We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.

It is shown, under the assumption of possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously. The measurement is based on teleportation method. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.

A concept of computational complexity is applied for analysis of classical and quantum dynamical systems. It is argued that evolution of wave functions in nonintegrable quatnum systems lies in complexity class EXP because of rapid growth of number of elementary computational operations needed to predict their future. On the other hand, evolution of wave functions in integrable systems can be predicted by the fast algorithms and thus it belongs to P class. This difference between integrable and nonintegrable systems in our approahc looks identically for classical and quantum systems. In this paper an informational approach is applied for analysis of dynamics in classical and quantum systems to find a universal different between integrable and nonintegrable motion. As a basic tool to analyze compleixty of dynamics we use a number of elementary computational operations O(T) (computational complexity) needed to determine a state of a sytem for time interval T.

In this paper we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimenion. Entanglement can be classified in the framework of the scaling theory of phase transition. There is a profound difference between the classical correlations, whose correlation length diverges at the phase transiton, and non-local quantum correlations that remain, in general, short ranged.

Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It is shown next, how for quantum computation with qubits can be used two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford algebras, and discussed well known applications to product operator formalism in NMR, Jordan-Wigner construction in fermionic quantum computations. It is introduced universal set of quantum gates for higher dimensional system ("qudit"), as some generalization of these models. Finally it is briefly mentioned possible application of such algebraic methods to design of quantum processors (programmable gates arrays) and dsicussed generalization to quantum computation wiht continuous variables.

The main quantum information measures are discussed with respect to their relation to physics. It is argued that the basic term to choose betweenthe possible ways to measure quantum information is compatibility/incompatibility of the quantum states, resulting in coherent information and here suggested compatible information measures. A sketch of information optimization of a quantum experimental setup is proposed.

There is investigated theoretical possibility to make quantum computer elements by means of Ion Lithography with resolution of details about 2 nm. The axisymmetrical combined immersion lenses of three types are investigated for this aim in a whole range of working regimes from the edge of pure electrostatic regime to the edge of combined mirror regime. Simple analytical approximations are derived for four main ion-optical parameters of combined lenses: focal length f, coefficient of chromatic aberration Cd, coefficient of spherical aberration of the third order Cs, and Amper-turns in the magnetic coil of combined lens NI. These parameters are expressed in form of functions of dimensionless quantity (formula available in paper) is the energy of ions at the lithographic target and W₀ is the initial energy of ions. It is shown that axial aberrations of combined lenses (Cc and Cs) and focal length f have a maximum under absence of magnetic field (when lenses are pure electrostatic). It is shown that under ττ yeilds 0 parameters Cc, Cs, f and NI, as functions of quantity τ, take forms: Cc~τ^1/6, Cs~τ^1/4, f~τ^1/3, NI~τ^(-1/2). It is shown also that the Ion Lithographic image (by using heavy ions in non-resist regime) could have 2*10¹² pixels under resoltuion 2nm in the frame 3×3mm².

The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistitic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not empoly collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of "antedate" coding).

In this paper we fil a gap in previous work by proving the conjectured formula for the antanglement-assisted capacity of quantum channel with additive input constraint (such as Bosonic Gaussian channel). The main tools are the coding theorem for classical-quantum constrained channels and a finite dimensional approximation of the input density operators for the entanglement-assisted capacity.

Safety of quantum communications is, in the first place, the result of the quantum nature of the signal, sending by the sender Alice to the receiver Bob. But when we discuss the safety of the quantum communications as a whole we have to take into account all objects taking place in the process of creation and communciation of information. One of such object is the sending station, which is a classical one. As such it can be eavesdropped by classical means and this fact can reduce sharply the safety of quantum channel. In this noe we demonstrate, that dense coding and quantum properits of the channel give the possibility to raise the safety of classical sending station against the eavesdropping.

A new quantum mechanical notion - Conditional Density Matrix - proposed by the authors, is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of quantum systems into subsystems and reunifications of subsystems into new joint systems. Conditional Density Matrix assigns a quantum state to a subsystem of a composite system under condition that another part of the composition system is in some pure state. It is shown that conditional density matrix naturally arises by expanding of reduced density matrix.

A road map for the fabrication of epitaxial metallic electrodes, quantum dots and wires is considered for potential application in solid-state qubit technology. The nanotechnology developed includes high quality low-roughness film epitaxy, probe lithography and subtractive techniques for the fabrication of epitaxial nanostructures with a lateral resolution down to 10 nm.

Quantum cryptography is essentially the quantum key distribution (QKD). In the context of QKD, one from two partners (Alice) generates and sends a sequence of qubits through a private quantum channel to another partner (Bob) and Bob receives the sequence and measures the state of each qubit. After the quantum transmission stage, Alice and Bob have almost identical qubit sequences. The erros are due to physical imperfections in the channel and presence of an eavesdropper. The next stage in QKD is key reconciliation (i.e. finding and correcting discrepancies between Alice's string and that of Bob). This reconciliation can be done by public discussion. Let us suppose there is a secret quantum channel between Alice and Bob through which Alice transmits a n-bit string A=(A₁, A₂,...,A_n)ε{0,1}ⁿ. Then Bob receives a n-bit string B=(B₁, B₂,...,B_n)ε{0,1)ⁿ. The string B differs from A due to the presence of noise and eavesdropper in the channel. One can estimate the bit error probability in the channel. For example, Bob can choose a random subset from his string and send it to Alice in public. Then Alice compares the received string with her corresponding subset and calculates the total number of protocol steps. The cascade scheme uses the interaction over the public channel to correct the secret strings by dividing them into the blocks of a fixed length. The length is determined from the bit error probability. A simple interactive routine is applied in each of these blocks. An error found in some block results in some action with other blocks. It is important to optimize the error-finding routines in standalone blocks as well as to organize the effective constrution of blocks with the object of protocol benchmark, information leakage and number of interactions between partners.

We present the first findings of the transmission phase shift π/2 in the 0.7(2e²/h) structure of the quantum staircase and in the Kondo-correlated states revealed by an open system which represents a short quantum wire that is inserted within one of the arms of the Aharonov-Bohm (AB) ring inside the p-type self-assembled silicon quantum well prepared on the n-type Si (100) wafer. The quantum well of the p-type is naturally formed between δ-barriers by short-time diffusion of boron. The phase shift in the 0.7(2e²/h) structure caused by heavy holes is found to be changed from π to π by electrically-detected NMR of the ²⁹Si nuclei thereby verifying the spin polarization in a quantum wire. The optical nuclear polarization of the ²⁹Si nuclei induced by circularly polarized light in the n-type Si(100) wafer is shown to effect also on the coherent transport of holes through the quantum wire inserted within one of the AB ring's arms. The quantum conductance revealed by the quantum wire that is embedded in the AB ring inside self-assembled silicon quantum well in the weak localization regime is studied to demonstrate the coherence of the single-hole transport and negative magnetic resistance effect. The positive/negative transformation of the magnetoresistance in the weakest magnetic fields is found to be caused by the electrically-detected NMR of the ²⁹Si nuclei thereby verifiying the effect of the nuclear spin polarization on a weak antilocalization.

Quantum neural technology is a hypothetical but promising new field of informatics, which combines together the main ideas of both quantum and neural computing. There is a hope that this combination can resolve many problems of already existing classical neural technology, and also can give new opportunities to future quantum computing. Comparing with classical neural technology its quantum analog can enhance dramatically the capacity of neural modesl of associative memory, to facilitate the creation of neural hardware by eliminating the wiring problem, etc. On the other hand, as it will be argued in presented paper, quantum neural system can be used for realization of controllable quantum gates, which can be used in quantum computers, and in particular, in so-called type-II quantum computers.

We investigate theoretically the Zeeman effect on the lowest confined hole in quantum dots. In frame of tight-binding approach we propose a method of calculating the Lande factor for localized states. The principal values of the g-factor for the ground hole state in the self-assembled Ge/Si quantum dot are calculated. We find the strong g-factor anisotropy - the components g_xx, g_yy are one order smaller than the g_zz-component, g_zz=15.71, g_xx=1.14, g_yy=1.76. The efficiency of the developed method is demonstrated by calculating the size-dependence of g-factor and by establishment of the connectin with 2D case. The g-factor anisotropy increases with the island and the ground hole state g-factor goes to heavy hole g-factor. The analysis of the wave function structure shows that g-factor and its size-dependence are mainly controlled by the contribution of the state with J_z=±3/2.

A novel solid state quantum comptuer is discussed. Nuclear spins-qubits are the basic elements of quantum register, while single electron resonant transfer is used to obtain complex many-qubit gates. The electron's quantum dynamics analyiss shows the possibility of individual addressing in large registers. Planar and ensemble architectures are also proposed.

The processes of four-photon interactin in optical distributed feedback ssytems have been considerd. The conditions for using such systems as the base of quantum logic gates realization are clarified taking into account different energy exchange processes between interacting modes.

The problem of possible violation of the second law of thermodynamics is discussed. It is noted that the task of the well known challenge to the second law called Maxwell's demon is put in order a chaotic perpetual motion and if any ordered Brownian motion exists then the second law can be broken without this hypothetical intelligent entity. The postulate of absolute randomness of any Brownian motion saved the second law in the beginning of the 20th century when it was realized as perpetual motion. This postulate can be proven in the limits of classical mechanics but is not correct according to quantum mechanics. Moreover some enough known quantum phenomena, such as the persistent current at non-zero resistance, are an experimental evidence of the non-chaotic Brownian motion with non-zero average velocity. An experimental observation of a dc quantum power soruce is interperted as evidence of violation of the second law.

A state ψ = α/00] + β/01] + γ/10] +δ/11] of a system of two qubits is separable if the equality among pair-wise products αδ = βγ holds. This paper generalize this form of condition for distinguishing among separable and entangled states of systems of n qubits. Given a pure state /ψ_N] of a quantum system composed of n qubits, where N = 2ⁿ, this paper defines minimal sets of equalities among pair-wise products of amplitudes of /ψN] for characterizing two forms of separability of /ψ_N]: (i) into a tensor product of n qubit states /ψ₂]₀ x/ψ₂]₁ x...x/ψ₂]_n-1, and (ii), into a tensor product of 2 subsystems states /ψ_p]x/ψ_Q] with P=2^p and Q=2^q such that p+q=n.

A spin state of an electron in a quantum dot (quantum bit) could be tested by a spin-polarized current passing through the narrow constriction in a quantum wire placed near the dot. A fairly strong tunnel coupling between the quantum dot and the constriction is required to enhance an exchange interaction. Charge related phenomena such as a charge blockade and single electron flow through the narrow constriction are examined. The conditions when a spin blockade dominates are revealed.

Thanks to resent achievements in the Electron Beam Lithography (EBL) and Focused Ion Beam (FIB) lithography was built new type of electron devices: vacuum field emission nanodiode and nanodiode and nanotriode. Nanodiode and nanotriode have cathode about 2 nm in diameter, anode current 10 nA and gate potential 10 V. These devices display new quatnum properties. In the paper of Driscill-Smith et al was experimentally displayed series of the interference oscillation in the transconductance of nanotriode by linear chaging of the gate potential. The model of quantum potential box used by the authors of the work has does not explain the effect. In the present paper is made an attempt to explain the properties of nanotriode by means of the quansi-classical eikonal method and the diffraction theory. Simultaneously it is suggested to change the parameters of the nanotriode to display clearer quantum properties.

It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of 31P donor atoms having nuclear spin I=1/2. It is considered here, as main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity and of spin temperature whereby the required decoherence suppression is obtained. It is discussed the random phase error suppression in the ensemble quantum register basic states.

We study a realistic quantum computational model with the permanent interaction of diagonal type between qubits. Its universality was proven in quant-ph/0202030. We propose two types of control over computations: random and periodical NOTs. The slowdown of computations in comparison with the abstract model is estimated. It is shown how fermionic computations can be implemented in the framework of this model.

The InAs/AlGaSb heterostructures are promising candidates for fabricating the quantum computer due to the large electron g-factor in the bulk InAs and hence large spin splitting of electron-like Landau levels in a quantizing magnetic field. The two lowest electron-like spin levesl can be used as a qubit of a quantum computer. Then the one-qubit operations can be performed by the circulary polarized light of photon energy approximately equal to the spin splitting of levels. These transitions rae possible because of the mixing of the states of different spin orientations caused by the spin-orbit interaction. Previously it has been found that the additional AlGaSb layer can essentially enhance the spin splitting of electron-like levels when the magnetic field is normal to the InAs/AlGaSb interface due to the hybridization of electron and hole levels. Here we investigate the Landau-level structures in strained InAs/GaSb heterostructures using the scattering matrix method and Burt's envelope function theory. We obtain somewhat different results. The spin splitting of electron-like Landau levels considerably enlarges when the hybridization of electron and hole levels becomes negligibly small with the magnetic field increasing. We find that this splitting depends essentially on the lattice-mismatched strain and can be as large as 15 meV at magnetic field B ≥ 15 T for the structure grown on InAs.