A. P. Shurupov

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)

Experimental Estimation of Entanglement at the Quantum Limit

Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.

Experimental estimation of quantum discord for a polarization qubit and the use of fidelity to assess quantum correlations

INRIM, I-10135, Torino, Italy(Dated: May 22, 2013)We address the experimental determination of entropic quantum discord for systems made of a pair of polar-ization qubits. We compare results from full and partial tomography and found that the two determinations arestatistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. De-spite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-dampedstates, their entropic discord may be largely different from that predicted for these classes of states, such thatno reliable estimation procedure beyond tomography may be effectively implemented. Our results, togetherwith the lack of an analytic formula for the entropic discord of a generic two-qubit state, demonstrate that theestimation of quantum discord is an intrinsically noisy procedure. Besides, we question the use of fidelity as afigure of merit to assess quantum correlations.

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.

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.

Optimal estimation of entanglement in optical qubit systems

We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to precision. In particular, we present a set of experiments aimed at measuring the amount of entanglement for states belonging to different families of pure and mixed two-qubit two-photon states. Our scheme is based on visibility measurements of quantum correlations and achieves the ultimate precision allowed by quantum mechanics in the limit of Poissonian distribution of coincidence counts. Although optimal estimation of entanglement does not require the full tomography of the states we have also performed state reconstruction using two different sets of tomographic projectors and explicitly shown that they provide a less precise determination of entanglement. The use of optimal estimators also allows us to compare and statistically assess the different noise models used to describe decoherence effects occurring in the generation of entanglement.

Separable Schmidt modes of a nonseparable state

Two-photon states entangled in continuous variables such as wavevector or frequency represent a powerful resource for quantum information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several non-overlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comb-like spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of non-overlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.

On quantum key distribution using ququarts

A comparative analysis of quantum key distribution protocols using qubits and ququarts as information carriers is presented. Several schemes of incoherent attacks that can be used by an eavesdropper to obtain secret information are considered. The errors induced by the eavesdropper are analyzed for several key distribution protocols.

Two-photon spectral amplitude of entangled states resolved in separable Schmidt modes

The ability to access high dimensionality in Hilbert spaces represents a demanding key-stone for state-of-the-art quantum information. The manipulation of entangled states in continuous variables, wavevector as well frequency, represents a powerful resource in this sense. The number of dimensions of the Hilbert space that can be used in practical information protocols can be determined by the number of Schmidt modes that it is possible to address one by one. In the case of wavevector variables, the Schmidt modes can be losslessly selected using single-mode fibre and a spatial light modulator, but no similar procedure exists for the frequency space. The aim of this work is to present a technique to engineer the spectral properties of biphoton light, emitted via ultrafast spontaneous parametric down conversion, in such a way that the two-photon spectral amplitude (TPSA) contains several non-overlapping Schmidt modes, each of which can be filtered losslessly in frequency variables. Such TPSA manipulation is operated by a fine balancing of parameters like the pump frequency, the shaping of pump pulse spectrum, the dispersion dependence of spontaneous parametric down-conversion crystals as well as their length. Measurements have been performed exploiting the group velocity dispersion induced by the passage of optical fields through dispersive media, operating a frequency-to-time two-dimensional Fourier transform of the TPSA. Exploiting this kind of measurement we experimentally demonstrate the ability to control the Schmidt modes structure in TPSA through the pump spectrum manipulation.

Separable Schmidt modes of an entangled state

Two-Photon Spectral Amplitude of entangled states is engineered to produce a losslessly decomposition in non-overlapping single Schmidt modes. The method relies on spontaneous parametric down-conversion pumped by a comb-like spectrum radiation.