Evgueni Karpov

Quantum key distribution over 25 km with an all-fiber continuous-variable system

We report on the implementation of a reverse-reconciliated coherent-state continuous-variable quantum key distribution system, with which we generated secret keys at a rate of more than 2 kb/s over 25 km of optical fiber. Time multiplexing is used to transmit both the signal and phase reference in the same optical fiber. Our system includes all experimental aspects required for a field implementation of a quantum key distribution setup. Real-time reverse reconciliation is achieved by using fast and efficient low-density parity check error correcting codes.

Friedrichs model with virtual transitions. Exact solution and indirect spectroscopy

The Friedrichs-type model of interaction between matter (multilevel system) and radiation including virtual transitions is considered. The canonical Bogolubov transformation diagonalizing the total Hamiltonian is constructed. It is pointed out that the transformation is improper when the discrete part of the spectrum of system is “dissolved” in the continuous one. The new vacuum state for the total Hamiltonian is obtained. The time evolution of the bare vacuum and the bare operators is calculated. Using the exact solution, the result of Passante, Petrosky, and Prigogine [Physica A 218, 437 (1995)] that the transition from the bare vacuum state to the true vacuum leads to the emission of real photons is confirmed. The dressing of the bare vacuum at the presence of resonances is an irreversible process. The relation of the result with the idea of “indirect spectroscopy” is discussed.

Equivalence relations for the classical capacity of single-mode Gaussian quantum channels.

We prove the equivalence of an arbitrary single-mode Gaussian quantum channel and a newly defined fiducial channel preceded by a phase shift and followed by a Gaussian unitary operation. This equivalence implies that the energy-constrained classical capacity of any single-mode Gaussian channel can be calculated based on this fiducial channel, which is furthermore simply realizable with a beam splitter, two identical single-mode squeezers, and a two-mode squeezer. In a large domain of parameters, we also provide an analytical expression for the Gaussian classical capacity, exploiting its additivity, and prove that the classical capacity cannot exceed it by more than 1/ln2 bits.

Quantum Zeno and anti-Zeno effects in the Friedrichs model

We analyze the short-time behavior of the survival probability in the frame of the Friedrichs model for different formfactors. We have shown that this probability is not necessary analytic at the time origin. The time when the quantum Zeno effect could be observed is found to be much smaller than usually estimated. We have also studied the anti-Zeno era and have estimated its duration.

Explicit construction of a time superoperator for quantum unstable systems

Abstract A time superoperator T conjugate to the Liouville superoperator LH=[H,] is constructed for a quantum system with one excited state or unstable particle. While there is no time operator conjugate to the Hamiltonian in the wave function space due to the positivity of energy, T may exist in the density matrix space as the spectrum of LH covers all the real axis. This is the first example of an observable that can only be formulated in the Liouville–von Neumann space of density matrices. In our example the expectation value of T gives the lifetime of the unstable particle. Once the time superoperator is obtained it is easy to define an entropy superoperator.

Capacity of a bosonic memory channel with Gauss-Markov noise

We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a “quantum water-filling” solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit of an infinite number of modes. The method can also be applied to a more general noise environment which is constructed by a stationary Gauss process. The extension of our results to the case of broadband bosonic channels with colored Gaussian noise should also be straightforward.

Entanglement-enhanced classical capacity of quantum communication channels with memory in arbitrary dimensions

We study the capacity of d-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.

Cloning quantum entanglement in arbitrary dimensions

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of d-dimensional quantum systems prepared in an arbitrary isotropic state. It maximizes the entanglement of formation contained in the two copies of any maximally entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of isotropic states. For large d, the entanglement of formation of each clone tends to one-half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one-fourth the input entanglement in the large-d limit.

Structure and time-dependent mechanical behavior of highly oriented polyethylene

The structures of polyethylene films and film fibers, having different orientation degrees and prepared by orientational crystallization and orientational drawing, have been investigated by electron microscopy and X-ray diffraction and specific features of the supermolecular structures and differences in the mechanical properties of the samples obtained by these methods have been discovered. Thermomechanical tests have also shown that samples prepared by the two techniques demonstrate different behavior on heating. The time-dependent behavior of the mechanical properties – tensile strength and elastic modulus – have been studied. The phenomenon of slow relaxation of the elastic modulus has been observed for the samples obtained by orientational drawing. It is shown that a long-term decrease in the elastic modulus can be attributed to the presence of structural elements capable of relaxation due to a weak connection between them, their small sizes, and the inhomogeneity of the sample deformation during orientational drawing.

Extending Hudson’s theorem to mixed quantum states

According to Hudson’s theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step toward the extension of this theorem to mixed quantum states by finding upper and lower bounds on the degree of non-Gaussianity of states with positive Wigner functions. The bounds are expressed in the form of parametric functions relating the degree of non-Gaussianity of a state, its purity, and the purity of the Gaussian state characterized by the same covariance matrix. Although our bounds are not tight, they permit us to visualize the set of states with positive Wigner functions.