Polarization correlation in the two-photon decay of atomic hydrogen: nonlocality versus entanglement

From the work by Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], photon pairs from the 2s _1/2 → 1s _1/2 (two-photon) decay of atomic hydrogen are known to be quantum mechanically correlated. In these experiments, the polarization states of the photons emitted in back-to-back geometry were shown to violate the Bell inequality as a qualitative sign of nonlocality and entanglement. In the present contribution, we analyze how these nonlocal quantum correlations, as given by the violation of the Bell inequality, differ from the concurrence as a true entanglement measure. Results are shown for both quantifiers in dependence of the decay geometry and the initial polarization of the atoms for the 2s _1/2 → 1s _1/2 and 3d _5/2 → 1s _1/2 two-photon decay of atomic hydrogen. These results display the difference between nonlocality and entanglement and, hence, may stimulate further experiments on nonlocal quantum correlations in atomic systems.     

The effects of colored quadratic noise on a turbulent transition in liquid4He

Liquid⁴He presents an important physical system for the experimental study of noise-induced dynamical transitions. At temperatures belowT in the He II phase, the flow of heat in the liquid helium is limited by a kind of superfluid turbulence. The steady-state properties of this turbulence are adequately described by a dense tangle of quantized vortex lines in the superfluid component of the He II. The turbulence undergoes a continuous transition as the heat current is increased. At this transition the intrinsic fluctuations in the dissipation and the relaxation time both become large [D. Griswold, C. P. Lorenson, and J. T. Tough,Phys. Rev. B 35:3149 (1987)]. These observations are consistent with a model of the transition as an imperfect pitchfork bifurcation [M. Schumaker and W. Horsthemke,Phys. Rev. A 36:354 (1987)]. External noise can be easily added to the driving heat current. Small-amplitude noise simply causes the system to fluctuate about the deterministic steady states. Large-amplitude noise causes dramatic changes. The stochastic steady states of the turbulence show noise-induced bistability [D. Grisowld and J. T. Tough,Phys. Rev. A 36:1360 (1987)]. Comparison with the imperfect pitchfork model is difficult because the noise is colored, quadratic, and large. Nevertheless, an approximate result obtained by Schumaker and Horsthemke is in good qualitative agreement with the data.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Growing mechanisms in the QKPZ equation aaand the DPD models

The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)] with quenched noise (QKPZ) [Phys. Rev. Lett. 74, 920 (1995)]. We express the evolution equations for the mean height and the roughness into two contributions: the local and the lateral one in order to compare them with the local and the lateral contributions obtained for the directed percolation depinning models (DPD) introduced independently by Tang and Leschhorn [Phys. Rev A 45, R8309 (1992)] and Buldyrev et al. [Phys. Rev A 45, R8313 (1992)]. These models are classified in the same universality class of the QKPZ although the mechanisms of growth are quite different. In the DPD models the lateral contribution is a coupled effect of the competition between the local growth and the lateral one. In these models the lateral contribution leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness. Received 7 April 2000 and Received in final form 7 March 2001     

On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

Some MIT researchers [Phys. Rev. A 75, 042327 (2007)] have recently claimed that their implementation of the Slutsky-Brandt attack [Phys. Rev. A 57, 2383 (1998); Phys. Rev. A 71, 042312 (2005)] to the BB84 quantum-key-distribution (QKD) protocol puts the security of this protocol “to the test” by simulating “the most powerful individual-photon attack” [Phys. Rev. A 73, 012315 (2006)]. A related unfortunate news feature by a scientific journal [G. Brumfiel, Quantum cryptography is hacked, News @ Nature (april 2007); Nature 447, 372 (2007)] has spurred some concern in the QKD community and among the general public by misinterpreting the implications of this work. The present article proves the existence of a stronger individual attack on QKD protocols with encrypted error correction, for which tight bounds are shown, and clarifies why the claims of the news feature incorrectly suggest a contradiction with the established “old-style” theory of BB84 individual attacks. The full implementation of a quantum cryptographic protocol includes a reconciliation and a privacy-amplification stage, whose choice alters in general both the maximum extractable secret and the optimal eavesdropping attack. The authors of [Phys. Rev. A 75, 042327 (2007)] are concerned only with the error-free part of the so-called sifted string, and do not consider faulty bits, which, in the version of their protocol, are discarded. When using the provably superior reconciliation approach of encrypted error correction (instead of error discard), the Slutsky-Brandt attack is no more optimal and does not “threaten” the security bound derived by Lütkenhaus [Phys. Rev. A 59, 3301 (1999)]. It is shown that the method of Slutsky and collaborators [Phys. Rev. A 57, 2383 (1998)] can be adapted to reconciliation with error correction, and that the optimal entangling probe can be explicitly found. Moreover, this attack fills Lütkenhaus bound, proving that it is tight (a fact which was not previously known).     

The mechanism of producing energy-polarization entangled photon pairs in the cavity-quantum electrodynamics scheme

We investigate theoretically two photon entanglement processes in a photonic-crystal cavity embedding a quantum dot in the strong-coupling regime. The model proposed by Johne et al. (Johne R, Gippius N A, Pavlovic G, Solnyshkov D D, Shelykh I A and Malpuech G 2008 Phys. Rev. Lett. 100 240404), and by Robert et al. (Robert J, Gippius N A and Malpuech G 2009 Phys. Rev. B 79 155317) is modified by considering irreversible dissipation and incoherent continuous pumping for the quantum dot, which is necessary to connect the realistic experiment. The dynamics of the system is analysed by employing the Born–Markov master equation, through which the spectra for the system are computed as a function of various parameters. By means of this analysis the photon-reabsorption process in the strong-coupling regime is first observed and analysed from the perspective of radiation spectrum and the optimal parameters for observing energy-entangled photon pairs are identified.     

Relevant multi-setting tight Bell inequalities for qubits and qutrits

In the celebrated paper [D. Collins, N. Gisin, J. Phys. A Math. Gen. 37 (2004) 1775], Collins and Gisin presented for the first time a three-setting Bell inequality (here we call it CG inequality for simplicity) which is relevant to the Clauser–Horne–Shimony–Holt (CHSH) inequality. Inspired by their brilliant ideas, we obtained some multi-setting tight Bell inequalities, which are relevant to the CHSH inequality and the CG inequality. Moreover, we generalized the method in the paper [J.L. Chen, D.L. Deng, Phys. Rev. A 79 (2009) 012115] to construct Bell inequality for qubits to higher dimensional system. Based on the generalized method, we present, for the first time, a three-setting tight Bell inequality for two qutrits, which is maximally violated by nonmaximally entangled states and relevant to the Collins–Gisin–Linden–Massar–Popescu inequality.     

Continuous Variable Entanglement and Violation of Bell Inequality for Two Modes in a Three-Level Cascade Atomic System

Continuous variable entanglement and violation of Bell inequality for two modes are investigated in a three-level cascade atomic system. Entanglement of the system is demonstrated according to the entanglement criterion [Phys. Rev. Lett. 84 （2000）2722]. Violation of Bell inequality is studied within the framework of a quantum theory of multiwave mixing. It is shown that there are some states that are entangled but do not violate the Bell inequality.     

A different way to verify the violation of the WWŻB inequality

The solution to Bell theorem for N-qubits was widely studied in [M. ?ukowski, ?. Brukner, Phys. Rev. Lett. 88, 210401 (2002)]. Here we present a different way to obtain the solution of that theorem for the dichotomic experiment. In order to obtain a solution for the Werner-Wolf-?ukowski-Brukner WW?B inequality a new correlation function is proposed. This new correlation function expresses directly the constraints imposed by local theories. We use the general Greenberger-Horne-Zeilinger (GHZ) state, whereof, as it is well known, emerges a family of entangled states that do not violate the WW?B inequality [M. ?ukowski, ?. Brukner, W. Laskowski, M. Wie?niak, Phys. Rev. Lett. 88, 210402 (2002)], i.e. it can be described by a local realistic theory, to illustrate our results.     

Perturbation expansion, Bogoliubov inequality and integral representations in nonextensive Tsallis statistics

By using integral representations the perturbation expansion and the Bogoliubov inequality in nonextensive Tsallis statistics are investigated in a unified way. This procedure extends the analysis performed recently by Lenzi et al. [Phys. Rev. Lett. 80, 218 (1998)] to the quantum (discrete spectra) case, for q<1. An example is presented in order to illustrate the method. Received 19 November 1998     

Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state

A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state [A.I. Lvovsky et al., Phys. Rev. Lett. 87, 050402 (2001)]. Received 16 July 2001     

Bell Inequalities and Group Symmetry

Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr G?ney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S ₄ is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.     

Multipartite Generalized Bell Inequality with an Arbitrary Number of Settings

We derive a generalized Bell inequality for N qubits which involves an arbitrary number of settings for each of the local measuring apparatuses. The inequality forms a necessary condition for the existence of a local realistic model for the values of a correlation function, given in a n-setting Bell experiment. We show that a local realistic model for the values of a correlation function, given in a two-setting Bell experiment, cannot construct a local realistic model for the values of a correlation function, given in an arbitrary number of n-setting Bell experiment, even though there exist two-setting models for the n measurement directions chosen in the given n-setting experiment. Therefore, the property of two-setting model is different from the property of n-setting model. We discuss classification of local realistic theories in further detail more than the result presented in (J. Phys. A: Math. Theor. 41:155308, 2008). The generalized Bell inequality covers the previous results correctly.     

Mermin's n-particle Bell inequality and operators' noncommutativity

The relationship between the noncommutativity of operators and the violation of the Bell inequality is exhibited in the light of the n-particle Bell-type inequality discovered by Mermin (Phys. Rev. Lett. 65 (1990) 1838). It is shown, in particular, that the maximal amount of violation of Mermin's inequality predicted by quantum mechanics decreases exponentially by a factor of 2^−m/2 whenever any m among the n single-particle commutators happen to vanish.     

Experimental demonstration of single photon nonlocality

In this Letter we experimentally implement a single photon Bell test based on the ideas of S. Tan et al. [Phys. Rev. Lett. 66, 252 (1991)]] and L. Hardy [Phys. Rev. Lett. 73, 2279 (1994)]]. A double homodyne measurement is used to measure correlations in the Fock space spanned by zero and one photons. Local oscillators used in the correlation measurement are distributed to two observers by copropagating it in an orthogonal polarization mode. This method eliminates the need for interferometrical stability in the setup, consequently making it a robust and scalable method.     

Measurement of angular dependence of M X-ray production cross-sections in Re,Bi and U at 5.96 keV

The M X-ray production differential cross sections in Re, Bi and U elements have been measured at the 5.96 keV incident photon energy in an angular range 135°–155°. The measurements were performed using a ⁵⁵Fe source and a Si(Li) detector. The present results contradict the predictions of Cooper and Zare [Atomic Collision Processes, Gordon and Breach, New York (1969)] and experimental results of Kumar et al. [J. Phys. B: At. Mol. Opt. 34, 613 (2001)]. that, after photoionization of inner shells, the vacancy state has equal population of magnetic substates and the subsequent X-ray emission is isotropic, but confirm the predictions of the calculations of Flügge et al. [Phys. Rev. Lett. 29, 7 (1972)] and experimental results of Sharma and Allawadhi [J. Phys. B: At. Mol. Opt. 32, 2343 (1999)] and Ertugrul [Nucl. Instrum. Meth. B 119, 345 (1996)]. Total M X-ray production cross sections from the decay at the 5.96 keV photon energies are found to be in good agreement with the calculated theoretical results using the theoretical values of M shell photoionization cross section.     

Polarization-momentum hyper-entangled two photon states

We present a parametric source which allows the engineering of polarization-momentum hyperentangled two photon states based on linear optics and a single type-I nonlinear crystal. The nonlocal character of these states has been verified by various tests, including the “All Versus Nothing” test of local realism [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001)], which represents a generalization of the GHZ to the case of two entangled particles and two observers. We have also created a complete and deterministic Bell-state measurement by a novel experimental scheme which adopts polarization-momentum hyper-entanglement and requires linear optics and single photon detectors. The text was submitted by the authors in English.     

Economical phase-covariant cloning with multiclones

This paper presents a very simple method to derive the explicit transformations of the optimal economical 1 to M phase-covariant cloning. The fidelity of clones reaches the theoretic bound [D'Ariano G M and Macchiavello C 2003 Phys. Rev. A 67 042306]. The derived transformations cover the previous contributions [Delgado Y, Lamata L et al, 2007 Phys. Rev. Lett.98 150502] in which M must be odd.     

Quantum Authenticated Direct Communication Using Bell States

Two protocols of quantum direct communication with authentication [Phys. Rev. A 73:042305, 2006] were recently proposed by Lee, Lim and Yang, based on the correlation of Greenberger-Horne-Zeilinger (GHZ) states. However, Zhang et al. showed that in the two protocols the authenticator Trent can eavesdrop the secret message by subtle strategies [Phys. Rev. A 75:026301, 2007]. In this paper, we propose two authenticated quantum direct communication (AQDC) protocols using Bell states. Users can identify each other by checking the correlation of Bell states. Alice can directly send a secret message to Bob without any previously shared secret using the remaining Bell states after authentication. The two proposed AQDC protocols are implemented under the condition that there is a quantum link between Alice and Bob and that there is no quantum link between Alice and Bob respectively, similar to the ones proposed by Lee, Lim and Yang [Phys. Rev. A 73:042305, 2006]. The proposed AQDC protocols not only fix the leaks in the AQDC protocols proposed by Lee, Lim and Yang, but also economize the quantum resource.     

A genuine 3N-qubit entanglement and controlled teleportation

A genuine 3N-qubit entanglement is derived based on N GHZ trios and controlled teleportation. The state is a complementarity to the genuine 2N-qubit entangled state constructed with N Bell states by Yeo-Chua for N = 2 [Phys. Rev. Lett. 96, 060502 (2006)] and by Chen-Zhu-Guo for any N [Phys. Rev. A 74, 032324 (2006)]. By means of the measures proposed in Phys. Rev. A 74, 022314 (2006), the entanglement of the constructed state is quantified and classified with the well-known GHZ, W and Chen-Zhu-Guo's 2N-qubit entangled state.     

A MEAN-FIELD VERSION OF THE SSB MODEL FOR X-CHROMOSOME INACTIVATION

Nicodemi and Prisco recently proposed a model for X-chromosome inactivation in mammals, explaining this phenomenon in terms of a spontaneous symmetry-breaking mechanism [Phys. Rev. Lett. 99 (2007) 108104]. Here we provide a mean-field version of their model.