E. V. Moreva

Anisotropically and high entanglement of biphoton states generated in spontaneous parametric down-conversion

We show both theoretically and experimentally that biphoton wave packets generated via spontaneous parametric down-conversion can be strongly anisotropic and highly entangled. The conditions under which these effects exist are found and discussed.

Statistical estimation of the efficiency of quantum state tomography protocols.

Y u. I. Bogdanov, G.Brida,M.Genovese, S. P. Kulik, E. V. Moreva, A. P. Shurupov 1 Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia 2 INRIM, I-10135, Torino, Italy 3 Faculty of Physics, Moscow State University, 119992, Moscow, Russia 4 Moscow National Research Nuclear University ”MEPHI”, Russia and 5 Dipartimento di Fisica, Politecnico di Torino, I-10129, Torino, Italy (Dated: February 18, 2010)

Polarization states of four-dimensional systems based on biphotons

We discuss the concept of polarization states of four-dimensional quantum systems based on frequency non-degenerate biphoton field. Several quantum tomography protocols were developed and implemented for measurement of an arbitrary state of ququart. A simple method that does not rely on interferometric technique is used to generate and measure the sequence of states that can be used for quantum communication purposes.

Optimization of a quantum tomography protocol for polarization qubits

An operational method has been proposed for estimating the efficiency of quantum cryptography protocols for quantum states with discrete variables. The method is based on the estimate of the quality of the protocol by means of a universal asymptotic distribution of the characteristic of the accuracy of the reconstruction of the quantum state, which is called fidelity. For a specially designed measurement matrix, the condition number, which is minimal for the optimal protocol, is introduced. The method has been tested in a numerical simulation and real experiments with polarization qubits. It has been shown that the optimal choice of a polarization transformer makes it possible to strongly improve the quality of the reconstruction of states.

Statistical reconstruction of mixed states of polarization qubits

The method of estimating the adequacy, completeness, and accuracy of quantum tomography protocols is generalized to the case of mixed states of polarization qubits. The efficiency of the method is illustrated based on mathematical modeling and experimental investigation of some practically important quantum tomography protocols.

Quantum polarization transformations in anisotropic dispersive media

Based on the concept of χ -matrix and Choi–Jamiolkowski states we develop the approach of quantum process reconstruction. The key part of the work is devoted to the adequacy of applied reconstruction models. The approach is tested with the statistical reconstruction of the polarization transformations in anisotropic and dispersive media realized by means of quartz plates and taking into account the spectral structure of input polarization states.

Optical polarization echo: Manifestation and study by methods of quantum tomography of states and processes

The polarization echo effect is demonstrated, which is manifested in the identity of a composite polarization transformation irrespective of the spectrum of the input polarization state. The pure input state transfers during its evolution to a completely mixed state and then returns to the initial state. The stages of this evolution are completely analogous to the corresponding stages of the “classical” spin echo effect. The adequacy of transformations performed for conditionally prepared one-photon polarization states is verified by the tomography of the quantum process.

Practical implementation of multilevel quantum cryptography

The physical principles of a quantum key distribution protocol using four-level optical systems are discussed. Quantum information is encoded into polarization states created by frequency-nondegenerate spontaneous parametric down-conversion in collinear geometry. In the scheme under analysis, the required nonorthogonal states are generated in a single nonlinear crystal. All states in the selected basis are measured deterministically. The results of initial experiments on transformation of the basis polarization states of a four-level optical system are discussed.

Mathematical modeling of the accuracy characteristics in problems of precision quantum tomography of biphoton states

A model that approximately takes into account instrumental errors in problems of precision reconstruction of quantum states is considered. The model is based on the notion of coherence volume, which characterizes the quality of the experimental and technological realization of the measurement protocol of a quantum state. Various sources of instrumental errors that affect the reconstruction accuracy of quantum states are mathematically modeled. It is shown that, for precision tomography of quantum states, one should take into account random coincidences that occur because the operating time of the photon detection system is finite. Among other possible sources of instrumental errors of the measurement protocol, one should take into account errors of the rotation angles and optical thicknesses of polarization plates, a possible drift in the parameters of the pump laser, and so on.

Quantum tomography of the optical four level states

We discuss a procedure of measurement of an arbitrary quantum state of an optical system in Hilbert space with the dimension d=4. Such states can be realized using a collinear frequency-nondegenerate regime of spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. A high accuracy of the reconstruction of the states (above 99%) indicates that the procedures proposed for reconstructing the quantum state of the system are adequate.