Quantum cryptography via parametric downconversion

The use of quantum bits (qubits) in cryptography holds the promise of secure cryptographic quantum key distribution schemes. It is based usually on single-photon polarization states. Unfortunately, the implemented ``qubits'' in the usual weak pulse experiments are not true two-level systems, and quantum key distribution based on these imperfect qubits is totally insecure in the presence of high (realistic) loss rate. In this work, we investigate another potential implementation: qubits generated using a process of parametric downconversion. We find that, to first (two-photon) and second (four-photon) order in the parametric downconversion small parameter, this implementation of quantum key distribution is equivalent to the theoretical version. Once realistic measurements are taken into account, quantum key distribution based on parametric downconversion suffers also from sensitivity to extremely high (nonrealistic) losses. By choosing the small parameter of the process according to the loss rates, both implementations of quantum key distribution can in principle become secure against the attack studied in this paper. However, adjusting the small parameter to the required levels seems to be impractical in the weak pulse process. On the other hand, this can easily be done in the parametric downconversion process, making it a much more promising implementation.Comment: 6 pages, Latex (a special style file is attached). Presented in QCM'98 conference. Similar results regarding the insecurity of weak-pulse schemes were also presented by Norbert Lutkenhaus in the same conferenc

Interval oscillation theorems for asecond-order linear differential equation

AbstractInterval oscillation criteria are given for the forced second-order linear differential equation Ly(t) = (p(t)y′)′ + q(t)y = ƒ(t), tε (0, ∞), where p, q, ƒ are locally integrable functions and p(t) > 0, for t > 0. No restriction is imposed on ƒ(t) to be the second derivative of an oscillatory function as assumed by Kartsatos [1). Our results also allow both q and f to change sign in the neighborhood at infinity. In particular, we show that all solutions of y″ + c(sin t)y = tβ cos t with β ≥ 0 are oscillatory, for c ≥ 1.3448. This improves an estimate given by Nasr [2] for the linear equation

Image and Coherence Transfer in the Stimulated Down-conversion Process

The intensity transverse profile of the light produced in the process of stimulated down-conversion is derived. A quantum-mechanical treatment is used. We show that the angular spectrum of the pump laser can be transferred to the stimulated down-converted beam, so that images can also be transferred from the pump to the down-converted beam. We also show that the transfer can occur from the stimulating beam to the down-converted one. Finally, we study the process of diffraction through an arbitrarily shaped screen. For the special case of a double-slit, the interference pattern is explicitly obtained. The visibility for the spontaneous emitted light is in accordance with the van Cittert - Zernike theorem for incoherent light, while the visibility for the stimulated emitted light is unity. The overall visibility is in accordance with previous experimental results

Entanglement dynamics of three-qubit states in noisy channels

We study entanglement dynamics of the three-qubit system which is initially prepared in pure Greenberger-Horne- Zeilinger (GHZ) or W state and transmitted through one of the Pauli channels $\sigma_z, \, \sigma_x, \, \sigma_y$ or the depolarizing channel. With the help of the lower bound for three-qubit concurrence we show that the W state preserves more entanglement than the GHZ state in transmission through the Pauli channel $\sigma_z$. For the Pauli channels $\sigma_x, \, \sigma_y$ and the depolarizing channel, however, the entanglement of the GHZ state is more resistant against decoherence than the W-type entanglement. We also briefly discuss how the accuracy of the lower bound approximation depends on the rank of the density matrix under consideration.Comment: 2 figures, 32 reference

Quantum teleportation of light beams

We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies and phase fluctuations. The inferred fidelity for input coherent states is F = 0.61 +- 0.02, which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69. The teleportation protocol is explained in detail, including a discussion of discrepancy between experiment and theory, as well as of the limitations of the current apparatus.Comment: 17 pages, 19 figures, submitted to PR

Constraint on teleportation over multipartite pure states

We first define a quantity exhibiting the usefulness of bipartite quantum states for teleportation, called the quantum teleportation capability, and then investigate its restricted shareability in multi-party quantum systems. In this work, we verify that the quantum teleportation capability has a monogamous property in its shareability for arbitrary three-qutrit pure states by employing the monogamy inequality in terms of the negativity.Comment: 4 pages, 1 figur

Quantum spiral bandwidth of entangled two-photon states

We put forward the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state in spontaneous parametric downconversion. We obtain the bandwidth using the eigenstates of the orbital angular momentum of the biphoton states, and reveal its dependence with the length of the down converting crystal and waist of the pump beam. The connection between the quantum spiral bandwidth and the entropy of entanglement of the quantum state is discussed.Comment: 10 pages, 3 figure

Quantum diffraction and interference of spatially correlated photon pairs generated by spontaneous parametric down-conversion

We demonstrate one- and two-photon diffraction and interference experiments utilizing parametric down-converted photon pairs (biphotons) and a transmission grating. With two-photon detection, the biphoton exhibits a diffraction-interference pattern equivalent to that of an effective single particle that is associated with half the wavelength of the constituent photons. With one-photon detection, however no diffraction-interference pattern is observed. We show that these phenomena originate from the spatial quantum correlation between the down-converted photons.Comment: 4 pages, 5 figure

On quantum teleportation with beam-splitter-generated entanglement

Following the lead of Cochrane, Milburn, and Munro [Phys. Rev. A {\bf 62}, 062307 (2000)], we investigate theoretically quantum teleportation by means of the number-sum and phase-difference variables. We study Fock-state entanglement generated by a beam splitter and show that two-mode Fock-state inputs can be entangled by a beam splitter into close approximations of maximally entangled eigenstates of the phase difference and the photon-number sum (Einstein-Podolsky-Rosen -- EPR -- states). Such states could be experimentally feasible with on-demand single-photon sources. We show that the teleportation fidelity can reach near unity when such ``quasi-EPR'' states are used as the quantum channel.Comment: 7 pages (two-column), 7 figures, submitted to Phys. Rev. A. Text unmodified, postscript error correcte

Experimental investigation of continuous variable quantum teleportation

We report the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field. Our experiment was stably locked for long periods, and was analyzed in terms of fidelity, F; and with signal transfer, T_{q}=T^{+}+T^{-}, and noise correlation, V_{q}=V_{in|out}^{+} V_{in|out}^{-}. We observed an optimum fidelity of 0.64 +/- 0.02, T_{q}= 1.06 +/- 0.02 and V_{q} =0.96 +/- 0.10. We discuss the significance of both T_{q}>1 and V_{q}<1 and their relation to the teleportation no-cloning limit.Comment: 4 pages, 4 figure