of our understanding of the universe and what Quantum Origin as well as Quantum States symbolizes in terms of mathematically representing the universe as we know it. Following the same rational and logic with Quantum Similarity we have a much bigger picture of the mathematical framework that our universes is under. This will henceforth be one of the main papers in a series of others that explains our universe through Quantum physics and infinitely expanding loops and ripples in time.

The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper assessment of the computational capacity of pyramidal neurons, we have analyzed an extensive dataset of three-dimensional digital reconstructions from the NeuroMorpho.Org database, and quantified basic dendritic or axonal morphometric measures in different regions and layers of the mouse, rat or human cerebral cortex. Physical estimates of the total number and type of ions involved in neuronal electric spiking based on the obtained morphometric data, combined with energetics of neurotransmitter release and signaling fueled by glucose consumed by the active brain, support highly efficient cerebral computation performed at the thermodynamically allowed Landauer limit for implementation of irreversible logical operations. Individual proton tunneling events in voltage-sensing S4 protein α-helices of Na + , K + or Ca 2+ ion channels are ideally suited to serve as single Landauer elementary logical operations that are then amplified by selective ionic currents traversing the open channel pores. This miniaturization of computational gating allows the execution of over 1.2 zetta logical operations per second in the human cerebral cortex without combusting the brain by the released heat.

A group of scientists from ITMO University has demonstrated the possibility of modifying terahertz pulses in order to use them for data transmission. [25] Shortcomings of security breach notifications, best practices for phishing warnings and lessons learned from the use of analytics to improve student performance are among several studies University of Michigan researchers will present beginning this weekend in the United Kingdom. [24] But moral questions about what data should be collected and how it should be used are only the beginning. [23] A self-driving vehicle has to detect objects, track them over time, and predict where they will be in the future in order to plan a safe manoeuvre. [22] In order to improve world food conditions, a team around computer science professor Kristian Kersting was inspired by the technology behind Google News. [21] Small angle X-ray scattering (SAXS) is one of a number of biophysical techniques used for determining the structural characteristics of biomolecules. [20] A deep neural network running on an ordinary desktop computer is interpreting highly technical data related to national security as well as-and sometimes better than-today's best automated methods or even human experts. [19] Scientists at the National Center for Supercomputing Applications (NCSA), located at the University of Illinois at Urbana-Champaign, have pioneered the use of GPU-accelerated deep learning for rapid detection and characterization of gravitational waves. [18] Researchers from Queen Mary University of London have developed a mathematical model for the emergence of innovations. [17] Quantum computers can be made to utilize effects such as quantum coherence and entanglement to accelerate machine learning. [16] Neural networks learn how to carry out certain tasks by analyzing large amounts of data displayed to them. [15] Who is the better experimentalist, a human or a robot? When it comes to exploring synthetic and crystallization conditions for inorganic gigantic molecules, actively learning machines are clearly ahead, as demonstrated by British Scientists in an experiment with polyoxometalates published in the journal Angewandte Chemie. [14]

While the slogan "no measurement without disturbance" has established itself under the name Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities can be proven that describe a trade-off between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum. Measures of error and disturbance are here defined as figures of merit characteristic of measuring devices. As such they are state independent, each giving worst-case estimates across all states, in contrast to previous work that is concerned with the relationship between error and disturbance in an individual state.

Reports on experiments recently performed in Vienna [Erhard et al., Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of ±1-valued observables A,B are tightly bounded from below by a quantity that measures the degree of incompatibility of A and B. The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.

This paper explores the potential for creating quantum information systems which generate the conditions required to perform quantum computations by creating an environment where the specific computation is hidden and computed while hidden using homomorphic encryption and data manipulation techniques. How related existing concepts can be used in synthesis of a system based on classical computing to the end of creating quantum information systems

We argue that spinning black holes are capable to implement complex quantum information processes encoded in X-ray photons emitted by the accretion disk. Recently, numerical simulations showed that X-ray photons emitted by accretion disk acquire rotation of polarization angle and orbital angular momentum due to strong gravitational field in the vicinity of the rotating black holes. Based on these two degrees of freedom we construct a bipartite two-level quantum system of the accretion disks photons. To characterize the quantum states of this system we consider linear entropy for the reduced density matrix of polarization with the intention to exploit its direct relation with the photons degree of polarization. Since the X-ray radiation has a minimum degree of polarization located at the transition region of the accretion disk, the linear entropy is higher for the photons emitted on this region inferring a higher degree of entanglement for the composite system. We emphasize that for an extreme rotating black hole in the thermal state, the photons with energies at the thermal peak are maximally entangled in polarization and orbital angular momentum, leading to the creation of all four Bell states. Detection of the Bell states encoded by X-ray photons emitted nearby rotating black holes should be possible by equipment actually used in quantum information processing.

Quantum entanglement, a term coined by Erwin Schrodinger in 1935, is a mechanical phenomenon at the quantum level wherein the quantum states of two (or more) particles have to be described with reference to each other though these particles may be spatially separated. This phenomenon leads to paradox and has puzzled us for a long time. The behaviour of entangled particles is apparently inexplicable, incomprehensible and like magic at work. Locality has been a reliable and fruitful principle which has guided us to the triumphs of twentieth century physics. But the consequences of the local laws in quantum theory could seem "spooky" and nonlocal, with some theorists questioning locality itself. Could two subatomic particles on opposite sides of the universe be really instantaneously connected? Is any theory which predicts such a connection essentially flawed or incomplete? Are the results of experiments which demonstrate such a connection being misinterpreted? These question...

Andrei Khanov
16:04, 15 December 2020
58
Part eleven. Euclidean, non-Euclidean, matrix (quantum or informational) geometry of the universe.
Part ten. Einstein's lambda term and the quantum mechanical gap experiment.
Part nine. Planck universe. The Planck system of units is the forerunner of the matrix of physical quantities, more precisely, the matrix of human ideas about physical quantities.
Part eight. Reality and uncertainty. Let me repeat briefly what was discussed in the previous seven chapters. Along the way, I'll add explanations if they were not in the article itself. Nature, the universe, life - can be characterized (by a person, this is due to the structure of his thinking) - a continuous and indefinite quantum mechanical wave function - WF. In a philosophical context, WF is Being, in the esoteric context it is Tao, the Platonic world of ideas, in the poetic language of Aristotle - “the ether of the authenticity of human utterances, from which the sphere of fixed stars is woven, the personification of which is God”, physically it is a vacuum. Reality, in the mind of the observer, is the collapse of such a function - by this or that frame of reference. Therefore, there are many points of view or frames of reference.
Part seven. Matrix of physical quantities (continuation).
Part six. Neural network of physical quantities. Information universe.
History and perspectives of quantum mechanics. Part three
Part four. A cosmological odyssey of the lambda term.
Part five. Matrix and neural network.

in the text - an error, instead of G = G '/ (F = 1) = v4 / F = s2 / mt2. read G = G '/ (F = 1) = v4 / F = s3 / mt2.

Analytic potentials are built for all four 2S+1Πu/g states of Li2 dissociating to Li(2S) + Li(3P): 3b(33Πu), 3B(31Πu), 3C(31Πg), and 3d(33Πg). These potentials include the effect of spin-orbit coupling for large internuclear distances, and include state of the art long-range constants. This is the first successful demonstration of fully analytic diatomic potentials that capture features that are usually considered too difficult to capture without a point-wise potential, such as multiple minima, and shelves. Vibrational energies for each potential are presented for the isotopologues 6,6Li2, 6,7Li2, 7,7Li2, and the elusive `halo nucleonic molecule' 11,11Li2. These energies are claimed to be accurate enough for new high-precision experimental setups such as the one presented in {[}Sebastian \emph{et al.} Phys. Rev. A, \textbf{90}, 033417 (2014){]} to measure and assign energy levels of these electronic states, all of which have not yet been explored in the long-range region. Measuring energies in the long-range region of these electronic states may be significant for studying the ab initio vs experiment discrepancy discussed in [Tang et al. Phys. Rev. A, 84, 052502 (2014)] for the C3 long-range constant of Lithium, which has significance for improving the SI definition of the second.

It is imperative "now" to go beyond our anthropological limits, through an upright mental position, which I have called Conscious Evolutionary Consciousness PaleontoLogicaMente ISOCIC.  It is necessary to get out from under Einstein's skirts and finish the work he courageously started but left unfinished.

As I commented several times, trying to attract the attention of the unconscious to be unconscious, therefore nicknamed inCoScientists, is about time to step forward - evolutionary forward - with respect to Einstein’s “happiest thought”.

What causes the wave formation of the reality / particle duality to collapse is the interference of the same "conscious measurement" which absurdly does not want to take into account itself.  This can be done "simply" by accepting relativity without distinction between inertial and accelerated mass in an "infinitely accelerated" hypersphere of the universe as it is now accepted where any ray has the same number of points before any inertial observer "all about all "consciously conscious instantly entangled" causing "the collapse of the formation of the waves of reality.

Viktor T.Toth on QUORA

What is the simplest and easiest to understand way to explain how mass increases with velocity?

The simplest way: Mass does not increase with velocity.

Seriously. Mass does not increase with velocity.

When you move relative to an object (remember: motion is always relative, so an object moving relative to you or you moving relative to that object mean literally the same thing) that object does not change. It does not even know that you are moving relative to it. However, in your frame of reference, it is that object that moves, and as a result, it has kinetic energy as calculated by you. (For another observer, moving along with the object, the object is at rest and has zero kinetic energy.)

Some authors, especially in the older literature, combined this kinetic energy and the rest mass-energy of the object into a quantity called relativistic mass.

This quantity is meaningless. It differs for different observers moving at different speeds relative to the object. It really has no practical use whatsoever. It only confuses people, rather badly, about relativity theory.


Geoffrey Edwards on QUORA


As velocity increases the mass of the object increases in a linear fashion until infinite energy is required to move an infinite mass. Is time dilation a result of the gravitational field generated by the mass of the object?

No. Mass does not increase. The momentum of an object increases with velocity like this:

p = \gamma*m*v

where p is the usual letter for momentum and \gamma is the relativistic gamma factor. Early on, people noticed that you could absorb the gamma into the m, call it ‘relativistic mass’ (M = gamma*m) and recover the usual Newtonian relation:

p = Mv

As well, this mass had the usual property that if you pushed on the object along the direction of motion with force F you got an acceleration a = F/M. However, this particular analogy probably started to die when people first calculated the acceleration induced by a transverse force and found that it was NOT F/M.

Most analogies about relativity are fundamentally bad ideas because they explicitly break the fundamental basis of relativity, which is that intrinsic velocity, if it exists, cannot be measured. The mass of an object is what we would measure in the frame of reference of an object. It has to be invariant with velocity - a so called ‘scalar’. The orbits of the planets around the sun, for example, cannot depend on the sun’s motion through space (else we could use the orbits to measure the sun’s intrinsic velocity).

Most analogies have limits and are useful only inside those limits. The limit of this particular analogy is to simplify a single question …

If I apply an external force F along the line of motion of an object with velocity v, what is the acceleration?

… and that is it. The mass does not really increase. Because of this, the concept of relativistic mass has been discarded by pretty much everyone because it is invariably applied outside its domain of applicability.

E imperativo “ora” andare oltre i nostri limiti antropologici, tramite una stazione eretta mentale, che ho chiamato coscienza evolutiva cosciente PaleontoLogicaMente ISOCIC. Occorre uscire da sotto le sottane di Einstein e finire il lavoro da lui coraggiosamente iniziato ma lasciato incompiuto.

Come ho più volte commentato cercando di attirare l'attenzione dell'inconscio, essere inconsci, quindi soprannominati inCoScientists, è giunto il momento di fare un passo avanti - in avanti evolutivo - rispetto al "pensiero più felice" di Einstein.

Che fa collassare la formazione d’onda della dualità realtà/particelle è l'interferenza della stessa “misurazione cosciente” che assurdamente non vuole tenere conto di se stessa. Questo può essere fatto "semplicemente" accettando la relatività senza distinzione tra massa inerziale e accelerata in un'ipersfera dell'universo "infinitaMente accelerato" come è ora accettato in cui qualsiasi raggio ha lo stesso numero di punti prima di qualsiasi osservatore inerziale "tutto su tutto" coscientemente cosciente istantaneamente impigliato "  causando” il collasso della formazione delle onde della realtà.

Viktor T.Toth su Quora

Qual è il modo più semplice e facile da capire per spiegare come la massa aumenta con la velocità?

Il modo più semplice: la massa non aumenta con la velocità.

Sul serio.  La massa non aumenta con la velocità.

Quando ti muovi rispetto a un oggetto (ricorda: il movimento è sempre relativo, quindi un oggetto che si muove rispetto a te o tu che ti muovi rispetto a quell'oggetto significa letteralmente la stessa cosa) quell'oggetto non cambia.  Non sa nemmeno che ti stai muovendo rispetto ad esso.  Tuttavia, nel tuo sistema di riferimento, è quell'oggetto che si muove e, di conseguenza, ha energia cinetica calcolata da te.  (Per un altro osservatore, muovendosi insieme all'oggetto, l'oggetto è fermo e ha energia cinetica zero.)

Alcuni autori, specialmente nella letteratura più antica, combinarono questa energia cinetica e l'energia massa a riposo dell'oggetto in una quantità chiamata massa relativistica.


Questa quantità è priva di significato.  Differisce per diversi osservatori che si muovono a velocità diverse rispetto all'oggetto.  Non ha davvero alcuna utilità pratica.  Confonde solo le persone, piuttosto gravemente, sulla teoria della relatività.


Geoffrey Edwards su Quora


All'aumentare della velocità, la massa dell'oggetto aumenta in modo lineare fino a quando è necessaria un'energia infinita per spostare una massa infinita.  La dilatazione del tempo è il risultato del campo gravitazionale generato dalla massa dell'oggetto?

No. La massa non aumenta.  La quantità di moto di un oggetto aumenta con la velocità in questo modo:

p = \gamma*m*v

dove p è la solita lettera per la quantità di moto e \gamma è il fattore gamma relativistico.  All'inizio, le persone hanno notato che potevi assorbire la gamma nella m, chiamarla "massa relativistica" (M = gamma*m) e recuperare la solita relazione newtoniana:

p = Mv

Inoltre, questa massa aveva la solita proprietà che se si spingeva sull'oggetto lungo la direzione del moto con forza F si otteneva un'accelerazione a = F/M.  Tuttavia, questa particolare analogia probabilmente iniziò a scomparire quando le persone calcolarono per la prima volta l'accelerazione indotta da una forza trasversale e scoprirono che NON era F/M.

La maggior parte delle analogie sulla relatività sono fondamentalmente cattive idee perché rompono esplicitamente la base fondamentale della relatività, che è che la velocità intrinseca, se esiste, non può essere misurata.  La massa di un oggetto è ciò che misureremmo nel quadro di riferimento di un oggetto.  Deve essere invariante con la velocità - un cosiddetto "scalare".  Le orbite dei pianeti attorno al sole, ad esempio, non possono dipendere dal movimento del sole nello spazio (altrimenti potremmo usare le orbite per misurare la velocità intrinseca del sole).

La maggior parte delle analogie ha dei limiti e sono utili solo all'interno di quei limiti.  Il limite di questa particolare analogia è semplificare una sola domanda...

Se applico una forza esterna F lungo la linea di movimento di un oggetto con velocità v, qual è l'accelerazione?

... e basta.  La massa non aumenta davvero.  Per questo motivo, il concetto di massa relativistica è stato scartato praticamente da tutti perché è invariabilmente applicato al di fuori del suo dominio di applicabilità.

There are fundamental limits on how accurately one can determine the state of a quantum system due to the existence of non-orthogonal quantum states. The indistinguishability of quantum states poses a series of challenges in quantum communication and quantum information processing. In this report, we give an overview of various strategies for quantum state discrimination and discuss their connections.

I see fruitful interconnections between ethnology and quantum theory (following T. Görnitz, in the tradition of C. F. von Weizsäcker). In my master's thesis, I pursued them from a perspective of philosophy of science. Put in context within the intra-ethnological debate on cultural relativism, I address the 'trench warfare' between the natural sciences and the humanities, which goes back to the influences of classical physics. And I point out the interdependency between reductionist and holistics outlooks and how they are grounded in the science and epistemology of ethnology.
To give a more concrete example for said fruitful interconnections: With the Heisenberg uncertainty relation the transdisciplinary concept of the trade-off can be rethought or thought ahead. I use the example of concepts for gender equality, which are in the trade-off between social freedom and social security.

This thesis contains a theoretical treatment of the time-dependent quantum transport of electrons through molecular junctions. In particular, the nonequilibrium Green's function (NEGF) method is used to obtain the time-dependent current and current fluctuations in response to an arbitrarily time-dependent spatially homogeneous bias in the leads and molecular region. All subsystems in the nanojunction are assumed to be noninteracting throughout, and in addition the wide-band limit approximation (WBLA) is made in order to simplify the treatment of the lead-molecule coupling.

The theoretical work involves a complete analytical solution in the two-time plane of the Kadanoff-Baym equations for all components of the molecular region Green's function defined on the imaginary time Konstantinov-Perel' contour. This enables the derivation of expressions for time-dependent quantities such as the particle number in the molecular region and a generalized time-dependent Landauer-Büttiker (LB) formula for the current through an arbitrarily large conducting molecule. The partition-free approach is assumed for the switch-on of a bias in the leads, which enables us to study the effects on the transient transport of the initial coupling between the subsystems of the nanojunction.

The analytical expression for the full two-time Green's function is then used to study the quantum correlations between currents in the different leads. Using many-body methods, the two-time current correlation function is expressed in terms of a matrix product of Green's functions which are all known exactly. Therefore, in similar fashion to the generalized LB current, the current correlations generalize the LB theory of shot and thermal noise so that it is (i) partition-free and (ii) valid for an arbitrary time-dependent bias. To check its generality, this formula is shown to reproduce results for the zero- and finite-frequency current noise that are known from the literature on this topic.

The formulas for the current and current fluctuations are originally obtained in terms of integrals over the frequency and time planes. To render these formulas useful for calculations on large molecules they are then re-expressed with all frequency integrals replaced with special functions, which may be computed via the Padé expansion of the Fermi function. This results in a formalism which is ideally multiscale in time, i.e. which does not get more expensive with increasing number of time steps, and which can therefore be used to study the short-time transient and steady-state transport quantities with identical computational expense. Some numerical calculations of the current and noise response to the switch-on of a time-dependent bias are then performed.

The first kind of time-dependent driving considered in this thesis is periodic. Some preliminary calculations are performed on periodically-driven quantum dots, and the effect on the current of varying the driving frequency, temperature, lead-molecule coupling and driving amplitude is studied. Next, the problem of quantum pumping is considered, and sufficient conditions are found for a periodically driven system with zero time-average bias to generate a net time-averaged current through the system. The effects of finite size on the current response to static and periodic biases are investigated, again using the molecular wire as an illustrative model. Next, calculations of the quantum pump current are presented for a particular biharmonic bias model, and in particular the effect on this current of breaking the sinusoidal shape of the driving field. Finally, the discussion turns to calculations of the cross-lead current correlations in extended systems in response to static and periodic biases. By investigating molecular wires of different lengths and internal hopping parameters, a signature of the traversal time for electrons crossing the sample is found in both the transient and steady-state cross-lead current correlations.

As there are no restrictions on the nature of the time-dependent bias driving the system out of equilibrium, one can use this formalism to study the electronic response to a classically fluctuating bias in the leads. The second kind of time-dependent driving studied in this thesis is therefore non-deterministic, and exact formulas for the bias-averaged current response to a stochastic bias are derived for the first time. This problem is formally analogous to the use of the Langevin equation approach to obtain a relation between the conductance in a classical circuit and the strength of fluctuations in an external driving bias: the so-called Nyquist theorem. An exact quantum version of the Nyquist theorem is derived for a driving bias with colour noise which relates the strength of fluctuations, the correlation time of fluctuations, the temperature and conductance in a molecular junction. Due to the nonlinear relation between current and driving bias in these junctions, it is not always true that the conductance will decrease with increasing fluctuation strength. Instead, there can be particular intermediate values of the fluctuation strength at which peaks in the conductance are observed, in a stochastic resonance effect.

Page 1. Quantum Communications: Present Status and Future Prospects Prem Kumar, Joseph B. Altepeter, and Matthew A. Hall ... 16 J. Chen, et al. “Demonstration of a Quantum Controlled-NOT Gate in the Telecom Band,” Phys. Rev. Lett. 100, 133603 (2008). 17 NI Nweke, et al. ...

The theory of dual numerical means of random and experienced variables is briefly described in the framework of the new theory of experience and the chance that arises as an axiomatic synthesis of two dual theories — the Kolmogorov theory of probability and the theory of believability. A new term is introduced for the numerical mean of the experienced variable — mathematical reflection, which is dual to the mathematical expectation of a random variable within the framework of the new theory. The basic properties and examples of dual numerical means are considered.