Splitting four ensembles of two-qubit quantum information via three Einstein-Podolsky-Rosen pairs

Enlightened by Zhang and Cheung’s original idea [J. Phys. B 41, 015503 (2008)], we put forward a novel tripartite quantum information splitting scheme by using three Einstein-Podolsky-Rosen pairs as quantum channels. Our scheme is applicable for perfectly splitting four ensembles of quantum information known by the splitter in priori. In contrast to the general scheme using the same quantum channels [Eur. Phys. J. D 39, 459 (2006)], our scheme has distinct advantages in quantum resource consumption, quantum operation intensity, classical communication cost and efficiency when dealing with the four specific ensembles of quantum information.     

Quantum creation of the universe with a minimum scalar-field energy

The quantum creation of a closed Friedmann universe is studied on the basis of a Wheeler-DeWitt equation with two arguments — a scale factor and a scalar-field potential. In the quasiclassical approximation the wave function of the universe (WF) starts to evolve at a zero scalar field. A near-Planckian energy density of the field arises as a result of tunneling through a potential barrier. In our opinion, this variant of the scenario most closely resembles creation ex nihilo. The only parameter controlling quantum evolution is the mass of a quantum of the scalar field. In the paper by Khalatnikov and Schiller [JETP Lett. 57,1 (1993)], tunneling through the classically inaccessible region of the superpotential U(a,φ) is calculated by the instanton method. However, this method requires that the potential U(a,φ) satisfy special conditions in the space (a,φ). For this reason, in the present paper the tunneling calculation is performed by the method of characteristics for the quasiclassical approximation of the Wheeler-DeWitt equation under the barrier. The WKB theory, which has been well-developed for one-dimensional problems, is employed along each characteristic. It is shown that the corresponding turning points are also points where U(a, φ)=0. The total barrier penetrability is obtained by averaging over a bundle of characteristics. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 305–308 (10 September 1996)     

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).     

Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm

In papers [Jafarizadehn and Salimi, Ann. Phys. 322, 1005 (2007) and J. Phys. A: Math. Gen. 39, 13295 (2006)], the amplitudes of continuous-time quantum walk (CTQW) on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated with their adjacency matrix. Here in this paper, it is shown that the CTQW on any arbitrary graph can be investigated by spectral analysis method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition (GQD) have been introduced, where this is achieved simply by relaxing some of the constrains imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors of strata are identical with the orthonormal basis produced by Lanczos algorithm. Moreover, it is shown that probability amplitude of observing the walk at a given vertex is proportional to its coefficient in the corresponding unit vector of its stratum, and it can be written in terms of the amplitude of its stratum. The capability of Lanczos-based algorithm for evaluation of CTQW on graphs (GQD or non-QD types), has been tested by calculating the probability amplitudes of quantum walk on some interesting finite (infinite) graph of GQD type and finite (infinite) path graph of non-GQD type, where the asymptotic behavior of the probability amplitudes at the limit of the large number of vertices, are in agreement with those of central limit theorem of [Phys. Rev. E 72, 026113 (2005)]. At the end, some applications of the method such as implementation of quantum search algorithms, calculating the resistance between two nodes in regular networks and applications in solid state and condensed matter physics, have been discussed, where in all of them, the Lanczos algorithm, reduces the Hilbert space to some smaller subspaces and the problem is investigated in the subspace with maximal dimension.     

A quasi-classical trajectory study of the Cl + H<Subscript>2</Subscript> (D<Subscript>2</Subscript>) reaction on a new BW3 potential energy surface

Molecular reaction dynamics of Cl + H₂ (D₂) has been studied on the latest analytical potential energy surface called BW3 using the Monte Carlo quasi-classical trajectory method. Excitation functions, differential cross sections and angular distributions of HCl and DCl products have been calculated. The excitation functions of the Cl (²P_3/2) + n-H₂ and Cl(²P_3/2) + n-D₂ reactions are also studied. The results are compared with those of quasi-classical trajectory [M. Alagia et al.: Phys. Chem. Chem. Phys. 2 (2000); F. J. Aoiz et al.: J. Phys. Chem. 100 (1996)], quantum mechanical (QM) calculations [F. J. Aoiz et al.:J. Chem. Phys. 115 (2001)] and experimental data [S. H. Lee et al.: J. Chem. Phys. 110 (1999); F. Dong et al.: J. Chem. Phys. 115 (2001)]. Discussions are given to some new results.     

In search of the dark state of 5-methyl-2-hydroxypyrimidine using a numerical DFT/MRCI gradient

In a recent publication, Lobsiger et al. [Phys. Chem. Chem. Phys. 12, 5032 (2010)] presented infrared and electronic absorption spectra of supersonic jet-cooled 5-methyl-2-hydroxypyrimidine (5M2HP), the enol form of deoxythymine. In addition, they reported on the fast nonradiative decay of the S₁ population to a dark state. In the present paper, we have investigated the mechanism and rate constants of this nonradiative decay by means of quantum chemical multi-configuration methods. To this end, minima of the lowest excited singlet and triplet states as well as the minimum-energy crossing point of singlet and triplet potential energy hypersurfaces (PEHs) have been determined employing a numerical DFT/MRCI gradient where DFT/MRCI stands for a combination of density functional theory (DFT) and a semi-empirical multi-reference configuration interaction (MRCI) approach. Rate constants have been calculated in the Condon approximation using a time-dependent approach based on harmonic oscillator functions and electronic spin–orbit coupling matrix elements evaluated at the DFT/MRCI level. It is shown that the first excited triplet state possesses ³(n?→?π*) character in the gas phase. Fast intersystem crossing is mediated by the low-lying ³(π?→?π*) state whose PEH crosses both, the S₁ ¹(n?→?π*) and T₁ ³(n?→?π*) PEHs.     

Multiresolution quantum chemistry in multiwavelet bases: time-dependent density functional theory with asymptotically corrected potentials in local density and generalized gradient approximations

A multiresolution solver for fully numerical linear response calculations of excitation states via the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) is presented. The linear response method Yanai et al. previously reported [J. Chem. Phys., submitted] was limited to the Tamm–Dancoff approximation and could only use the Hartree–Fock exchange and the local-spin density approximation (LSDA) with a crude asymptotic correction. The present development enables us to perform full TD-HF/DFT calculations employing generalized gradient approximation (GGA) exchange-correlation potentials as well as hybrid ones. The linear response of TD-HF/DFT is computed by means of iteratively solving the coupled integral equations with the Green's functions. In this study, Tozer and Handy's asymptotic correction (AC) is applied to existing DFT exchange-correlations, and is found numerically stable and efficient. Furthermore, the new hybrid exchange-correlation functional CAM-B3LYP, which was recently proposed by Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], is implemented. The implementation requires a new separated representation of the integral kernel for the Coulomb-attenuated potential. We demonstrate linear response calculations free of basis set error for the excited states of Be, N₂, C₂H₄ and C₆H₆ using LSDA, HCTH, CAM-B3LYP and PBE0 exchange-correlation functionals. The mean absolute errors of the C₆H₆ calculations with HCTH and CAM-B3LYP are 0.12 and 0.18?eV, respectively. The second derivative of exchange-correlation functionals is represented fully numerically at O(N) computation cost.     

Elastic scattering of low-energy electrons by NO

We report elastic integral, momentum transfer and differential cross sections for electron scattering by N₂O for energies up to 50 eV. These results were obtained at the static-exchange approximation with the Schwinger Multichannel Method with Pseudopotentials [M.H.F. Bettega, L.G. Ferreira and M.A.P. Lima, Phys. Rev. A 47, 1111 (1993)]. In general our results show good agreement with experimental data and with other theoretical results but some discrepancies are found. We have also found a shape resonance around 4 eV in agreement with previous calculations using the R-matrix Method of Sarpal et al. [J. Phys. B 29, 857 (1996)]. On the other hand, the existence of a resonance at about 13 eV, clearly seen by the Schwinger Variational Iterative Method [Michelin et al., J. Phys. B 29, 2115 (1996)], can not be confirmed by our calculations. At this energy, our cross sections show a broad bump with no clear resonant behavior given by the eigenphase sum. Received: 13 November 1997 / Revised: 13 March 1998 / Accepted: 9 April 1998     

Einstein-Podolsky-Rosen paradox,Bell's inequality,and the projection postulate

Our aim is to understand the role of implicit assumptions which has been used by Einstein, Podolsky, and Rosen (EPR) in their famous article [Phys. Rev., 47, 777 (1935)] devoted to the so-called EPR paradox. We found that the projection postulate plays a crucial role in the EPR argument. It seems that EPR made a mistake in this paper — the projection postulate was applied not in its original form (as it has been formulated in von Neumann's book [Mathematical Foundations of Quantum mechanics, Princeton University Press (1955)] but in the form which was later formalized as Lüders' postulate [Ann. Phys., Lpz. 8, 322 (1951)]. Von Neumann's postulate was crucially modified by extending it to observables with degenerate spectra. This modification is the real source of “quantum nonlocality.” The use of the original von Neumann postulate eliminates this problem — instead of (an action at a distance)-nonlocality, we obtain a classical measurement nonlocality, which is related to the synchronization of two measurements (produced on the two parts of a composite system). If one uses correctly von Neumann's projection postulate, no “elements of reality” can be assigned to entangled systems. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

Dynamics of geometric discord and measurement-induced nonlocality at finite temperature

By using geometric measure of discord (GMOD) [B. Dakić, V. Vedral, Č. Brukner, Phys. Rev. Lett. 105, 109502 (2010)] and measurement-induced nonlocality (MIN) [S. Luo, S. Fu, Phys. Rev. Lett. 106, 120401 (2011)], we investigate quantum correlation of a pair of two-level systems, each of which is interacting with a reservoir at finite temperature T. We show that, for a broad class of states of the system, GMOD and MIN can endure sudden death, and there is no asymptotic decay for MIN while asymptotic decay exists for GMOD. We also give the dynamics of GMOD and MIN with respect to the temperature and illustrate their different characteristics.     

Local distinguishability by projective measurement

This paper proves that a set of orthogonal pure states are indistinguishable by restricted local projective measurement and classical communication if the sum of their Schmidt ranks is larger than the dimension of their joint Hilbert space. This result is useful in determining the local distinguishability of quantum states and is stronger in some respects than that of Hayashi et al [Phys. Rev. Lett. 96, 040501]. In addition, it presents a new method to determine the local distinguishability of orthogonal states by projecting measurement operators into their subspaces.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

Entanglement of Formation of an Arbitrary State of Two Rebits

We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex numbers. The differences provide insight into the nature of entanglement in standard quantum theory. Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. We give a contrasting formula for the entanglement of formation of an arbitrary state of two rebits, a rebit being a system whose Hilbert space is a 2-dimensional real vector space.     

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     

Main parameters of a coaxial electrostatic lens

Coaxial electrostatic lenses are used in combination with a magnetic field in plasma-optical and manometric devices [A. I. Morozov and S. V. Lebedev, in Reviews of Plasma Physics, Vol. 8, M. A. Leontovich (ed.), Consultants Bureau, New York (1980); V. P. Afanas’ev, A. A. Vydrik, L. P. Ovsyannikova, and E. V. Shpak, Sov. Phys. Tech. Phys. 25, 1049 (1980)]. Their employment in systems for transporting beams of high-energy charged particles is also known [P. Krejcik, B. V. King, and I. C. Kelly, Optik (Stuttgart) 55, 385 (1980)], since, along with quadrupole lenses, they have a large optical strength. Expressions for the trajectories of charged low-energy particles were obtained by L. P. Ovsyannikova and S. V. Pasovets [Sov. Phys. Tech. Phys. 32, 1422 (1987)] in the approximation of a rectangular field model with consideration of the variation of the energy at the entrance and exit from the field. The possibility, in principle, of focusing a parallel beam in a ring is demonstrated. Zh. Tekh. Fiz. 67, 81–82 (December 1997)     

Wave vector,local momentum and local coordinate from the perspective of information theory

In the context of informational analysis of atomic and molecular systems, the connection between local quantum observables and information measures is of interest. In this paper, analytical relationships for the imaginary part of the total local momentum (coordinate) in terms of information theoretic measures have been established. Moreover, on the basis of another scheme in which the relationship among densities of information energy, Shannon entropy and Fisher information has been proposed [M. Alipour and A. Mohajeri, Mol. Phys. 110, 403 (2012)], the general formulae for the imaginary part of the total local momentum and the corresponding variance are expressed. The presented proof may be viewed in light of the relation between the local wave vector and the information energy density. Through this study, another noteworthy application of information theory is highlighted.     

An Elementary Proof of Lyapunov Exponent Pairing for Hard-Sphere Systems at Constant Kinetic Energy

The conjugate pairing of Lyapunov exponents for a field-driven system with smooth inter-particle interaction at constant total kinetic energy was first proved by Dettmann and Morriss [Phys. Rev. E 53:R5545 (1996)] using simple methods of geometry. Their proof was extended to systems interacting via hard-core inter-particle potentials by Wojtkowski and Liverani [Comm. Math. Phys. 194:47 (1998)], using more sophisticated methods. Another, and somewhat more direct version of the proof for hard-sphere systems has been provided by Ruelle [J. Stat. Phys. 95:393 (1999)]. However, these approaches for hard-sphere systems are somewhat difficult to follow. In this paper, a proof of the pairing of Lyapunov exponents for hard-sphere systems at constant kinetic energy is presented, based on a very simple explicit geometric construction, similar to that of Ruelle. Generalizations of this construction to higher dimensions and arbitrary shapes of scatterers or particles are trivial. This construction also works for hard-sphere systems in an external field with a Nosé–Hoover thermostat. However, there are situations of physical interest, where these proofs of conjugate pairing rule for systems interacting via hard-core inter-particle potentials break down.     

On the Zero Mass Limit of Tagged Particle Diffusion in the 1-d Rayleigh-Gas

We consider the M→0 limit for tagged particle diffusion in a 1-dimensional Rayleigh-gas, studied originaly by Sinai and Soloveichik [Ya. G. Sinai, M. R. Soloveichik, Commun. Math. Phys. 104:423–443 (1986)], and by Szász and Tóth [D. Szász, B. Tóth, Commun. Math. Phys. 104:445–457 (1986)], respectively. In this limit we derive a new type of model for tagged particle diffusion, for which the two central particles, in addition to elastic collisions with the rest of the gas, interact with Calogero-Moser-Sutherland (i.e. inverse quadratic) potential. Computer simulations on this new model reproduce exactly the numerical value of the limiting variance obtained by Boldrighini, Frigio and Tognetti in [C. Boldrighini, S. Frigio, D. Tognetti, J. Stat. Phys. 108:703–712 (2002)]. Dedicated to Domokos Szász on his 65th birthday.     

Shaping of the electron distribution function in a striated solution

Numerous papers have been devoted to the investigation of striations in inert gases at low pressures (p⩽2 Torr) and small currents (i<100 mA) [A. V. Nedospasov, Sov. Phys. Usp. 11, 174 (1968); L. Pekarek, Sov. Phys. Usp. 11, 188 (1968); N. L. Oleson and A. W. Cooper, Adv. Electron. Electron Phys. 24, 155 (1968); P. S. Landa, N. A. Miskinova, and Yu. V. Ponomarev, Sov. Phys. Usp. 23, 813 (1980)]. Since the nature of striations is determined under these conditions by the nonlocal kinetics of the electrons in spatially periodic fields [L. D. Tsendin, Sov. J. Plasma Phys. 8, 228 (1982)], an investigation of the electron distribution function in space and time would be very interesting. The purpose of the present work is to experimentally investigate the potential profiles and distribution functions in S and P striations and to analyze the mechanism which shapes the distribution functions for striations of these types. Zh. Tekh. Fiz. 67, 14–21 (September 1997)     

Macro-scale matter wave generation in charged particle dynamics in a magnetic field,a consequence of quantum entanglement

Matter wave interference effects on the macro-scale predicted by the author in charged particle dynamics in a magnetic field [R.K. Varma, Phys. Rev. E 64, 036608 (2001)], and observed subsequently [R.K. Varma, A.M. Punithavelu, S.B. Banerjee, Phys. Rev. E 65, 026503 (2002); R.K. Varma, S.B. Banerjee, Phys. Scr. 75, 19 (2007)] have been shown here to be an interesting consequence of quantum entanglement between the parallel and perpendicular degrees of freedom of the particle. Treating the problem in the framework of the inelastic scattering theory, it is shown that these macro-scale matter waves are generated in the ‘parallel’ degree of freedom as a modulation of the plane wave state of the particle along the field concomitantly with the excitation of Landau levels in the perpendicular degree of freedom in an inelastic scattering episode. We highlight here the role of quantum entanglement leading to the generation of this macro-scale quantum entity which has been shown to exhibit observable consequences. This case also exemplifies a situation exhibiting quantum entanglement on the macro-scale.