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We consider the process of remote state preparation using a pure state | ψ 〉 with the maximal Schmidt number n. For any given state σ, pure or mixed, a construction of a positive operator-valued measure { M j } j = 0 n is provided. The classical outcome j = 0 indicates the failure of a remote preparation of σ. All other classical outcomes j > 0 correspond to unitary transformations of the receiver system such that σ can be prepared. The total probability of successful remote preparation depends on the state σ. Our protocol is a variation of conclusive teleportation and the classical bits required for this protocol are given by log 2 ( n + 1 ) , which is nearly half that of conclusive teleportation.

Within the framework of the perturbation theory, a simple formula for the probability of a photoprocess for the whole time of action of an ultrashort electromagnetic pulse has been derived, when the concept of spectral intensity of radiation and probability per unit time is inapplicable. In the obtained formula the total probability is expressed in terms of the cross-section of a photoprocess in a monochromatic field and the Fourier transform of electric field strength. The advanced approach is applied for the analysis of photoabsorption of an atom and a metal nanosphere under the action of a subcycle laser pulse with a changeable value of the carrier–envelope phase. The expressions for probability and energy of photoabsorption in the limit of a zero pulse duration have been obtained.

We present a scheme for probabilistic remote preparation of the four-particle Greenberger–Horne–Zeilinger (GHZ) class state by using two partial entangled three-particle GHZ states as the quantum channel. The successful total probability and classical communication cost are calculated. Our results show that such remote state preparation requires only 1 bit classical communication cost for the maximally entangled channel.

The photon emission intensity spectrum is calculated taking into account influence of multiple scattering (the LPM effect) under conditions of recent CERN SPS experiment. It is shown that the theory quite satisfactory describes data. The integral characteristics: the radiation length and total probability of photon emission are analyzed under influence of the LPM effect, and the asymptotic expansions of these characteristics are derived., Comment: 17 pages, 5 figures

Muon sticking probabilities are determined for the nuclear fusion in the symmetric muonic molecular ions ddμ and ttμ. In particular, the muon sticking probabilities have been computed for the two reaction channels in the (d,d)-reaction. The total probability of the ( 3 He μ) + ion formation (in the neutron channel) is ≈14.0423%, while analogous probabilities for the tμ and pμ atoms are ≈1.6870% and ≈0.0014%, respectively (in the proton channel). The final state probability for the ( 4 He μ) + ion formation in the (t,t; 4 He ,2n) -reaction in the ttμ ion is bounded between ≈4% and ≈7%. It is shown that comparison between computed and measured probabilities can improve our present understanding of the (t,t)-nuclear reaction.

The definition of conditional probabilities is based upon the existence of a joint probability. However, a reconstruction of the joint probability from given conditional probabilities imposes certain constraints upon the latter, so that if several conditional probabilities are chosen arbitrarily, the corresponding joint probability may not exist. Such an incompleteness in conditional probabilities can be eliminated by introducing complex probabilities. The physical meaning of the new mathematical formalism, as well as its relation to quantum probabilities, is discussed.

A criterion for stochastic resonance in a bistable system which is modulated by a harmonic force can be developed from the study of time dependent probability densities. The amplitude with which the probability density oscillates is a measure of the total probability flow between the potential wells. Stochastic resonance can be observed in an increase of the amplitude for specific values of the noise strength.

An explicit analytic solution of the Pauli master equation for the incoherent exciton motion in the infinite linear chain with a single trap is presented. The total probability to find the exciton in the chain is also calculated.

It is shown that in any quantum state ϕ the probability of the conditional, ϕ (A→B), is not equal to the conditional probability, ϕ(AB), for some projections A, B in the lattice P(M) of projections of a Neumann algebra M if → is Mittelstaedt's conditional in P(M) and ϕ(AB) is given by a conditional expectation. This difference between ϕ(A→B) and ϕ(AB) is shown to be generic and is interpreted as the impossibility to describe quantum statistical inference in terms of quantum logic in a certain way.