S. N. Molotkov

Relativistic quantum cryptography

A new protocol of quantum key distribution is proposed to transmit keys through free space. Along with quantum-mechanical restrictions on the discernibility of nonorthogonal quantum states, the protocol uses additional restrictions imposed by special relativity theory. Unlike all existing quantum key distribution protocols, this protocol ensures key secrecy for a not strictly one-photon source of quantum states and an arbitrary length of a quantum communication channel.

Quantum cryptography based on quantum dots

Network protocols are formulated for the phase-coding and correlated-photon-pairs quantum cryptosystems. These protocols are free of the restriction imposed on the distance between the two legitimate users by the transmission loss in the optical fiber. A single-photon source and a source of correlated photon pairs based on quantum dots are proposed.

Teleportation of the relativistic quantum field

The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-relativistic quantum mechanics, the teleportation of an unknown state of the quantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the state of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum) state common to both the unknown state and the EPR-pair. Due to the common vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in the relativistic theory the teleportation in the sense it is understood in the non-relativistic quantum mechanics proves to be impossible because of the impossibility of the realization of the appropriate measurement as a tensor product of the measurements related to the individual subsystems so that one can only speak of the amplitude of the propagation of the field as a whole.Abstract The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-relativistic quantum mechanics, the teleportation of an unknown state of the quantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the state of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum) state common to both the unknown state and the EPR-pair. Due to the common vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in the relativistic theory the teleportation in the sense it is understood in the non-relativistic quantum mechanics proves to be impossible because of the impossibility of the realization of the appropriate measurement as a tensor product of the measurements related to the individual subsystems so that one can only speak of the amplitude of the propagation of the field as a whole.

On the theory of the tunneling current modulation at the Larmor frequency due to precession of an individual spin on a paramagnetic center

We present a theory accounting for the singularity in the tunneling current spectrum at the Larmor frequency observed by Manassen et al. [Phys. Rev. Lett. 62 (1989) 2531]. The singularity arises due to coherent tunneling of pairs of electrons with opposite spins accompanied by spin reversal of both electrons in the course of their scattering on the paramagnetic center.

Quantum key distribution on composite photons, polarization qutrits

Polarization states of a photon are the most natural degrees of freedom for encoding classical information bits. The two-dimensional space of states associated with polarization degrees of freedom of the photon is insufficient for many problems of information transfer with quantum states. We propose to use the polarization degrees of freedom of composite states of photons (polarization qutrits) for secret cryptographic key distribution.

Electronic structure of the superconducting compounds Tl2Ba2CuO6 and Bi2Sr2CuO6

Abstract The tight-binding method is used to investigate the electronic band structure of Tl 2 Ba 2 CuO 6 and Bi 2 Sr 2 CuO 6 crystals. Partial densities of states on various atoms as well as valences of the elements in these compounds have been determined. The calculated band structure of the considered compounds turns out to have a quasi-two-dimensional nature and strongly resembles that of La 2 CuO 4 . The major contribution to the density of states at the Fermi level was found to come from the hybridized d-orbitals of copper and p-orbitals of oxygen located in the CuO 2 planes.

On the security of fiber optic quantum cryptography systems without the control of the intensity of quasi-single-photon coherent states

Internal losses in systems of quantum cryptography can be used at attacks by an eavesdropper. As a result, the security of keys cannot be ensured for a number of protocols. This problem can be solved by using geometrically uniform coherent states with a larger number of bases. The security of keys at the number of bases Nb/2 = 4 and the number of states Nb = 8 can be guaranteed even without the control of the intensity of input states.

On the resistance of relativistic quantum cryptography in open space at finite resources

The security of keys for the basic nonrelativistic BB84 protocol has been examined for more than 15 years. A simple proof of security for the case of a single-photon source of quantum states and finite sequences has been only recently obtained using entropy uncertainty relations. However, the existing sources of states are not strictly single-photon. Since sources are not single-photon and losses in a quantum channel—open space—are not a priori known and vary, nonrelativistic quantum cryptographic systems in open space cannot guarantee the unconditional security of keys. Recently proposed relativistic quantum cryptography removes fundamental constraints associated with non-single-photon sources and losses in open space. The resistance of a fundamentally new family of protocols for relativistic quantum key distribution through open space has been analyzed for the real situation with finite lengths of transmitted sequences of quantum states. This system is stable with real sources of non-single-photon states (weakened laser radiation) and arbitrary losses in open space.

Relativistic quantum cryptography for open space without clock synchronization on the receiver and transmitter sides

The security of keys in quantum cryptography is based on fundamental quantum mechanical exclusions (the exclusion of cloning and copying of nonorthogonal quantum states. The physical type of a quantum object that carries information (photon, electron, atom, etc.) is insignificant; only its state vector is important. In relativistic quantum cryptography for open space, both the time of the information carrier (photon that propagates with the extremely allowable velocity in a vacuum) and its quantum state are of fundamental importance. Joint fundamental constraints that are dictated by both special relativity and quantum mechanics on the discrimination of nonorthogonal quantum states allow one to formulate fundamentally new key distribution protocols that are stable against any attacks on a key and guarantee the security of keys for a nonstrictly single-photon source and any losses in the communication channel. Although this protocol is a real-time protocol in the Minkowski space-time, where the attack to the communication channel is detected by the delay of eavesdropper measurement results, the protocol does not require clock synchronization on the transmitter and receiver sides.

On the electronic spectrum of low-dimensional structures with the symmetry of borders

The features of the electronic spectrum in low-dimensional (quasi-one-dimensional) structures with symmetry of borders have been considered. It has been shown that, in the spinless case, the conical massless (Dirac) form of the spectrum (ɛ(k) ∝ ± |k|) appears in groups with glide planes. This spectrum is a consequence of forced degeneracy, which appears due to the joint action of the lattice symmetry elements and time reversal invariance. For the spinor representations, the conical shape of the spectrum appears in all groups.