Stanislav Straupe

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.

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.

Angular Schmidt modes in spontaneous parametric down-conversion

We report a proof-of-principle experiment demonstrating that appropriately chosen set of HermiteGaussian modes constitutes a Schmidt decomposition for transverse momentum states of biphotons generated in the process of spontaneous parametric down conversion. We experimentally realize projective measurements in Schmidt basis and observe correlations between appropriate pairs of modes. We perform tomographical state reconstruction in the Schmidt basis, by direct measurement of single-photon density matrix eigenvalues.

Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons

We report an experiment on preparation and characterization of general four-dimensional quantum states using ultrafast-pumped frequency-nondegenerate spontaneous parametric down-conversion. We also discuss two additional experimental schemeswhich offermore complete control of the state purity and entropy.

Entanglement of biphoton states: qutrits and ququarts

We investigate, in a general form, entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of, correspondingly, degenerate and non-degenerate spontaneous parametric down-conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and polarization entanglement are fully taken into account. In the case of qutrits, the most general three-parametric families of maximally entangled and non- entangled states are found, and anticorrelation of the degree of entanglement and polarization is shown to occur and to be characterized by a rather simple formula. Biphoton ququarts are shown to be two-qudits with the single-photon Hilbert space dimensionality d = 4, which differentiates them significantly from the often used two-qubit model (d = 2). New expressions for entanglement quantifiers of biphoton ququarts are derived and discussed. Rather simple procedures for a direct measurement of the degree of entanglement are described for both qutrits and ququarts.

Quantum state engineering with ququarts: Application for deterministic QKD protocol

We discuss the proof-of-principle demonstration of the extended deterministic Quantum Key Distribution (QKD) protocol based on ququarts. The experimental realization is based on the polarization degrees of freedom of two-mode biphotons, making the process of state preparation, transformation and measurement rather simple. The scheme uses only single nonlinear crystal for biphoton generation and linear optical elements for their following transformation and can be used as a base for further practical applications.

Experimental adaptive process tomography

Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of precision for state reconstruction. In this article we generalize an adaptive Bayesian approach to the case of process tomography and experimentally show its superiority in the task of learning unknown quantum operations. Our experiments with photonic polarization qubits cover all types of single-qubit channels. We also discuss instrumental errors and the criteria for evaluation of the ultimate achievable precision in an experiment. It turns out, that adaptive tomography provides a lower noise floor in the presence of strong technical noise.

Adaptive quantum tomography

We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We argue in favor of the Bayesian approach, highlighting both its advantages for a statistical reconstruction of unknown quantum states and processes, and utility for adaptive experimental design. The discussion is supported by an analysis of several recent experimental implementations and numerical recipes.

Self-calibrating tomography for angular Schmidt modes in spontaneous parametric down-conversion

We report an experimental self-calibrating tomography scheme for entanglement characterization in highdimensional quantum systems using Schmidt decomposition techniques. The self-tomography technique based on maximal likelihood estimation was developed for characterizing nonideal measurements in the Schmidt basis, allowing us to infer both Schmidt eigenvalues and detecting efficiencies.

Schmidt-like coherent mode decomposition and spatial intensity correlations of thermal light

We experimentally study the properties of coherent mode decomposition for the intensity correlation function of quasi-thermal light. We use the technique of spatial mode selection developed for studying the transverse entanglement of photon pairs, and show that it can be extended to characterize classical spatial correlations. Our results demonstrate the existence of a unique, for a given thermal source, basis of coherent modes, correlated in a way much resembling the Schmidt modes of spatially entangled photons.We experimentally study the properties of coherent mode decomposition for intensity correlation function of quasi-thermal light. We use the technique of spatial mode selection developed for studying transverse entanglement of photon pairs, and show that it can be extended to characterize classical spatial correlations. Our results demonstrate the existence of a unique for a given thermal source basis of coherent modes, correlated in a way much resembling the Schmidt modes of spatially entangled photons.