Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities. PACS numbers:Many interesting properties of composite quantum systems, such as entanglement or entropy, are not measured directly but are inferred, usually from a full specification of a quantum state represented by a density operator. However, it is interesting to note that some of these properties can be measured in the same way we measure and estimate average values of observables. Here we illustrate this by extracting a non-local quantity, the Renyi entropy of the composite system, from local measurements on two pairs of polarization entangled photons. This quantity is a non-linear function of the density operator. We then use our experimental data to demonstrate the violation of entropic inequalities, which can be also interpreted as the experimental demonstration of a non-linear entanglement witness.Consider a source which generates pairs of photons. The photons in each pair fly apart from each other to two distant locations A and B. Let us assume that the polarization of each pair is described by some density operator ̺, which is unknown to us. Following Schrödinger's remarks on relations between the information content of the total system and its sub-systems [1], it has been proven that for separable states global von Neumann entropy is always not less then local ones [2]. Subsequently a number of entropic inequalities have been derived, satisfied by all separable states [3,4,5,6]. The simplest one is based on the Renyi entropy, or the purity measure, Tr (̺ 2 ) and can be rewritten aswhere ̺ A and ̺ B are the reduced density operators pertaining to individual photons. The inequalities (1) involve non-linear functions of density operators and are known to be stronger than all Bell-CHSH inequalities [3,7]. There are entangled states which are not and S2 emit pairs of polarization-entangled photons. The entangled pairs are emitted into spatial modes 1 and 3, and 2 and 4. One photon from each pair is directed into location A and the other into location B. At the two locations photons impinge on beam-splitters and are then detected by photodetectors. There are four possible outcomes in this experiment: coalescence at A and coalescence at B, coalescen...

We report on theoretical and experimental demonstration of high-efficiency coupling of two-photon entangled states produced in the nonlinear process of spontaneous parametric down conversion into a single-mode fiber. We determine constraints for the optimal coupling parameters. This result is crucial for practical implementation of quantum key distribution protocols with entangled states.c 2008 Optical Society of America OCIS codes: 000.1600, 220.4830.Entangled-photon pairs generated in the nonlinear process of spontaneous parametric down conversion (SPDC) are proven to be a highly desirable means 1 for practical quantum cryptography 2 . The main difficulty of practical utilization of such system usually stems from a relatively low photon collection efficiency because of the complex spatial distribution of SPDC radiation and due to the broad spectral width of entangled-photon wave packets.The problem of coupling entangled photons into a fiber has been considered before by Kurtsiefer et al.3 . Assuming the pump to be a plane wave the emission angle of the SPDC has been calculated as a function of the wavelength. The waist of the focused pump beam has been chosen to maximally overlap the "impression" of the Gaussian mode of a single-mode fiber on the crystal 3 . It has been pointed out that the coupling efficiency may be significantly affected by transverse walk-off.In this letter we present a significantly modified approach allowing us to achieve a high-efficiency coupling of the SPDC pairs into single mode fibers. In particular, we demonstrate how the pump beam waist, crystal length, optical system magnification and the fiber mode field diameter (MFD) must obey a precise joint relation in order to ensure high coupling efficiency. We describe a The function Φ(q o , ω o ; q e , ω e ) = E p (q o + q e , ω o + ω e ) χ (2) (q o , ω o ; q e , ω e ) accounts for the phase matching conditions. E p (·) represents the amplitude of the plane-wave expansion of the pump field andInside the crystal the zcomponent of the wave-vector is defined as k z (q, ω) = [ω n(q, ω)/c] 2 − |q| 2 . All the information on the state is given by the amplitude A 1,2 (x 1 , t 1 ; x 2 , t 2 ) 5,6 of detecting the SPDC two-photons in space-time events at (x 1 , t 1 ) and (x 2 , t 2 ). The Fourier transform with respect to t 1 and t 2 of the two-photon amplitude A 1,2 (x 1 , t 1 ; x 2 , t 2 ) is given by A 1,2 (x 1 , ω o ; x 2 , ω e ) = dq o dq e Φ(q o , ω o ; q e , ω e ) · ·H 1 (x 1 ; q o , ω o ) H 2 (x 2 ; q e , ω e ) (2)

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This paper proposes a new protocol for quantum dense key distribution. This protocol embeds the benefits of a quantum dense coding and a quantum key distribution and is able to generate shared secret keys four times more efficiently than BB84 one. We hereinafter prove the security of this scheme against individual eavesdropping attacks, and we present preliminary experimental results, showing its feasibility.

Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities. PACS numbers: Many interesting properties of composite quantum systems , such as entanglement or entropy, are not measured directly but are inferred, usually from a full specification of a quantum state represented by a density operator. However, it is interesting to note that some of these properties can be measured in the same way we measure and estimate average values of observables. Here we illustrate this by extracting a non-local quantity, the Renyi entropy of the composite system, from local measurements on two pairs of polarization entangled photons. This quantity is a non-linear function of the density operator. We then use our experimental data to demonstrate the violation of entropic inequalities, which can be also interpreted as the experimental demonstration of a non-linear entangle-ment witness. Consider a source which generates pairs of photons. The photons in each pair fly apart from each other to two distant locations A and B. Let us assume that the polarization of each pair is described by some density operator ̺, which is unknown to us. Following Schrödinger's remarks on relations between the information content of the total system and its subsystems [1], it has been proven that for separable states global von Neumann en-tropy is always not less then local ones [2]. Subsequently a number of entropic inequalities have been derived, satisfied by all separable states [3, 4, 5, 6]. The simplest one is based on the Renyi entropy, or the purity measure , Tr (̺ 2) and can be rewritten as Tr (̺ 2 A) ≥ Tr (̺ 2), Tr (̺ 2 B) ≥ Tr (̺ 2), (1) where ̺ A and ̺ B are the reduced density operators pertaining to individual photons. The inequalities (1) involve non-linear functions of density operators and are known to be stronger than all Bell-CHSH inequalities [3, 7]. There are entangled states which are not S 2 S 1 A B 1 2 3 4 FIG. 1: An outline of our experimental setup. Sources S1 and S2 emit pairs of polarization-entangled photons. The entangled pairs are emitted into spatial modes 1 and 3, and 2 and 4. One photon from each pair is directed into location A and the other into location B. At the two locations photons impinge on beam-splitters and ar...